Topology optimization of continuum structures: A review

Applied Mechanics Reviews

Volumn 54, Issue 4, 2001, Pages 331-390

  Eschenauer, Hans A ^a   Olhoff, Niels ^b  

^a UNIVERSITY OF SIEGEN   (Germany)

^b AALBORG UNIVERSITY   (Denmark)

Author keywords

Approach by Growing and Degenerating a Structure (Material Removal); Approach by Inserting Holes New Applications of Topology Optimization; Definitions; Filtering Techniques Macrostructure Techniques; Formulations; Homogenization; Material Models Microstructure Techniques; Mathematical Physical Fundamentals; Perimeter

Indexed keywords

EID: 0000905135     PISSN: 00036900     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.1388075     Document Type: Article

References (426)

1. Alexandroff PS (1960), Combinatorial Topology I-III, Graylock Publ, Rochester NY.
2. Alt W, Ben-Tal A, Kocvara M, Nemirovski A, and Zowe J (1997), Free Material Design via Semidefinite Programming: The Multiload Case with Contact Conditions, Report No 219, Institute for Applied Mathematics, Univ of Erlangen-Nuremberg, Germany.
3. Anger G (ed) (1993), Inverse Problems: Principles and Applications in Geophysics, Technology and Medicine.
4. Atrek E (1991), SHAPE User’s Manual, Engineering Mechanics Research Corp, Troy, Michigan.
5. Bagge M (1999), Remodeling of bone structure, DCAMM Report S 84, PhD-Thesis, Dept of Solid Mech, Technical Univ of Denmark.
6. Beckers M (1996), Optimisation topologique de structure en variables Discrete, Tech Report, Universite de Liege.
7. Beckers M (1997), Optimisation de structures en variable discrete, These de Doctorat No 181, Universite de Liege, Belgium.
8. Belegundu A, Mistree F (eds) (1998), Optimization in industry-1997, ASME, New York.
9. Bendsoe MP (1995), Optimization of Structural Topology, Shape and Material, Springer, Heidelberg.
10. Bendsoe MP and Mota Soares CA (eds) (1993), Topology Design of Structures, NATO ASI, Kluwer Academic Publishers, Dordrecht.
11. Bennet JA, Botkin ME (eds) (1986), The Optimum Shape: Automated Structural Design, Plenum Press, New York.
12. Bensoussan A, Lions J-L, and Papanicolaou G (1978), Asymptotic Analysis for Periodic Structures, North Holland, Amsterdam.
13. Bergmann HW (ed) (1989), Optimization: Methods and Applications, Possibilities and Limitations, Springer, Berlin, Heiderlberg, New York.
14. Bestle D and Schiehlen W (eds) (1995/1996), Optimization of Mechanical Systems, Stuttgart, Germany (1995), Kluwer Academic Publishers, Dordrecht, The Netherlands (1996).
15. Blachut J and Eschenauer H (eds) (2001), Emerging Methods for Multidisciplinary Optimization, Lecture Notes CISM Course, Udine, Italy 2000, Springer, Wien/New York.
16. Bloebaum CL (2000), WCSMO 3—Third World Congress of Structural and Multidisciplinary Optimization, 1999, Proceedings, Buffalo NY.
17. Borrwall T and Petersson J (2000a), Topology optimization using regularized intermediate control, Report LiTH-IKP-R-1086, Division of Mechanics, Mechanical Engineering Systems, Linköping Univ, Sweden, 24 pp.
18. Borrwall T and Petersson J (2000b), Large scale topology optimization in 3D using parallel computing, Report LiTH-IKP-R-1130, Division of Mechanics, Mechanical Engineering Systems, Linkoping Univ, Sweden, 42 pp.
19. Bourbaki N (1955), Eléments des Mathématique, Hermann, Paris.
20. Bourdin B (1999), Filters in topology optimization, DCAMM Report No 627, Dept of Mathematics, Technical Univ of Denmark.
21. Cherkaev A (2000), Variational Methods for Structural Optimization, Applied Mathematical Sciences 140, Springer-Verlag, New York.
22. Cherkaev AV and Kohn RV (eds) (1997), Topics in the Mathematical Modelling of Composite Materials, Vol 31 of Progress in Nonlinear Differential Equations and Their Applications, Birkhauser, Boston.
23. Courant R and Hilbert D (1968), Methods of Mathematical Physics I, Interscience Pub, New York.
24. Duysinx P (1995), Optimization topologique: Du milieu a la structure elastique, PhD Thesis, Faculty of Applied Sciences, Univ of Liege, Belgium.
25. Duysinx P (1997), Layout optimization: A mathematical programming approach, DCAMM Report 540, Dept of Solid Mechanics, Technical Univ of Denmark.
26. Eschenauer H (1968), Thermo-elastic plate equations: Buckling of a cantilever plate (in German), Doctoral Thesis, TH Darmstadt.
27. Eschenauer H, Becker, W and Schumacher A (1998), Multidisciplinary structural optimization in aircraft design (in German), Final Report, BMBF-Bundesvorhaben DYNAFLEX.
28. Eschenauer H and Olhoff N (eds) (1982), Optimization Methods in Structural Design, EUROMECH-Colloquium 164, B.I.-Wissen-schaftsverlag, Wien.
29. Eschenauer H, Olhoff N, and Schnell W (1996/97), Applied Structural Mechanics: Fundamentals of Elasticity, Load-Bearing Structures, Structural Optimization, Springer, Berlin, Heidelberg, New York, 398 p, 179 Figs.
30. Eschenauer HA, Koski J, and Osyczka A (eds) (1990), Multicriteria Design Optimization, Springer, Berlin.
31. Eschenauer HA, Mattheck C, and Olhoff N (1991), Engineering Optimization in Design Processes, Lecture Notes in Engineering, Springer, Berlin, Heidelberg, New York.
32. Eschenauer HA and Schnell W (1993), Elastizitatstheorie-Grundlagen, Flachentragwerke, Strukturoptimierung, 3, Aufl, BI Wissenschaftsverlag, Mannheim.
33. Evans LC and Gariepy RF (1992), Measure Theory and Fine Properties of Functions, CRC Press, Boca Ratan.
34. Fernandes PR, Rodrigues H, Guedes JM (1996), Topology Optimization of 3d Linear Elastic Structures with a Constraint on “Perimeter,” IDMEC/CPM’96/004, Instituto Superior Technico, IDMEC, Lisboa/Portugal.
35. Foldager J (1999), Design of composite structures, PhD Thesis, Institute of Mechanical Engineering, Aalborg Univ.
36. Franz W (1960/64), Topology I (General Topology), Topology II (Algebraic Topology) (in German), De Gruyter (Samml, Goschen), Berlin.
37. Galilei G (1638), Discorsi e Dimonstrazioni Mathematiche, a Due Nuove Scienze Attenenti alla Mecanica; Movimenti Locali, Leida.
38. Gallagher RH and Zienkiewicz OC (eds) (1973), Optimum Structural Design—Theory and Applications, John Wiley and Sons, London.
39. Gibianski LV and Cherkaev AV (1984), Design of Composite Plates of External Rigidity, Tech Report No 914, Ioffe Physico-Technical Institute, Acad. Sci. USSR, Leningrad, USSR (in Russian), English translation in: Cherkaev AV, Kohn RV (eds) (1997), Topics in the Mathematical Modelling of Composite Materials, Vol 31 of Progress in Nonlinear Differential Equations and Their Applications, Birkhauser, Boston MA.
40. Gibianski LV and Cherkaev AV (1987), Microstructures of composites of exremal rigidity and exact estimates of provided energy density (in Russian), Tech Report 1155, A. F. Ioffe Physical-Technical Institute, Academy of Sciences of the USSR, Leningrad, English Translation in: Cherkaev A. V and Kohn R. V. (eds) (1997), Topics in the Mathematical Modelling of Composite Materials, Birkhauser: New York.
41. Gilmore B, Hoeltzel DA, Azarm S, and Eschenauer HA (1993), Advances in design automation, Proc of the 1993 ASME DETC, Albuquerque, New Mexico/USA, Vol 1/2, ASME, New York.
42. Goldberg DE (1989), Genetic Algorithms in Search, Optimization and Machine Learning, Addison Wesley
43. Green AE and Zerna W (1968), Theoretical Elasticity, Clarendon Press, Oxford, 2nd Ed.
44. Gutkowski W and Mroz Z (eds) (1997), Second World Congress of Structural and Multidisciplinary Optimization, WCSMO-2, Institute of Fundamental Technological Research, Warsaw, Poland, Vol 182.
45. Hammer VB (1994), Design of composite laminates with optimized stiffness, strength and damage properties, Ph.D.-thesis, DCAMM Report S 72, Dept for Solid Mechanics, Technical Univ of Denmark.
46. Haug EJ, Choi KK, and Komkow V (1985), Design Sensitivity Analysis of Structural Systems, Academic Press, Orlando FL.
47. Henschen S (2001), Topologieoptimierungen von Bauteilen mittels lokaler Verfahren unter Berücksichtigung der globalen Konfigurationsentropie, Doctoral Thesis, RWTH Aachen, Faculty of Applied Sciences.
48. Hilton PJ and Wylie S (1960), Homology Theory, an Introduction to Algebraic Topology, Cambridge.
49. Hocking JG and Young GS (1961), Topology, Addison-Wesley Publ. Co, Massachussetts.
50. Hornlein H and Schittkowski K (eds) (1993), Software Systems for Structural Optimization, Vol 110 International Series of Numerical Mathematics, Birkhauser, Basel.
51. Jager J (1980), Fundamental Topology (in German), Schoningh-Verlag, Paderborn.
52. Jänich K (1996), Topology (in German), 3rd Ed, Springer-Verlag, Berlin, Heidelberg.
53. Kelley JL (1955), General Topology, Van Nostrand, Toronto, New York, London.
54. Kneppe G (1986), Direct solution strategies for the shape optimization of plate and shell structures (in German), Doctoral Thesis, Univ of Siegen, Fortschrittsberichte VDI-Reihe I, Nr. 135, Düsseldorf: VDI-Verlag.
55. Koethe G (1960), Topologically Linear Domains 1 (in German), Springer-Verlag, Berlin, Gottingen, Heidelberg.
56. Krawietz A (1986), Material Theory (in German), Springer, Berlin, Heidelberg, New York, Tokyo.
57. Krein MG and Nudelman AA (1977), The Markov Moment Problem and Extrenal Problems, Translation of Mathematical Monographs, 50, American Mathematical Society
58. Krog LA (1996), Layout optimization of disk, plate, and shell structures, Ph.D. thesis, Special Report No 27, Inst. of Mech. Eng., Aalborg Univ, Denmark.
59. Kull K, Ramm R, Reiner R (eds) (1995), Evolution and Optimization (in German), S Hirzel, Stuttgart.
60. Lagrange JL (1770-1773), Sur la Figure des Colonnes, Miscellania Taurinensia.
61. Langhaar HL (1962), Energy Methods in Applied Mechanics, John Wiley and Sons, New York.
62. Lanzcos C (1962), The Variational Principles of Mechanics, Univ of Toronto Press, Toronto.
63. Larsen UD, Sigmund O, and Bouwstra S (1995), Fabrication of compliant micromechanisms and materials with negative Poisson’s ratio (manuscript).
64. Levy M (1873), La Statique Graphique et ses Applications aux Con-structiones, Academie des Sciences, Paris.
65. Lewinski T and Sokolowski J (1999), Topological derivative for nucleation of non-circircular voids, Research Report No 3798, INRIA Lorraine, Nancy, France, 37 pp.
66. Lurie KA (1993), Applied Optimal Control Theory of Distributed Systems, Plenum Press, New York/USA.
67. Lurie KA and Cherkaev AV (1982), Exact estimates of conductivity of mixtures composed of two isotropic media taken in prescribed proportion, Report No 783, Ioffe Physico-Technical Institute, Acad. Sci. USSR, Leningrad, USSR (in Russian), English translation in: Cherkaev AV, Kohn RV (eds) (1997), Topics in the Mathematical Modelling of Composite Materials, Vol 31 of Progress in Nonlinear Differential Equations and Their Applications, Birkhauser, Boston, MA, USA.
68. Mattheck C (1991), Trees-the Mechanical Design, Heidelberg.
69. Mattheck C (1992), Design in Nature (in German), Freiburg.
70. Maute K (1998), Topology and shape optimization of thin-walled structures (in German), Ph.D.-Thesis, Report No 25, Institut für Baustatik, Universität Stuttgart.
71. Metzger K (1893), Wind as a Decisive Factor for the Growth of Trees (in German), Mündener Forstliche Hefte, Drittes Heft, Berlin.
72. Michlin SG (1962), Variational Methods in Mathematical Physics (in German), Akademie-Verlag.
73. Mota Soares CA (ed) (1986), Computer aided optimal design: Structural and mechanical systems, NATO/NASA/NSF/USAF Advanced Study Institute, Troia/PORTUGAL, June 29-July 11, 1986, Vol 2, Center for Mechanics and Materials of the Technical Univ of Lisbon.
74. Neuber N (1985), Theory of Notch Stresses (in German), Springer, Berlin, Heidelberg.
75. Olhoff N and Rozvany GIN (eds) (1995), Structural and Multidisciplinary Optimization, Proc of WCSMO-1, Elsevier Science, Oxford/UK.
76. Pedersen P (ed) (1993), Optimal Design with Advanced Materials, Proceedings IUTAM-Symposium Lyngby/DENMARK, Elsevier Science Publ, Amsterdam/The Netherlands.
77. Pedersen P (1998), Elasticity—Anisotropy—Laminates, Solid Mechanics, Technical Univ of Denmark DTU.
78. Pedersen P and Bendsoe MP (eds) (1999), IUTAM Symposium Synthesis in Bio Solid Mechanics, Copenhagen/Denmark, May 24-27, 1998, Kluwer, Dordrecht.
79. Petersson J (1996), A finite element analysis of optimal variable thickness sheets, Mat. Report No 1996-44, Dept of Math., Technical Univ of Denmark.
80. Petersson J (1998), Some convergence results in perimeter-controlled topology optimization, Tech Report LiTH-IKP-R-995, Institute of Technology, Dept of Mech Eng, Linköping Univ.
81. Pontrjagin LS (1957/58), Topological Classes I, II (in German), Leipzig.
82. Prager W (1961), Introduction to Continuum Mechanics (in German), Birkhauser Verlag, Basel.
83. Prager W (1969), Optimality criteria derived from classical extremum principles, SM Studies Series, Solid Mechanics Division, Univ of Waterloo, Ontario/CANADA.
84. Prasad B (ed) (1989), CAD/CAM Robotics and Factories of the Future, Vol 2 (Proc of 3rd Int Conf CARS and FOF’88), Springer, Berlin.
85. Querin OM (1997), Evolutionary structural optimization: Stress based formulation and implementation, PhD Dissertation, Dept of Aeronaut Eng, Univ of Sydney, Australia.
86. Querin OM, Steven GP, and Xie YM (1996), EVOLVE User Guide, Dept of Aeronaut Eng, Univ of Sydney, Australia.
87. Reiter TJ (1996), Functional adaption of bone and application in optimal structural design, Report, VDI Reihe 17, Nr. 145, VDI Verlag, Düsseldorf, Germany, 146 pp.
88. Rozvany GIN (ed) (1991), Optimization of large structural systems, NATO-ASI Lecture Notes.
89. Rozvany GIN (ed) (1997), Topology optimization in structural mechanics, Vol 374 of CISM Course and Lectures, Springer, Vienna/Austria.
90. Rozvany GIN, Bends0e MP, and Kirsch U, (1995), Layout optimization of structures, Applied Mechanics Reviews, 48, 41-119.
91. Rozvany GIN, Olhoff N (eds) (2001), Topology Optimization of Structures and Composite Continua, NATO ARW, Budapest, Hungary, May 8-12, 2000, Kluwer Academic Publishers, Dordrecht, The Netherlands.
92. Rozvany GIN, Zhou M, and Sigmund O (1992), Topology optimization in structural design, Research Report in Civil Engineering, 59, Univ of Essen/Germany.
93. Sanchez-Palencia E (1980), Non-Homogeneous Media and Vibration Theory, Lecture Notes in Physics 127, Springer, Berlin.
94. Schubert H (1960), Topology (in German), Teubner, Stuttgart.
95. Schumacher A (1996), Topology optimization of component structures using hole positioning criteria (in German), Doctoral Thesis, FOMAAS-Report Nr T09-01.96, Univ of Siegen.
96. Sedov LI (1966), Foundations of the Non-Linear Mechanics of Continua, London: Pergamon Press.
97. Sigmund O (1994a), Design of material structures using topology optimization, PhD thesis, DCAMM report S 69, Dept of Solid Mechanics, Technical Univ of Denmark.
98. Sokolnikoff IS (1964), Tensor-Analysis—Theory and Applications to Geometry and Mechanics of Continua, New York: John Wiley & Sons, 2nd ed.
99. Sokolowski J and Zochowski A (1997), On topological derivative in shape optimization, Research Report No 3170, INRIA Lorraine, Nancy, France.
100. Sokolowski J and Zochowski A (2000), Topological derivatives of shape functionals for elasticity systems, Research Report, INRIA Lorraine, Nancy, France, 16 pp.
101. Soto CA (1993), Shape optimization of plate structures using plate homogenization with applications in mechanical design, PhD thesis, Dept of Mechanical Engineering, Michigan State Univ.
102. Stadler W (ed) (1988), Multicriteria Optimization in Engineering and in the Sciences, Plenum Press, New York.
103. Steven GP, Querin OM, and Li Q (1999a), Publications Collection Volume 2, 1996-1997, Structural Optimization Research Group of Australasia (SORGA), Dept Aeronaut Eng, Univ of Sydney, Australia, 247 pp.
104. Steven GP, Querin OM, and Li Q (1999b), Publications Collection Volume 3, 1998, Structural Optimization Research Group of Australasia (SORGA), Dept Aeronaut Eng, Univ of Sydney, Australia, 278 pp.
105. Steven GP and Xie YM (1997), Evolutionary Structural Optimization, Springer-Verlag, London, 188 pp.
106. Szabo I (1977), History of Mechanical Principles (in German), Birkhauser-Verlag, Basel, Stuttgart.
107. Taylor JE and Bendsoe MP (2000), A mutual energy formulation for optimal structural design, MAT-Report No 2000-20, Inst of Math, Technical Univ of Denmark.
108. Thomsen J (1992), Optimization of properties of anisotropic materials and topologies of structures (in Danish), PhD-thesis, Inst of Mech Eng, Aalborg Univ, Denmark.
109. Topping BHV and Papadrakis M (eds) (1994), Advances in Structural Optimization, CIVIL-COMP Ltd, Edinburgh/UK.
110. Truesdell C (1965), Continuum Mechanics IV-Problems ofNonlinear Elasticity, Gordon and Breach, New York.
111. Truesdell C (1965), The Elements of Continuum Mechanics, Springer, Berlin, Heidelberg, New York.
112. Tsai SW, Halpin JC, and Pagano NJ (eds) (1968), Composite Materials Workshop, Technomic Pub, Stamford CT.
113. Van Gemert RJ (1996), Additive evolutionary structural optimization, Undergraduate Honours Thesis, Dept of Aeronaut Eng, Univ of Sydney, Australia.
114. Vinson JR and Sierakowski RL (1987), The Behavior of Structures Composed of Composite Materials, Martinus Nijhoff Publ, Dordrecht, The Netherlands.
115. Washizu K (1982), Variational Methods in Elasticity and Plasticity, 3rd Ed, Pergamon Press, New York.
116. Weinert M (1994), Sequential and parallel strategies for finding optimal layouts of complex shell structures (in German), PhD-Dissertation, Uni-GH Siegen, FOMAAS, TIM-Bericht Nr T05-05.94.
117. Wheedon RL and Zygmund A (1977), Measure and Integral: an Introduction to Real Analysis, Monographs in Pure and Applied Math, 43, Marcel Dekker, New York.
118. Wolfersdorf LV (1994), Inverse and Ill-posed Problems (in German), Berlin: Akademie-Verlag.
119. Wolff J. (1892): On the transformation of bones (in German) Berlin.
120. Young V (1997), Bi-directional Evolutionary Structural Optimization (BESO), 2-D and 3-D, Undergraduate Honours Thesis, Dept of Aeronaut Eng, Univ of Sydney, Australia.
121. Akgün MA (2001), Damage tolerant topology optimization under multiple damage configurations, In: Rozvany GIN, Olhoff N (eds): Topology Optimization of Structures and Composite Continua, NATO aRw, Budapest, Hungary, May 8-12, 2000, Kluwer Academic Publishers, Dordrecht, The Netherlands (to appear).
122. Allaire G (1994), Explicit lamination parameters for threedimensional shape optimization, J Control and Cybernetics 23, 311-326.
123. Allaire G (2001), Shape optimization with general objective functions using partial relaxation, In: Rozvany GIN, Olhoff N (eds): Topology Optimization of Structures and Composite Continua, NATO ARW, Budapest, Hungary, May 8-12, 2000, Kluwer Academic Publishers, Dordrecht, The Netherlands (to appear).
124. Allaire G and Aubry S (1999), On optimal microstructures for a plane shape optimization problem, Struct. Optim. 17, 86-94.
125. Allaire G, Bonnetier E, Francfort G, and Jouve F (1995), Shape optimization by the homogenization method, Report, Lab d’Analyze Numerique, Universite Paris 6.
126. Allaire G and Kohn R V (1993), Optimal design for minimum weight and compliance in plane stress using extremal microstructures, Eur. J. Mech, A/Solids 12(6), 839-878.
127. Almgren, RF (1985), An isotropic three-dimensional structure with Poisson’s ratio = — 1, J. Elasticity 15, 427-430.
128. Ambrosio L and Buttazzo G (1993), An optimal design problem with perimeter penalization, Calc. Var. 1, 55-69.
129. Atkin RJ and Craine RE (1976), Continuum theory of mixtures: Applications, J. Inst. Math. Applies 17(2), 153-207.
130. Atrek E (1989), SHAPE: A program for shape optimization of continuum structures, Proc First Int Conf.: Opti’89, Comp. Mechanics Publications, Berlin: Springer Verlag, 135-144.
131. Atrek E (1993), SHAPE: A structural shape optimization program, In: Hörnlein H, Schittkowski K (eds): Software Systems for Structural Optimization, Vol 110 International Series of Numerical Mathematics, Basel: Birkhauser Verlag, 229-249.
132. Atrek E and Agarwal B (1992), Shape optimization of structural design, In: Billingsley K R, Brown III, H U Derohanes E (eds): Scientific Excellence in Supercomputing-The IBM 1990 Contest Prize Papers, Univ of Georgia, Athens/GA: Baldwin Press.
133. Atrek E and Kodali R (1989), Optimum design of continuum structures with SHAPE, In: Prasad B. (ed): CAD/CAM Robotics and Factories of the Future, Vol 2 (Proc of 3rd Int Conf CARS and FOF-’88), Berlin: Springer, 11-15.
134. Avellaneda M (1987), Optimal bounds and microgeometrics for elastic two-phase composites, SIAM, J. Appl. Math. 47(6), 1216-1228.
135. Avellaneda M, and Milton GW (1989), Bounds on the effective elasticity tensor composites based on two-point correlation, In: Hui D, Kozik T J (eds): Composite Material Technology, ASME, 89-93.
136. Banichuk NV (1993), Shape design sensitivity analysis for optimization problems with local and global functionals, Mech. Struct. and Mach. 21(3), 375-397.
137. Banichuk NV, Barthold F-J, Falk A, and Stein E (1995), Mesh refinement for shape optimization, Struct. Optim. 9, 46-51.
138. Baumgartner A, Harzheim L, and Mattheck C (1992), SKO: Soft Kill Option: The biological way to find an optimum structure topology, Int. J. Fatigue 14(6), 387-393.
139. Beckers, M (1999), Topology optimization using a dual method with discrete variables, Struct. Optim. 17, 14-24.
140. Beckers M and Fleury C (1997), Topology optimization involving discrete variables, In: Gutkowski W, Mroz Z (eds): Second World Congress of Structural and Multidisciplinary Optimization, WCSMO-2, Institute of Fundamental Technological Research, Warsaw, Poland, Vol 2, 533-538.
141. Bendsoe MP (1982), G-closure and homogenization problems arising in plate optimization, In: Eschenauer H, Olhoff N (eds): Optimization Methods in Structural Design, EUROMECH-Colloquium 164, Wien: B.1.-Wissenschaftsverlag, 270-275.
142. Bendsoe MP (1989), Optimal shape design as a material distribution problem, Struct. Optim., 1, 193-202.
143. Bendsoe MP (1997), Variable-topology optimization: Status and challenges, In: Wunderlich W (ed): Proc ICTAM, Kyoto, August 25-31, 1996, Elsevier Science BV, Amsterdam, The Netherlands.
144. Bendsoe MP (1999), Variable-topology optimization: Status and challenges, In: Wunderlich W. (ed): Proc European Conf on Computational Mechanics—ECCM’99, Aug 31-Sept 3, 1999, Munich, Germany, CD-Rom, Tech Univ of Munich, Germany, 21 pp.
145. Bendsoe MP and Diaz A (1998), A method for treating damage related criteria in optimal topology design of continuum structures, Struct. Optim. 16 (2/3), 108-115.
146. Bendsoe MP, Diaz A, and Kikuchi N (1993), Topology and generalized layout optimization of elastic structures, In: Bendsoe MP, Mota Soares CA (eds): Topology Design of Structures, Dordrecht: Kluwer Academic Publishers, 159-205.
147. Bendsoe MP, Diaz A, Lipton R, and Taylor JE (1994a), Optimal design of material properties and material distribution for multiple loading conditions, Int. J. of Num. Meth. Engng 38, 1149-1170.
148. Bendsoe MP, Guedes JM, Haber RB, Pedersen P, and Taylor JE (1994b), An analytical model to predict optimal material properties in the context of optimal structural design, J. Appl. Mech. 61, 930-937.
149. Bendsoe MP, Guedes JM, Plaxton S, and Taylor JE (1996), Optimization of structure and material properties for solids composed of softening material, Int. J. Solids Struct 33, 1799-1813.
150. Bendsoe MP and Kikuchi N (1988), Generating optimal topologies in structural design using a homogenization method, Comp. Meths. Appl. Mech. Engrg 71, 197-224.
151. Bendsoe MP and Sigmund O (1999), Material interpolations in topology optimization, Arch. Appl. Mech. 69, 635-654.
152. Bennet JA and Botkin ME (1983), Shape optimization of twodimensional structures with geometric problem description and adaptive mesh refinement, AIAA/ASME/AsCe/AHS 24th Structures, Sturc-tural Dynamics and Materials Conf (Part I), Lake Tahoe, Nevada/USA, 422-431.
153. Bennet JA, and Botkin ME (1985), Structural shape optimization with geometric description and adaptive mesh refinement, AIAA J. 23, 458-464.
154. Ben-Tal A and Taylor JE (1991), A unified model for elastoplatic structural analysis via dual variational principles, In: Komkov V (ed): Proc SIAM-Dayton Conf on Design Theory.
155. Bletzinger K-U and Kimmich S, Ramm, E (1991), Effecient modeling in shape optimal design, Computing Systems in Engineering 2, 483-495.
156. Botkin ME (1981), Shape optimization of plate and shell structures, AIAA/ASME/ASCE/AHS 22nd Structural Dynamics and Materials Conf (Part I), Atlanta, GA, 242-249.
157. Bourgat JF (1977), Numerical experiments of the homogenization method for operators with periodic coefficients, Lecture Notes in Mathematics 740, Springer-Verlag, Berlin, 330-356.
158. Bremicker M, Kikuchi N, Chirehdast M, and Papalambros PY (1991), Integrated topology and shape optimization in structural design, Mech. Struct. and Mach 19(4), 551-587.
159. Bruns TE and Tortorelli DA (2000a), Topology optimization of nonlinear elastic structures and compliant mechanisms, Comp. Meth. Appl. Mech. Engrg. (to appear).
160. Bruns TE and Tortorelli DA (2000b), Topology optimization of geometrically nonlinear structures and complaint mechanisms, In: Bloe-baum CL (ed): WCSMO-3-Proc Third World Congress of Structural and Multidisciplinary Optimization, May 17-21, 1999, Buffalo NY, CD-Rom, Univ of Buffalo.
161. Buhl T, Pedersen CBW, and Sigmund O (2000), Stiffness design of geometrically nonlinear structures using topology optimization, Struct. Multidisc. Optim 19, 93-104.
162. Bulman S and Hinton E (2000), Constrained adaptive topology optimization of engineering structures, In: Bloebaum CL (ed): WCSMO-3-Proc Third World Congress ofStructural and Multidisciplinary Optimization, May 17-21, 1999, Buffalo NY, CD-Rom, Univ of Buffalo.
163. Burns RH and Crossley FRE (1964), Kinetostatic synthesis of flexible link mechanisms, ASME-Paper, 68(36).
164. Burns T and Cherkaev A (1997), Optimal distribution of multimaterial composites for torsional beams, Struct. Optim. 13, 4-11.
165. Buttazzo G and Dal Maso G (1993), An existence result for a class of shape optimization problems, Arch. Rational Mech. Anal. 122, 183-195.
166. Canfield S and Frecker M (2000), Topology optimization of compliant mechanisms for displacement amplifcation, In: Bloebaum CL (ed): WCSMO-3- Proc Third World Congress of Structural and Multidisciplinary Optimization, May 17-21, 1999, Buffalo NY, CD-Rom, Univ of Buffalo.
167. Carter DR and Fyhrie DP (1990), Femoral head apparent density distribution predicted from bone stresses, J. Biomech. 23, 1-10.
168. Carter DR, Fyhrie DP, and Whalen RT (1987), Trabecular bone density and loading history: Regulation of connective tissue biology by mechanical energy, J. Biomech. 20, 785-794.
169. Carter DR and Hayes WC (1977), The compressive behavior of bone as a two-phase porous structure, J. Bone and Joint Surg. 59-A, 954-962.
170. Carter DR, Orr TE, and Fyhrie DP (1989), Relationship between loading history and femoral cancellous bone architecture, J. Biomech. 22, 231-244.
171. Cea J (1986), Conception optimale ou identification de forme, calcule rapide de la derivee directionelle de la fonction coiit, MAAN, 30(3), 371-402.
172. Cea J, Gioan A, and Michel J (1973), Quelques resultats sur Identification de domains, CALCOLO.
173. Cea J and Malanowski K (1970), An example of a max-min problem in partial differential equations, SIAM J. Control 8, 305-316.
174. Chang K-H and Choi KK (1992), A geometry-based parameterization method for shape design of elastic solids, Mech. Struct. Mach. 20(2), 215-252.
175. Chang KH and Tang PS (2000), Integration of topology and shape design optimizations for structural components, In: Bloebaum CL (ed): WCSMO-3-Proc Third World Congress of Structural and Multidisciplinary Optimization, May 17-21, 1999, Buffalo NY, CD-Rom, Univ of Buffalo.
176. Cheng G (1981), On non-smoothness in optimal design of solid, elastic plates, Int. J. Solids Struct. 17, 795-810.
177. Cheng G (1997), Some development of structural topology optimization, In: Tatsumi T, Watanabe E, and Kambe T (eds): Theoretical and Applied Mechanics 1996, Elsevier Sciences BV, Amsterdam, 379-394.
178. Cheng G and Guo X (1997), s-related approach in structural topology optimization, Struct. Optim. 13(4), 258-266.
179. Cheng G and Jiang Z (1992), Study on topology optimization with stress constraints, J. Eng. Optim. 20, 129-148.
180. Cheng G and Olhoff N (1981), An investigation concerning optimal design of solid elastic plates, Int. J. Solids Struct. 17, 305-323.
181. Cheng G and Olhoff N (1982), Regularized formulation for optimal design of axisymmetric plates, Int. J. Solids Struct. 18(2), 153-169.
182. Cherkaev AV and Gibiansky LV (1993), Coupled estimates for the bulk and shear moduli of a two-dimensional isotropic elastic composite, J. Mech. Phys. Solids 41(5), 937-980.
183. Cherkaev AV and Gibiansky LV (1994), Variational principles for complex conductivity, viscoelasticity and similar problems with complex moduli, J. Math. Physics 35(1), 127-145.
184. Cherkaev AV and Gibiansky LV (1996), External structures of multiphase heat conducting composites, Int. J. Solids Struct 33(18), 2609-2618.
185. Cherkaev AV and Palais R (1996), Optimal design of threedimensional axisymmetric elastic structures, Struct. Optim. 12, 35-45.
186. Clausen T (1851), Uber die Form architektonischer Saulen, Bull. Phys-Math de l’Academy St. Petersburg, 9, 368.
187. Cowin SC (1987), Bone remodeling of diaphyseal surfaces by torsional loads: Theoretical predictions, J. Biomech. 20, 1111-1120.
188. Cowin SC, Hart RT, Balser JR, and Kohn DH (1985), Functional adaptation in long bones: Establishing in vivo values for surface remodeling rate coefficients, J. Biomech. 18, 665-684.
189. Cristescu M and El-Yafi F (1986), Interactive shape optimization, In: Mota Soares CA (ed): Computer Aided Optimal Design: Structural and Mechanical Systems, nAtO/NASA/nSf/USAF Advanced Study Institute, froia/PORTUGAL, June 29-July 11, 1986, Vol 2, Center for Mechanics and Materials, Tech Univ of Lisbon, 262-271.
190. Dems K and Mroz Z (1983), Variational approach by means of adjoint systems to structural optimization and sensitivity analysis Part I, Int. J. Solids Struct. 19, 677-692.
191. Dems K and Mroz Z (1984), Variational approach by means of adjoint systems to structural optimization and sensitivity analysis Part II, Int. J. Solids Struct. 20, 527-552.
192. De Rose Jr GCA and Diaz AR (1999), Single scale wavelet approximations in layout optimization, Struct. Optim. 18, 1-11.
193. De Rose Jr GCA and Diaz AR (2000), Solving three-dimensional layout optimization problems using fixed scale wavelets, Comput. Mech. 25(2), 274-285.
194. Diaz A and Bendsoe MP (1992), Shape optimization of structures for multiple loading situations using a homogenization method, Struct. Optim. 4, 17-22.
195. Diaz A and Lipton R (1997), Optimal material layout for 3D elastic structures, Struct. Optim. 13, 60-64.
196. Diaz A, Lipton R, and Soto CA (1994), A new formulation of the problem of optimum reinforcement of Reissner-Midlin plates, Comp. Meth. Appl. Mechs. Eng123, 121-139.
197. Diaz A, and Sigmund O (1995), Checkerboard patterns in layout optimization, Struct. Optim. 10, 40-45.
198. Diaz AR and Kikuchi N (1992), Solutions to shape and topology eigenvalue optimization problems using a homogenization method, Int. J. Num. Math. Eng 35, 1487-1502.
199. Diaz AR and Lipton R (2000), Optimal material layout in threedimensional elastic structures subjected to multiple loads, Mech. Struct. Mach. 28(2/3).
200. Duysinx P (2000), Topology optimization with different stress limits in tension and compression, In: Bloebaum CL (ed): WCSMO-3-Proc 3d World Congress of Structural and Multidisciplinary Optimization, May 17-21, 1999, Buffalo NY, CD-Rom, Univ of Buffalo.
201. Duysinx P and Bendsoe MP (1998), Topology optimization of continuum structures with local stress constraints, Int. J. Num. Meths. Eng. 43(18), 1453-1478.
202. th AIAA/USAF/NASAISsMo Symp on Multidisciplinary Analysis and Optimization, Vol 1, AIAA, 1501-1509.
203. Eschenauer HA (1988), Multicriteria optimization techniques for highly accurate focussing systems, In: Stadler W (ed): Multicriteria Optimization in Engineering and in the Sciences, Plenum Press, New York, 309-354.
204. Eschenauer HA (1992), Multidisciplinary modeling and optimization in design processes, ZAMM 72, 6, T437-T447.
205. Eschenauer HA (1998), Development of highly precise radio telescopes: A typical multidisciplinary problem, In: Belegundu A and Mistree F (eds): Optimization in ind ASME, 13-30.
206. Eschenauer HA (1999), Multidisciplinary engineering strategies for product and process development—modeling, simulation, optimization, applications, In: Toropov VV (ed): Engineering Design Optimization, Product and Process Development, Proc 1st ASMO UK/ISSMO Conf on Engineering Design Optimization, MCB Univ Press, Bradford, 1-17.
207. Eschenauer HA, Gatzlaff H, and Kiedrowski HW (1980), Entwicklung und Optimierung hochgenauer Panelstrukturen, Technische Mitteilungen Krupp, Forsch-Berichte, 38, 43-57.
208. Eschenauer HA, Geilen J, and Wahl H J (1993), SAPOP: An optimization procedure for multicriteria structural design, In: Hörnlein H and Schittkowski K (eds): Software Systems for Structural Optimization, Vol 110 International Series of Numerical Mathematics, Basel: Birkhauser Verlag, 207-227.
209. Eschenauer HA, Kobelev VV, and Schumacher A (1994), Bubble method for topology and shape optimization of structures, Struct. Optim. 8, 42-51.
210. Eschenauer HA and Schumacher A (1993a), Bubble Method: A special strategy for finding best possible initial designs, Proc of 1993 ASME Design Tech Conf-19th Design Automation Conf, Albuquerque, New Mexico, Sept. 19-22, Vol 65-2, 437-443.
211. Eschenauer HA and Schumacher A (1993b), Possibilities of applying various procedures of topology optimisation to components subject to mechanical loads, ZAMM 73, T392-T394.
212. Eschenauer HA and Schumacher A (1997), Topology and shape optimization procedures using hole positioning criteria-theory and applications, In: Rozvany GIN (ed): Topology Optimization in Structural Mechanics, Vol 374 of CISM Courses and Lectures, Wien: Springer, 135-196
213. Eschenauer HA, Schumacher A, and Vietor T (1993), Decision makings for initial designs made of advanced materials, In: Bendse MP and Mota Soares CA (eds): Topology Design of Structures, Dordrecht: Kluwer Academic Publ, 469-480.
214. Eschenauer HA and Wahl HJ (1993), A decomposition strategy for optimization of structures using the FE-submodel-technique, ZAMM 73, T395-T397.
215. Farin G (1991), Splines in CAD/CAM, In: Surveys on Mathematics for Industry, Springer-Verlag, Austria, 1991, pp. 39-73.
216. Fernandes P, Guedes JM, and Rodrigues H (1999a), Topology optimization of three-dimensional linear elastic structures with a constraint on “perimeter,” Comput. Struct. 73, 583-594.
217. Fernandes P, Rodrigues H, and Jocobs C (1999b), A model of bone adaptation using a global optimization criterion based on the trajec-torial theory of Wolff, Comp. Meth. Biomech. Biomed. Eng. 2, 125-138.
218. Fleury C (1986), Shape optimal design by the convex linearization method, In: Bennet JA and Botkin ME. (eds): The Optimum Shape: Automated Structural Design, New York: Plenum Press, 297-320.
219. Foldager J (1997), Design optimization of laminated composite plates divided into rectangular patches with use of lamination parameters, In: Gutkowski W and Mroz Z (eds): Proc WCSMO 2-Second World Congress of Structural and Multidisciplinary Optimization, Inst of Fundamental Technological Research, Warsaw, Vol 2, 669-675.
220. Foldager J, Olhoff N, and Hansen JS (1998), A general procedure forcing convexity in ply angle optimization in composite laminates, Struct. Optim. 16(2/3), 201-211.
221. Foldager JP, Hansen JS, and Olhoff N (2000), A convex formulation in ply-angle optimization, In: Bloebaum CL (ed): WCSMO-3-Proc 3rd World Congress ofStructural and Multidisciplinary Optimization, May 17-21, 1999, Buffalo NY. CD-Rom, Univ of Buffalo.
222. Folgado J and Rodrigues H (1997), Topology optimization methods applied to the design of orthopaedics implants, In: Gutkowski W and Mroz Z (eds): WCSMO-2: Second World Congress of Structural and Multidisciplinary Optimization, Inst of Fundamental Technological Research, Warsaw, Poland, Vol 2, 563-568.
223. Folgado J and Rodrigues H (1998), Structural optimization with a nonsmooth buckling load criterion, Control Cybernetics 27(2), 235-253.
224. Folgado J, Rodrigues H, and Guedes JM (1995), Layout design of plate reinforcements with a buckling load criterion, In: Olhoff N and Rozvany GIN (eds): Structural and Multidisciplinary Optimization, ISSMO, Goslar, Germany, Oxford: Pergamon, 659-666.
225. Francfort GA and Murat F (1986), Homogenization and optimal bounds in linear elasticity, Arch. Rat. Mech. Anal 94, 307-334.
226. Frecker M, Kikuchi N, and Kota S (1997), Optimal design of compliant mechanisms, In: Gutkowski W and Mroz Z (eds): Proc WC-SMO 2-Second World Congress of Structural and Multidisciplinary Optimization, Inst. of Fundamental Technological Research, Warsaw, Vol 1, 345-350.
227. Frecker M, Kikuchi N, and Kota S (1999), Topology optimization of compliant mechanisms with multiple outputs, Struct. Optim. 17, 269-278.
228. Freudenthal AM and Geiringer H (1958), The mathematical theories of the inelastic continuum, In: Flügge S, Handbuch der Physik VI, Berlin, Gottingen, Heidelberg: Springer, 229-269.
229. Fukunaga H and Vanderplaats GN (1991), Stiffness optimization of orthotropic laminates composites using lamination parameters, AIAA J 29, 641-646.
230. Garreau S, Masmoudi M, and Guillaume P (1999), The topological sensitivity for linear isotropic elasticity, ECCM'99, Munich/Germany.
231. Grauer M and Boden H (1993), On the solution of nonlinear engineering optimization problems on parallel computers, FOMAAS Research Report, TIM01-03.94, 96-105.
232. Grenestedt JL and Gudmundsson P (1993), Layup optimization of composite material structures, In: Pedersen P (ed): Optimal Design with Advanced Materials, Proc IUTAM Symp, 311-336.
233. Guedes JM and Kikuchi N (1990), Pre- and postprocessing for materials based on the homogenization method with adaptive element methods, Comput. Meth. Appl. Mech. Eng. 83, 143-198.
234. Guedes JM and Taylor JE (1997), On the prediction of material properties and topology for optimal continuum structures, Struct. Optim. 14, 193-199.
235. Guillaume P and Masmoudi M (1994), Computation of high order derivatives in optimal shape design, Numerische Mathematik. 67, 231-250.
236. Haber RB and Bendse MP (1998), Problem formulation, solution procedures and geometric modeling: Key issues in variable-topology optimization, In: Proc 7th AIAA/USAF/NASA/ISSMO Symp on Multidisciplinary Analysis and Optimization, Vol 1, AIAA, 1864-1837.
237. Haber RB, Jog CS, and Bendsoe MP (1994), Variable-topology shape optimization with a control on perimeter, In: Advances in Design Automation, Vol 69, ASME, 261-272.
238. Haber RB, Jog CS, and Bendse MP (1995), The perimeter method—a new approach to variable-topology shape optimization, In: Olhoff N, Rozvany GIN (eds): Structural and Multidisciplinary Optimization, Proc of WCSMO-1, Elsevier Science, Oxford/UK, 153-160.
239. Haber RB, Jog CS, and Bendsoe MP (1996), A new approach to variable-topology design using a constraint on the perimeter, Struct. Optim. 11, 1-12.
240. Haftka RT (1984), An improved computational approach for multilevel optimum design, J. Struct. Mech. 12, 245-261.
241. Hajela P (1990), Genetic Search—An approach to the nonconvex optimization problem, AIAA J 28, 1205-1210.
242. Hajela P, Lee E, and Lin C-Y (1993), Genetic algorithms in structural topology optimization, In: Bendse MP, Mota Soares CA (eds): Topology Design of Structures, Kluwer Academic Publ, Dordrecht, 117-134.
243. Hajela P and Vittal S (2000), Evolutionary computing and structural topology optimization-A state of the art assessment, In: Olhoff N and Rozvany G (eds): Lecture Notes, NATO Advanced Research Workshop, Kluwer Academic Publ (to appear).
244. Hammer VB (1999), Optimal laminate design subject to single membrane loads, Struct. Optim. 17, 65-74.
245. Hammer VB, Bendsoe MP, Lipton R, and Pedersen P (1997), Param-etrization in laminate design for optimal compliance, Int. J. Solids Struct. 34(4), 415-434.
246. Hammer VB and Olhoff N (2000a), Topology optimization of continuum structures subjected to pressure loading, Struct. Multidisc. Op-tim 19, 85-92.
247. Hammer VB and Olhoff N (2000b), Topology optimization with design dependent loads, In: Bloebaum CL (ed): WCSMO 3-Third World Congress of Structural and Multidisciplinary Optimization, Buffalo NY 1999.
248. Hartzheim L and Graf G (1995), Optimization of engineering components with the SKO method, Proc of 9th Int Conf on Vehicle Structural Mechanics and CAE, April 4-6, 1995, Troy MI, 235-243.
249. Hartzheim L and Graf G (1997), Shape and topology optimization in automotive industry, High Performance Computing in Automotive Design, Engineering and Manufacturing, Proc of 3rd Int Conf on High Performance Computing in Automotive Industry, Oct. 7-10, 1996, Paris, France, 167-182.
250. Hartzheim L, Graf G, Klug S, and Liebers J (1999), Topology optimisation in practice, ATZ, Automobiltechnische Zeitschrift 101, 7/8, 11-16.
251. Hashin Z and Shtrikman, S (1963), A variational approach to the theory of the elastic behavior of multiphase materials, J. Mech. Phys. Solids. 11, 127-140.
252. Hassani B and Hinton E (1998), A review of homogenization and topology optimization, Comput Struct 71(6), Part I: Homogenization theory for media with periodic structure 707-718, Part II: Analytical and numerical solution of homogenization equations 719-738, Part III: Topology optimization using optimality criteria 739-756.
253. Henkel F-O, Schumann-Luck A, and Atrek E (1991), Formoptimierung mit NISA-SHAPE, XX, Int Finite Element Congress (FEM’91), Baden-Baden/Germany.
254. Hinton E, Sienz J, Bulman S, and Hassani B (1997), Fully integrated design optimization of engineering structures using adaptive finite element models, In: Gutkowski W and Mroz Z (eds.): Proceedings WCSMO 2-Second World Congress of Structural and Multidisciplinary Optimization, Inst of Fundamental Technological Research, Warsaw, Vol 1, 73-78.
255. Huiskes R, Weinans H, Grooteboer HJ, Dalstra M, Fudala B, and Slooff TJ (1987), Adaptive bone-remodeling theory applied to prosthetic-design analysis, J. Biomech. 22, 1135-1150.
256. Imam MH (1982), Three-dimensional shape optimization, Int J Numer Methods Eng 18, 661-673.
257. Jacobsen JB, Olhoff N, and Ronholt E (1997), Generalized shape optimization of three-dimensional structures using materials with optimum microstructures, Mech. Mat. 28, 207-225.
258. Jog C and Haber RB (1996), Stability of finite element models for distributed-parameter optimization and topology design, Comp. Meth. Appl. Mech. Eng. 130, 203-226.
259. Jog CS and Haber RB (1995), Checkerboard and other spurious modes in solutions to distributed-parameter and topology design problems, In, Olhoff N and Rozvany GIN (eds): WCSMO-1-First World Congress of Structural and Multidisciplinary Optimization, Pergamon Press, Oxford, UK, 237-242.
260. Jog CS, Haber RB, and Bendsoe MP (1994), Topology design with optimized adaptive materials, Int. J. Num. Meths. Eng. 37, 1323-1350.
261. Kemmler R, Schwartz S, and Ramm E (2000), Topology optimization including geometrically nonlinear response, In: Bloebaum CL (ed):WCSMO-3-Proc Third World Congress of Structural and Multidisciplinary Optimization, May 17-21, 1999, Buffalo NY, CD-Rom, Univ of Buffalo.
262. Kikuchi N, Chung KY, Torigaki T, and Taylor JE (1986), Adaptive finite element methods for shape optimization of linearly elastic structures, Comp. Meth. Appl. Mech. Eng. 57, 67-89.
263. Kim CJ, Pisano AP, and Muller RS (1992), Silicon-processed overhanging microgripper, J. Microelectromech. Systems, 1, 31-36.
264. Kirsch U (1990), On the relationship between optimum structural topologies and geometries, Struct Optim 2, 39-45.
265. Kita E and Tanie H (1999), Topology and shape optimization of continuum structures using GA and BEM, Struct Optim 17, 130-139.
266. Kohn RV and Strang G (1986a), Optimal design in elasticity and plasticity, Num. Meths. Eng. 22, 183-188.
267. Kohn RV and Strang G (1986b), Optimal design and relaxation of variational problems, Comm. Pure Appl. Math. 39, Part I: 1 -25, Part II: 139-182; Part III: 353-357.
268. Korycki R, Eschenauer HA, and Schumacher A (1993), Incorporation of adjoint method sensitivity analysis within the optimization procedure SAPOP, In: Proc of 11th Polish Conf. on Computer Methods in Mechanics, May 11-15.
269. Krog LA and Olhoff N (1995/96), Topology optimization of integral rib reinforcement of plate and shell structures with weighted-sum and max-min objectives, In: Bestle D and Schiehlen W (eds): Optimization ofMechanical Systems, Stuttgart, Germany (1995), Kluwer Academic Publ, Dordrecht, The Netherlands (1996), 171-179.
270. Krog LA and Olhoff N (1997), Topology and Reinforcement layout optimization of disk, plate, and shell structures, In: Rozvany GIN (ed): Topology Optimization in Structural Mechanics, Vol 374 of CISM Course and Lectures, Springer, Vienna, Austria, 237-322.
271. Krog LA and Olhoff N (1999), Optimum topology and reinforcement design of disk and plate structures with multiple stiffness and eigen-frequency objectives, Comput Struct 72, 535-563.
272. Kutylowski R (2000), On an effective topology procedure, Struct. Multidisc. Optim 20 49-56.
273. Lakes R (1993), Design considerations for materials with negative Poisson’s ratio, J. Mech. Design, 115, 696-700.
274. Lekszycki T (2000), Application of optimally conditions in modeling of the adaptation phenomenon of bones, In: Bloebaus C. L. (ed), WCSMO-3-Proc Third World Congress of Structural and Multidisciplinary Optimization, May 17-21, 1999, Buffalo NY, CD-Rom, Univ of Buffalo.
275. Leon L (1908), Uber die Storungen der Spannungsverteilung, die in elastischen Korpern durch Bohrungen und Blaschen entstehen, Osterr, Wochenzeitschrift fur den offentlichen Baudienst, Nr 9, 163-168.
276. Levinson M (1965), The complementary energy theorem in finite elasticity, J. Appl. Mech 32, Dec, 826-828.
277. Lewinski T, Sokolowski J, and Zochowski A (2000), Justification of the bubble method for the compliance minimization problems of plates and spherical shells, In: Bloebaum CL (ed): WCSMO-3-Proc Third World Congress of Structural and Multidisciplinary Optimization, May 17-21, 1999, Buffalo NY, CD-Rom, Univ of Buffalo.
278. Lin C-Y and Hajela P (1992), Genetic search strategies in multicriterion optimal design, Struct Optim 4, 144-156.
279. Lipton R (1994), Optimal bounds on effective elastic tensors for orthotropic composites, Proc R. Soc. Lond. A, 443, 399-410.
280. Lipton R (1994a), On optimal reinforcement of plates and choice of design parameters, J. Control Cybernetics 23(3), 481-493.
281. Lipton R (1994b), Optimal design and relaxation for reinforced plates subject to random transverse loads, J. Probabilistic Eng. Mech. 9, 167-177.
282. Lipton R and Diaz A (1995), Moment formulations for optimum layout in 3D elasticity, In: Olhoff N and Rozvany GIN (eds): Structural and Multidisciplinary Optimization, Pergamon Press, Oxford, UK, 161-168.
283. Lipton R and Diaz A (1997a), Optimal material layout for 3-D elastic structures, Struct Optim 13, 60-64.
284. Lipton R and Diaz A (1997b), Reinforced Mindlin plates with extremal stiffness, Int. J. Solids Struct 34(28), 3691-3704.
285. Liu J-S, Parks GT, and Clarkson PJ (1999a), Topology optimization of both trusses and continuum structures using a unified metamorphic development method, Proc of 1st ASMO UK/ISSMO Conf on Engineering Design Optimization, llkley, West Yorkshire, UK, 257-264.
286. Liu J-S, Parks GT, and Clarkson PJ (1999b), Metamorphic Development: A new topology optimization method for truss structures, Proc of 40th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conf, St Louis MO, April 12-15, 1999, AIAA-99-1387, 1578-1588.
287. Liu J-S, Parks GT, and Clarkson PJ (1999c), Can a structure grow towards an optimum topology layout?-Metamorphic Development: a new topology optimization method, Proc 3rd World Congress of Structural and Multidisciplinary Optimization (WCSMO-3), Buffalo NY, May 17-21, 1999.
288. Liu JS, Parks GT, and Clarkson PJ (2000), Metamorphic development: A new topology optimization method for continuum structures, Struct. Multidisc. Optim 20, 288-300.
289. Lurie KA and Cherkaev AV (1986), Effective characteristics of composite materials and the optimal design of structural elements, Uspe-khi Mekhaniki 9, 3-81
290. Cherkaev AV, Kohn RV (eds): Topics in the Mathematical Modelling of Composite Materials, Vol 31 of Progress in Nonlinear Differential Equations and Their Applications, Birkhauser, Boston MA, 1997, 175-258.
291. Lurie kA, Cherkaev AV, and Fedorov A (1982), Regularization of optimal design problems for bars and plates, Part I: JOTA 37, 499-522, Part II: JOTA 37, 523-543; Part III: JOTA 42, 247-284.
292. Ma ZD, Cheng HC, and Kikuchi N (1994), Structural design for obtaining desired eigenfrequencies by using the topology and shape optimization method, Comput. Syst. Eng. 5, 77-89.
293. Ma ZD, Kikuchi N, and Cheng HC (1995a), Topological design for vibrating structures, Comp. Meth. Appl. Mech. Eng. 121, 259-280.
294. Ma ZD, Kikuchi N, Cheng HC, and Hagiwara I (1995b), Topological optimization technique for free vibration problems, J. Appl. Mech. (March’95).
295. Magister R and Post PU (1995), Use of structural optimization in the development of pneumatic components, In: Olhoff N and Rozvany GIN (eds): Proc WCSMO 1-First World Congress of Structural and Multidisciplinary Optimization, Goslar, Pergamon Press, Oxford, 445-452.
296. Maier G (1973), Limit design in the absence of a given layout: A finite element zero-one programming problem, In: Gallagher RH and Zienkiewicz OC (eds): Optimum Structural Design-Theory and Applications, London: John Wiley and Sons, 223-239.
297. Martin RB (1972), The effects of geometric feedback in the development of osteoporosis, J. Biomech 5, 447-455.
298. Martin RB and Burr DB (1982), A hypothetical mechanism for the stimulation of Osteonal remodeling by fatigue damage, J. Biomech 15, 137-139.
299. Mattheck C, Baumgartner A, and Walther F (1995), Bauteiloptim-ierung durch die Simulation biologischen Wachstums, In: Kull, Ramm, Reiner (eds): Evolution und Optimierung, Stuttgart: S. Hirzel, 107-120.
300. Maute K and Ramm E (1994a), Adaptive techniques in topology optimization, 5th AIAA/USAF/NASA/ISSMO Symp on Multidisciplinary Analysis and Optimization, Vol 1, AIAA, 121-131.
301. Maute K and Ramm E (1994b), Adaptive topology optimization, Struct Optim 10, 100-112.
302. Maute K and Ramm E (1995), General shape optimization—an integrated model for topology and shape optimization, In: Olhoff N and Rozvany GIN (eds): WCSMO-1-First World Congress of Structural and Multidisciplinary Optimization, Pergamon Press, Oxford, UK, 299-306.
303. Maute K, Schwarz S, and Ramm E (1998), Adaptive topology optimization of elastoplastic structures, Struct. Optim. 15, 81-91.
304. Maute K, Schwarz S, and Ramm E (1999), Structural optimization, The interaction between form and mechanics, ZAMM 79(10), 651-673.
305. Maxwell JC (1989), On Reciprocal Figures, frames and diagrams of forces, Scientific Papers 2, 160-207.
306. Michell AGM (1904), The limits of economy of materials in frame structures, Philosophical Magazine, Series 6, Vol 8(47), 589-597.
307. Miki M (1982), Material design of composite laminates with required in-plane elastic properties, In: Hayashi T, Kawata K, Umekawa M (eds): Proc Progress in Science and Engineering of Composites, ICCM IV, Tokyo.
308. Miki M and Sugiama Y (1991), Optimal design of laminated composite plates using lamination parameters, AIAA J 29, 275-283.
309. Milton GV (1992), Composite material with Poisson’s ration close to-I, J. Mech. Phys. Solids 40(5), 1105-1137.
310. Milton GV and Cherkaev AV (1993), Materials with elastic tensors that range over the entire set compatible with thermodynamics, Paper presented at the joint ASCE-ASME-SES MettN, Univ of Virginia, Charlottesville VA.
311. Min S, Kikuchi N, Park YC, Kim S, and Chang S (1997), Optimal reinforcement design of structures under impact loads, In: Gutkowski W and Mroz Z (eds): ECSMO-2: Second World Congress of Structural and Multidisciplinary Optimization, Inst of Fundamental Technological Research, Warsaw, Poland, Vol 2, 583-588.
312. Min S, Kikuchi N, Park YC, Kim S, and Chang, S (1999), Optimal topology design of structures under dynamic loads, Struct. Optim. 17, 208-218.
313. Mlejnek HP (1991), Some aspects in the genesis of structures, In: Rozvany GIN (ed): Optimization of Large Structural Systems, NATO-ASI Lecture Notes.
314. Mlejnek HP (1995), Some recent extensions in the distribution of isotropic material, In: Olhoff N and Rozvany GIN (eds): WCSMO-1-First World Congress of Structural and Multidisciplinary Optimization, Pergamon Press, Oxford/UK, 225-230.
315. Mlejnek HP and Schirrmacher R (1993), An engineers approach to optimal material distribution and shape finding, Comp. Meth. Appl. Mech. Eng 106, 1-26.
316. Mroz Z and Bojczuk D (2000), Topological derivative concept in optimal design of structures, In: Bloebaum CL (ed): WCSMO-3-Proc Third World Congress of Structural and Multidisciplinary Optimization, May 17-21, 1999, Buffalo NY, CD-Rom, Univ of Buffalo.
317. Mullender MG, Huiskes R, and Weihnans H (1994), A physiological approach to the simulation of bone remodelling as a self-organizational control process, J. Biomech 11, 1389-1394.
318. Naghdi P M (1964), Non-linear thermoplastic theory of shells, In: Olszak W and Sawczuk A, Non Classical Shell Problems, Amsterdam: North-Holland Publ, 1-268.
319. Neves MM, Rodrigues H, and Guedes JM (1995), Generalized topology design of structures with a buckling load criterion, Struct. Optim. 10, 71-78.
320. Neves MM, Rodrigues H, and Guedes JM (2000), Optimal design of periodic linear elastic microstructures, Comput. Struct. 76, 421-429.
321. Niordson F (1982), Some new results regarding optimal design of elastic plates, In: Eschenauer H and Olhoff N. (eds): Optimization Methods in Structural Design, EUROMECH-Colloquium 164, Wien: B. I.-Wissenchaftsverlag, 380-386.
322. Niordson FI (1983), Optimal design of plates with a constraint on the slope of the thickness function, Int. J. Solids Struct 19, 141-151.
323. Nishiwaski S, Saitou K, Min S, and Kikuchi, N (2000a), Topological design considering flexibility under periodic loads, Struct. Multidisc. Optim. 19, 4-16.
324. Nishiwaki S, Silva ECN, Saitou K, and Kikuchi N (2000b), Topology optimization of actuators using structural flexibility, In: Bloebaum CL (ed): WCSMO-3—Proc Third World Congress of Structural and Multidisciplinary Optimization, May 17-21, 1999, Buffalo NY, CD-Rom, Univ of Buffalo.
325. Noll W (1958), A mathematical theory of the mechanical behavior of continuous media, Arch. Rational Mech. Anal. 2, 197-226.
326. Olhoff N (1996), On optimum design of structures and materials, Meccanica 31, 143-161.
327. Olhoff N (2001), Comparative study of optimizing the topology of plate-like structures via plate theory and 3-D theory of elasticity, In: Rozvany GIN and Olhoff N (eds): Topology Optimization of Structures and Composite Continua, NATO ARW, Budapest, Hungary, May 8-12, 2000, Kluwer Academic Publ, Dordrecht, The Netherlands (to appear).
328. Olhoff N, Bendsoe MP, and Rasmussen J (1991), On CAD-integrated structural topology and design optimization, Comp. Meths. Appl. Mech. Eng. 89, 259-279.
329. Olhoff N and Eschenauer H (1999), On optimal topology design in mechanics, In: Wunderlich W. (ed): Proc European Conf on Computational Mechanics-ECCM’99, August 31-September 3, 1999, Munich, Germany, CD-Rom, Technical Univ of Munich, Germany, 71 pp.
330. Olhoff N, Lurie KA, Cherkaev AV, and Fedorov A (1981), Sliding regimes of anisotropy in optimal design of vibrating plates, Int. J. Solids Struct. 17(10), 931-948.
331. Olhoff N, Roholt, E, and Scheel J (1998a), Topology optimization of three-dimensional structures using optimum microstructures, Struct. Optim. 16, 1-18.
332. Olhoff N, Ronholt E, and Scheel, J (1998b), Topology optimization of plate-like structures using 3-D elasticity and optimum 3-D microstructures, In: Proc 7th AIAA/USAF/NASA/ISSMO Symp on Multidisciplinary Analysis and Optimization, Vol 1, AIAA, 1853-1863.
333. Olhoff N and Taylor J (1983), On structural optimization, J. Appl. Mech. 50, 1134-1151.
334. Olhoff N, Thomsen J, and Rasmussen J (1993), Topology optimization of bi-material structures, In: Pedersen P (ed): Optimal Design with Advanced Materials, Lyngby, Denmark, Amsterdam: Elsevier, 191-206.
335. Ou JS and Kikuchi N (1996a), Optimal design of controlled structures, Struct Optim 11, 19-28.
336. Ou JS and Kikuchi N (1996b), Integrated optimal structural and vibration control design, Struct. Optim. 12, 209-216.
337. Pedersen CBW, Buhl T, and Sigmund O (2000), Topology synthesis of large-displacement complaint mechanisms, Int. J. Num. Meth. En-grg. (to appear).
338. Pedersen CWB, Buhl T, and Sigmund O (1999), Topology synthesis of large-displacement compliant mechanisms, 1999 ASME Design Engineering Tech Conf, Paper No DETC/DAC-8554, Las Vegas, Nov.’99 (to appear)
339. Pedersen NL (2000a), Maximization of eigenvalues using topology optimization, Struct. Multidisc. Optim. 20, 2-11.
340. Pedersen NL (2000b), Topology optimization of AFM probes with constraints on eigenvalues, In: Bloebaum CL (ed): WCSMO-3-Proc Third World Congress of Structural and Multidisciplinary Optimization, May 17-21, 1999, Buffalo NY, CD-Rom, Univ of Buffalo.
341. Pedersen NL (2001), On topology optimization of plates with prestress, Int. J. Num. Meth. Engrg. (to appear).
342. Pedersen P (1989), On optimal orientation of orthotropic materials, Struct. Optim. 1, 101 -106.
343. Pedersen P (1990), Bounds on elastic energy in solids of orthotropic materials, Struct. Optim. 2, 55-63.
344. Pedersen P (1991), On thickness and orientational design with orthotropic materials, Struct Optim, 3, 69-78.
345. Petersson J, Beckers M, and Duysinx P (2000), Almost isotropic perimeters in topology optimization: Theoretical and numerical aspects, In: Bloebaum CL (ed): WCSMO-3-Proc Third World Congress of Structural and Multidisciplinary Optimization, May 17-21, 1999, Buffalo NY, CD-Rom, Univ of Buffalo, NY.
346. Petersson J, and Sigmund O (1998), Slope constrained topology optimization, Int. J. Num. Meths. Eng. 41, 1417-1434.
347. Pettermann H E, Reiter T J, and Rammerstorfer F G (1997), Computational simulation of Internal bone remodeling, Arch. Computat. Methods Eng. 4, 4, 295-323.
348. Poulsen TA (2000), Multi-scale representations in design optimization, In: Bloebaum CL (ed): WCSMO-3—Proc Third World Congress of Structural and Multidisciplinary Optimization, May 17-21, 1999, Buffalo NY, CD-Rom, Univ of Buffalo.
349. Prager W (1974), A note on discretized Michell structures, Comput. Meth. Appl. Mech. Eng. 3, 349-355.
350. Prager W (1976), Transmission optimale des charges par flexion, Anales de l’Institute Technique du Batiment et de Travaux Publics, Serie: Theories et Methodes de Calcul, No 193, 82-91.
351. Querin OM, Steven, GP, and Xie YM (1997a), Improved computational efficiency using bi-directional evolutionary structural optimization (BESO), Abstract for 4th World Congress on Computational Mechanics (held in Argentina).
352. Querin OM, Steven GP, and Xie YM (1997b), Evolutionary structural optimization in 3D elasticity, Proc WCSMO-2, 2nd World Congress on Structural and Multidisciplinary Optimization, Zakopane, Poland, Vol 1, 143-148.
353. Querin OM, Steven GP, and Xie YM (1998), Evolutionary structural optimization (ESO) using a bidirectional algorithm, J. Eng. Comput. 15(8), 1031-1048.
354. Querin OM, Steven GP, and Xie YM (2001), Advances in evolutionary structural optimization: 1992-2000, In: Rozvany GIN, Olhoff N (eds): Topology Optimization of Structures and Composite Continua, NATO ARW, Budapest, Hungary, May 8-12, 2000, Kluwer Academic Publishers, Dordrecht, The Netherlands (to appear).
355. Ramm E, Bletzinger K-U, Reitinger R, and Maute K (1994), The challenge of structural optimization, In: Topping, BHV, Papadrakis M (eds): Advances in Structural Optimization, CIVIL-COMP Ltd, Edinburgh/UK, 27-57.
356. Reinhardt HJ, Seiffarth F, and Hao DN (1993), Approximate solutions of III-posed Cauchy problems for parabolic differential equations, In: Anger G (ed): Inverse Problems: Principles and Applications in Geophysics, Technology and Medicine, 284-298.
357. Reissner E (1965), On a variational theorem for finite elastic deformations, In: Truesdell C, Continuum Mechanics of Non Linear Elasticity, New York: Gordon and Breach, 103-109.
358. Reiter TJ (1993), Topologieoptimierung mittels eines bilogischen Wachstumsalgorithmus, ZAMM 73(7/8).
359. Reiter TJ (1995), Knochen-eine selbstoptimierende Struktur? In: Kull U, Ramm E, and Reiner R, Evolution und Optimierung, Stuttgart, S Hirzel, 121-135.
360. Reiter TJ and Rammerstorfer FG (1993), Simulation of natural adaptation of bone material and application in optimum composite design, In: Pedersen P. (ed): Optimal Design with Advanced Materials, Amsterdam, London: Elesevier, 25-36.
361. Rodrigues H, Guedes JM, and Bendsoe MP (2000), Hierarchical optimization of material and structure, In: Bloebaum CL (ed), WCSMO-3—Proc Third World Congress of Structural and Multidisciplinary Optimization, May 17-21, 1999, Buffalo NY, CD-Rom, Univ of Buffalo.
362. Rodrigues H, Miranda PS, and Guedes JM (2001), Optimization of porous coating distribution of noncemented hip prothesis, In: Roz-vany GIN and Olhoff N (eds.), Topology Optimization of Structures and Composite Continua, NATO ARW, Budapest, Hungary, May 8-12, 2000, Kluwer Academic Publ, Dordrecht, The Netherlands (to appear).
363. Rodrigues H, Soto CA, and Taylor JE (1999), A design model to predict optimal two-material composite structures, Struct Optim 177, 186-198.
364. Rodriguez(-Velasquez) J and Seireg A (1988), A geometric rule-based methodology for shape synthesis: 2-D cases, In: Proc 1988 ASME Int Computers in Engineering Conf and Exposition, San Francisco, CA, Vol 2, 35-41.
365. Rosen DW and Grosse IR (1992), A feature based shape optimization technique for the configuration and parametric design of flat plates, Eng. Comp. 8, 81-91.
366. Rossow HP and Taylor JE (1973), A finite element method for the optimal design of variable thickness sheets, AIAA J, 11, 1566-1569.
367. Rovati M and Taliercio A (1991), Optimal orientation of the symmetry axes of orthotropic 3D-materials, In: Eschenauer HA, Mattheck C, and Olhoff N (eds): Engineering Optimization in Design Processes, Berlin, Heidelberg, New York: Springer, 127-134.
368. Rozvany GIN, Bendsoe MP, and Kirsch U (1995), Layout Optimization of Structures, Appl. Mech. Rev. 48, 41-119.
369. Rozvany GIN and Prager W (1976), Optimal design of partially discretized grillages, J. Mech. Phys. Solids 24, 125-136.
370. Rozvany GIN, Zhou M, and Birker T (1992), Generalized shpae optimization without homogenization, Struct. Optim. 4, 250-252.
371. Rozvany GIN, Zhou M, Birker T, and Sigmund O (1993), Topology optimization using interactive continuum-type optimality criteria (COC) methods for discretized systems, In: Bendsoe MP and Mota Soares CA (eds): Topology Design of Structures, Dordrecht: Kluwer Academic Publishers.
372. Rozvany GIN, Zhou M, Rotthaus M, Gollub W, and Spengemann F (1989), Continuum-type optimality criteria methods for large finite element systems with displacement constraints, Parts I and II, Struct. Optim. 1, 47-72.
373. Sankaranaryanan S, Haftka RT, and Kampania RK (1993), Truss topology optimization with stress and displacement constraints, In: Bendsoe MP, and Mota Soares CA (eds): Topology Design of Structures, Dordrecht: Kluwer Academic Publ, 71-78.
374. Schmit LA and Mallet RH (1963), Structural syntheses and design parameters, In: Hierarchy Journal of the Structural Division, Proc of ASCE, Vol 89, No 4, 269-299.
375. Schwarz S, Maute K, Menrath H, and Ramm E (1997), Adaptive topology optimization including elastoplasticity. In: Gutkowski W, Mroz Z (eds): Proc WCSMO 2—Second World Congress ofStructural and Multidisciplinary Optimization, Inst of Fundamental Technological Research, Warsaw, Vol 2, 569-576.
376. Shonauer M, Kallel L, and Jouve F (1996), Mechanical inclusions identification by evolutionary computation, Revue europeenne des element finis 5(5-6), 619-648.
377. Sienz J and Hinton E (1997), Reliable structural optimization with error estimation, adaptivity and robust sensitivity analysis, J. Comp. Struct. 64, 31-63.
378. Sigmund O (1994b), Materials with prescribed constitutive parameters: An inverse homogenization problem, Int. J. Solids Struct. 31, 2313-2329.
379. Sigmund O (1995), Design of material structures using topology optimization, In: Olhoff N and Rozvany GIN (eds): WCSMO-1—First World Congress of Structural and Multidisciplinary Optimization, Pergamon Press, Oxford/UK.
380. Sigmund O (1997), On the design of compliant mechanisms using topology optimization, J. Mech. Struct. Mach. 25, 493-524.
381. Sigmund O (1998a), Systematic design of electrothermomechanical microactuators using topology optimization, In: Modelling and Simulation of Microsystems, Semiconductors, Sensors and Actuators, MSM98, Santa Clara, CA/USA, 1492-1500.
382. Sigmund O (1998b), Topology optimization in multiphysics problems, In: Proc of 7th AIAA/USAF/NASA/ISSMO Symp on Multidisciplinary Analysis and Optimization, Vol 1, AIAA, 1492-1500.
383. Sigmund O (1999), Topology optimization: A tool for the tailoring of structures and materials, Philosophical Transactions of the Royal Society: Science into the Next Millennium (Issue 2, Mathematics, Physics and Engineering), 211-228.
384. Sigmund O (2000a), Topology optimization of multi-material, multiphysics structures, In: structures using topology optimization, In: Bloebaum CL (ed): WCSMO-3-Proc. Third World Congress of Structural and Multidisciplinary Optimization, May 17-21, 1999, Buffalo NY, CD-Rom, Univ of Buffalo.
385. Sigmund O (2000b), Design of multiphysics actuators using topology optimization, Part I: One-material structures, Part II: Two-material structures, In. J. Num. Meth. Engrg. (to appear).
386. Sigmund O (2000c), A 99 line topology optimization code written in, Matlab. Struct. Multidisc. Optim. (to appear).
387. Sigmund O and Petersson J (1998), Numerical instabilities in topology optimization: A survey on procedures dealing with checkerboards, mesh-dependencies and local minima, Struct. Optim., 16(1), 68-75.
388. Sigmund O and Torquato S (1997), Design of materials with extreme thermal expansion using a three-phase topology optimization method, J. Mech. Phys. Solids 45, 1037-1067.
389. Sigmund O, Torquato S, and Aksay IA (1998), On the design of 1-3 piezocomposites using topology optimization, J. Mat. Res, 13, 1038-1048.
390. Sobieszczanski-Sobieski J (1988), Optimization by decomposition: a step from hierarchic to non-hierarchic systems, Proc 2nd NASA/Air Force Symp on Recent Advances in Multidisciplinary Analysis and Optimization, Hampton VA, Sept. 28-30, 1988.
391. Sobieszczanski-Sobieski J (1989), Multidisciplinary optimization for engineering systems, In: Bergmann HW (ed): Optimization: Methods and Applications, Possibilities and Limitations, Springer, Berlin, Heidelberg, New York, 42-62.
392. Sobieszczanski-Sobieski J, Bloebaum CL, and Hajela P (1988), Sensitivity of control-augmented structure obtained by a system decomposition method, Proc of the IAA/ASME/ASCE/AHS 29th Structures, Structural Dynamics, and Materials Conf, Williamsburg VA, April 18-20, 1988, Paper-No 88-2205.
393. Soto CA and Diaz A (1993a), Layout of plate structures for improved dynamic response using a homogenization method, In: Gilmore B, et al (eds): Advances in Design Automation, Proc of the 1993 ASME DETC, Albuquerque NM, 667-674.
394. Soto CA and Diaz A (1993b), On the modelling of ribbed plates for shape optimization, Struct. Optim. 6, 175-188.
395. Soto CA and Diaz AR (1993c), A model for layout optimization of plate structures. In: Pedersen P (ed): Optimal Design with Advanced Materials, Lyngby, Denmark, Amsterdam: Elsevier, 337-350.
396. Soto CA and Diaz AR (1993d), Optimum layout of plate structures using homogenization, In: Bendsoe MP, Mota Soares CA (eds): Topology Design of Structures, Sesimbra/PORTUGAL, Nato-ASI, Dordrecht: Kluwer Academic Publ, 407-420.
397. Suryatama D and Bernitsas MM (2000), Topology and performance redesign of complex structures by large admissible perturbations, Struct. Multidisc. Optim 20, 138-153.
398. Suzuki K and Kikuchi N (1991), Optimization using the homogenization method: Generalized layout design of three-dimensional shells for car bodies, In: Rozvany GIN (ed): Optimization of Large Structural Systems, NATO-ASI Lecture Notes, 110-126.
399. Swan CC, and Arora JS (1997), Topology design of material layout in structured composites of high stiffness and strength, Struct. Optim. 13, 45-59.
400. Tanaka M, Adachi T, and Tomita Y (1995), Optimum design of lattice continuum material suggested by mechanical adaptation of cancellous bone, In: Olhoff N and Rozvany GIN (eds): WCSMO- I—First World Congress ofStructural and Multidisciplinary Optimization, Pergamon Press, Oxford, UK, 185-192.
401. Taylor JE (1993), A global extremum principle for the analysis of solids composed of softening material, Int. J. Solids. Struct 30(15), 2057-2069.
402. Taylor JE (1998), An energy model for the optimal design of linear continuum structures, Struct. Optim. 16, 116-127.
403. Taylor JE (2000), Addendum to: An energy model for the optimal design of linear continuum structures, Struct. Multidisc. Optim 19, 317-320.
404. Theocaris PS and Stavroulakis GE (1998), Multilevel optimal design of composite structures including materials with negative Poisson’s ratio, Struct. Optim. 15, 8-15.
405. Thierauf G (1996), Optimal topologies of structures: homogenization, pseudo-elastic approximation and the bubble-method, Engineering Computations, Vol 13, No 1, MCB Univ Press, Bradford/UK.
406. Topping BHV and Khan AI (1991), Parallel computations for structural analysis, re-analysis and optimization, Proc of NATO: DFG Advances Study Institute “Optimization of Large Structural Systems,’ Berchtesgaden, Germany, Sept. 23-Oct. 4, 1991.
407. Truesdell C and Noll W (1965), The non-linear field theories of mechanics, In: Fluegge W (ed): Handbuch der Physik III/3, Berlin, Heidelberg, New York: Springer.
408. Truesdell C and Toupin R (1960), The classical field theories, In: Flugge S, Handbuch der Phasik III/I, Berlin-Gottingen-Heidelberg: Springer.
409. Tsai SW and Pagano NJ (1968), Invariant properties of composite materials, In: Tsai SW, Halpin JC, and Pagano MJ (eds.), Composite Materials Workshop, Technomic Publ Stamford CT, 233-255.
410. Wolff J (1870), Uber eine innere Architektur der Knochen und ihre Bedeutung fur die Frage vom Knochenwachstum, Archiv fur die pa-thologische Anatomie und Physiologie und fur klinische Medizin (Vir-chovs Archiv) 50, 389-453.
411. Wolfram S (1983), Statistical mechanics of cellular automata, Rev. Modern Phys. 55, 601-644.
412. Wu CC and Arora JS (1988), Design sensitivity analysis of nonlinear buckling load, J. Computational Mech. 3, 129-140.
413. Xie YM and Steven GP (1993), A simple evolutionary procedure for structural optimization, J. Comput Struct 49(5), 885-896.
414. Yamakawa H, Asakawa Y, and Ukida K (1995), Simultaneous optimization of topology of structural system and control system by using genetic algorithms, In: Olhoff N and Rozvany GIN (eds): WCSMO-1-First World Congress ofStructural and Multidisciplinary Optimization, Pergamon Press, Oxford, UK, 623-628.
415. Yamakawa H and Takagi Y (2000), Some examinations of optimization for topology, shape of structural systems and design of control systems using genetic algorithms, In, Bloebaum CL (ed), WCSMO-3—Proc Third World Congress of Structural and Multidisciplinary Optimization, May 17-21, 1999, Buffalo NY, CD-Rom, Univ of Buffalo.
416. Yang RJ and Chen CJ (1998), Stress-based topology optimization, Struct. Optim. 12, 98-105.
417. Yang RJ and Chuang CH (1994), Optimal topology design using linear programming, J. Comput Struct. 52(2), 265-275.
418. Young V (1998), 3-D bi-directional evolutionary structural optimization (BESO), Proc Australasian Conf on Structural Optimization (held in Sydney), 275-282.
419. Young V, Querin OM, Steven GP, and Xie YM (1999), 3D and multiple load case bi-directional evolutionary structural optimization (BESO), Struct. Optim. 18, 183-192.
420. Yuge K and Kikuchi N (1995), Optimization of a frame structure subjected to a plastic deformation, Struct. Optim. 10, 197-208.
421. Zhao C, Hornby P, Steven GP, and Xie YM (1998), A generalized evolutionary method for numerical topology optimization of structures under static loading conditions, Struct. Optim. 15(3-4), 251-260.
422. Zhao CB, Steven GP, and Xie YM (1996), Evolutionary natural frequency optimization of thin plate bending vibration problems, Struct. Optim. 11, 244-251.
423. Zhao CB, Steven GP, and Xie YM (1997), Evolutionary optimization of maximizing the difference between two natural frequencies of a vibrating structure, Struct. Optim. 13, 148-154.
424. Zhou M and Rozvany GIN (1991), The COC algorithm, Part II: Topological, geometrical and generalized shape optimization, Comput. Meth. Appl. Mechs. Eng. 89, 309-336.
425. Zhou M and Rozvany GIN (2001), On the validity of ESO type methods in topology optimization, Struct. Multidisc. Optim. (to appear).
426. Zhou M, Shyy YK, and Thomas HL (2000), Checkerboard and minimum member size control in topology optimization, In: Bloebaum CL (ed): WCSMO-3—Proc Third World Congress ofStructural and Multidisciplinary Optimization, May 17-21, 1999, Buffalo NY, CD-Rom, Univ of Buffalo.