Shape optimization of biomorphic ceramics with microstructures by homogenization modeling

Analysis, Modeling and Simulation of Multiscale Problems

Volumn , Issue , 2006, Pages 395-424

  Hoppe, Ronald H W ^a,b   Petrova, Svetozara I ^a,c  

^a UNIVERSITY OF AUGSBURG   (Germany)

^b University of Houston   (United States)

^c BULGARIAN ACADEMY OF SCIENCES   (Bulgaria)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 70449725466     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1007/3-540-35657-6_14     Document Type: Chapter

References (38)

1. G. Allaire. Shape Optimization by the Homogenization Method. Springer, Berlin-Heidelberg-New York, 2002.
2. N. Bakhvalov and G. Panasenko. Averaging Processes in Periodic Media. Nauka, Moscow, 1984.
3. M. P. Bendsøe. Optimization of Structural Topology, Shape, and Material. Springer, Berlin, 1995.
4. M. P. Bendsøe and O. Sigmund. Topology Optimization: Theory, Methods and Applications. Springer, Berlin-Heidelberg-New York, 2003.
5. A. Bensoussan, J. L. Lions, and G. Papanicolaou. Asymptotic Analysis for Periodic Structures. Elsevier, North-Holland, Amsterdam, 1978.
6. R. Blaheta. Displacement decomposition - incomplete factorization preconditioning techniques for linear elasticity problems. Numer. Linear Algebra Appl., 1(2), 107-128, 1994.
7. R. H. Byrd, M. E. Hribar, and J. Nocedal. An interior point algorithm for large scale nonlinear programming. SIAM J. Optim., 9(4), 877-900, 1999.
8. C. Carstensen and S. A. Funken. Averaging technique for FE-a posteriori error control in elasticity. Part I: Conforming FEM. Comput. Methods Appl. Mech. Engrg., 190, 2483-2498, 2001.
9. R. M. Chamberlain, C. Lemaréchal, H. C. Pedersen, and M. J. D. Powell. The watchdog technique for forcing convergence in algorithms for constrained optimization. Math. Progr. Study, 16, 1-17, 1982.
10. M. Elices. Structural Biomaterials. Princeton University Press, 2000.
11. A. S. El-Bakry, R. A. Tapia, T. Tsuchiya, and Y. Zhang. On the formulation and theory of the Newton interior-point method for nonlinear programming. J. Optim. Theory Appl., 89, 507-541, 1996.
12. K. Eriksson, D. Estep, P. Hansbo, and C. Johnson. Introduction to adaptive methods for differential equations. Acta Numerica, 105-158, 1995.
13. A. V. Fiacco and G. P. McCormick. Nonlinear Programming. Sequential Unconstrained Minimization Techniques. John Wiley and Sons, New York, New York, 1968. Republished by SIAM, Philadelphia, Pennsylvania, 1990.
14. K. R. Frisch. The Logarithmic Potential Method of Convex Programming. Memorandum, University Institute of Economics, Oslo, Norway, 1955.
15. A. Forsgren, P. E. Gill, and J. R. Shinnerl. Stability of symmetric ill-conditioned systems arising in interior methods for constrained optimization. SIAM J. Matrix Anal. Appl., 17, 187-211, 1996.
16. A. Forsgren, P. E. Gill, and M. H. Wright. Interior methods for nonlinear optimization. SIAM Review, 44, 525-597, 2002.
17. D. M. Gay, M. L. Overton, and M. H. Wright. A primal-dual interior method for nonconvex nonlinear programming. Advances in Nonlinear Programming, (Y. Yuan, ed.), Kluwer, Dordrecht, Holland, 31-56, 1998.
18. L. J. Gibson, M. F. Ashby. Cellular Solids, Structure, and Properties. Pergamon Press, New York, 1988.
19. P. Greil, T. Lifka, and A. Kaindl. Biomorphic cellular silicon carbide ceramics from wood: I. Processing and microstructure. J. Europ. Ceramic Soc., 18, 1961-1973, 1998.
20. P. Greil, T. Lifka, and A. Kaindl. Biomorphic cellular silicon carbide ceramics from wood: II. Mechanical properties. J. Europ. Ceramic Soc., 18, 1975-1983, 1998.
21. R. H. W. Hoppe, S. I. Petrova, and V. Schulz, Primal-dual Newton-type interior-point method for topology optimization. J. Optim. Theory Appl., 114(3), 545-571, 2002.
22. R. H. W. Hoppe and S. I. Petrova. Optimal shape design in biomimetics based on homogenization and adaptivity. Math. Comput. Simul., 65, 257-272, 2004.
23. R. H. W. Hoppe and S. I. Petrova. Primal-dual Newton interior point methods in shape and topology optimization. Numer. Linear Algebra Appl., 11(5-6), 413-429, 2004.
24. R. H. W. Hoppe and S. I. Petrova. Efficient solvers for 3-D homogenized elasticity model. In J. Dongarra et al., eds., Lect. Notes Comput. Sci., Springer, 3732, 857-863, 2006.
25. K. A. Hudgins, A. K. Dillow, and A. M. Lowman. Biomimetic Materials and Design: Biointerfacial Strategies, Tissue Engineering, and Targeted Drug Delivery. Marcel Dekker, New York, 2002.
26. V. V. Jikov, S. M. Kozlov, and O. A. Oleinik. Homogenization of Differential Operators and Integral Functionals. Springer, 1994.
27. N. Olhoff and J. E. Taylor. On structural optimization. J. Appl. Mech., 50, 1139-1151, 1983.
28. T. Ota, M. Takahashi, T. Hibi, M. Ozawa, S. Suzuki, Y. Hikichi, and H. Suzuki. Biomimetic process for producing SiC wood. J. Amer. Ceram. Soc., 78, 3409-3411, 1995.
29. J. W. Ruge and K. Stüben. Algebraic multigrid (AMG). In S. F. McCormick, ed., Multigrid Methods, Frontiers in Applied Mathematics, volume 5, SIAM, Philadelphia, 1986.
30. E. Sanchez-Palencia, Non-homogeneous Media and Vibration Theory. Lecture Notes in Physics, volume 127, Springer, Berlin-Heidelberg, 1980.
31. J. Sokolowski and J.-P. Zolésio. Introduction to Shape Optimization. Springer Series in Computational Mathematics, volume 16, Springer, 1992.
32. K. Suzuki and N. Kikuchi. A homogenization method for shape and topology optimization. Comput. Meth. Appl. Mech. Engrg., 93, 291-318, 1991.
33. R. J. Vanderbei and D. F. Shanno. An interior-point algorithm for nonconvex nonlinear programming. Comput. Optim. Appl., 13, 231-252, 1999.
34. H. A. Van Der Vorst. Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems. SIAM J. Sci. Stat. Comput., 13, 631-644, 1992.
35. E. Vogli, H. Sieber, P. Greil. Biomorphic SiC-ceramic prepared by Si-gas phase infiltration of wood. J. Europ. Ceramic Soc., 22, 2663-2668, 2002.
36. G. Wittum. On the convergence of multigrid methods with transforming smoothers. Theory with applications to the Navier-Stokes equations. Numer. Math., 57, 15-38, 1989.
37. M. H. Wright. Ill-conditioning and computational error in interior methods for nonlinear programming. SIAM J. Optim., 9, 84-111, 1998.
38. O. C. Zienkiewicz and J. Z. Zhu. A simple error estimator and adaptive procedure for practical engineering analysis. Intern. J. Numer. Methods Engrg., 24, 337-357, 1987.