Wave Propagation in Viscoelastic and Poroelastic Continua: A Boundary Element Approach

Lecture Notes in Applied and Computational Mechanics

Volumn 2, Issue , 2001, Pages

  Schanz, Martin ^a  

^a TECHNICAL UNIVERSITY OF BRAUNSCHWEIG   (Germany)

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EID: 10044236155     PISSN: 16137736     EISSN: None     Source Type: Book Series    
DOI: None     Document Type: Article

References (192)

1. Ablowitz, M.J.; Fokas, A.S.: Complex Variables: Introduction and Applications. Cambridge Texts in Applied Mathematics. Cambridge University Press, Cambridge, 1997.
2. Achenbach, J.D.: Wave Propagation in Elastic Solids. North Holland, 1980.
3. Ahmad, S.; Manolis, G.D.: Dynamic Analysis of 3-D Structures by a Transformed Boundary Element Method. Computational Mechanics, 2,185-196, 1987.
4. Antes, H.: A Boundary Element Procedure for Transient Wave Propagations in Twodimensional Isotropic Elastic Media. Finite Elements in Analysis and Design, 1, 313-322,1985.
5. Antes, H.: Anwendungen der Methode der Randelemente in der Elastodynamik und der Fluiddynamik. Mathematische Methoden in der Technik 9. B. G. Teubner, Stuttgart, 1988.
6. Antes, H.: Static and Dynamic Analysis of Reissner-Mindlin Plates. In Boundary Element Analysis of Plates and Shells. (Beskos, D.E., Ed.), Springer Series in Computational Mechanics, Springer-Verlag, Berlin, Heidelberg, New York, 312-340, 1991.
7. Antes, H.: A Boundary Element Formulation for the Dead Weight Integral in 2-D Elastodynamic BEM. Mechanics Research Communications, 19(4),273-278, 1992.
8. Antes, H.: Fundamental Solution and Integral Equations for Timoshenko Beams. Computers & Structures, (submitted).
9. Antes, H.: On the Completeness of Fundamental Solutions for Harmonic Problems. Engineering Analysis with Boundary Elements, (submitted).
10. Antes, H.; Jäger, M.: On Stability and Efficiency of 3D Acoustic BE Procedures for Moving Noise Sources. In Computational Mechanics, Theory and Applications. (Atluri, S.N.; Yagawa, G.; Cruse, T.A., Eds.), Vol. 2, Heidelberg, Springer-Verlag, 3056-3061, 1995.
11. Antes, H.; Panagiotopoulos, P.D.: The Boundary Integral Approach to Static and Dynamic Contact Problems-Equality and Inequality Methods. Int. Series of Numerical Mathematics 108. Birkhauser, Basel, 1992.
12. Apsel, R.J.; Luco, J.E.: On the Green's Functions for a Layered Half-Space. Part II. Bulletin of the Seismological Society of America, 73(4), 931-951, 1983.
13. Ayres, E: Theory and Problems of Matrices. Schaum's Outline Series. McGraw Hill Book Company, 1962.
14. Badiey, M.; Cheng, A.H.-D.; Mu, Y.: From Geology to Geoacoustics-Evaluation of Biot-Stoll Sound Speed and Attenuation for Shallow Water Acoustics. Journal of the Acoustical Society of America, 103(1), 309-320, 1998.
15. Badmus, T.; Cheng, A.H.-D.; Grilli, S.: A Laplace-Transform Based ThreeDimensional BEM for Poroelasticity. International Journal for Numerical Methods in Engineering, 36(1), 67-85, 1993.
16. Bagley, R.L.; Torvik, PJ.: A Theoretical Basis for the Application of Fractional Calculus to Viscoelasticity. Journal of Rheology, 27(3), 201-210, 1983.
17. Bagley, R.L.; Torvik, PJ.: On the Fractional Calculus Model of Viscoelastic Behaviour. Journal of Rheology, 30(1),133-155,1986.
18. Banerjee, P.K.; Ahmad, S.; Wang, H.C.: Advanced Development of BEM for Elastic and Inelastic Dynamic Analysis of Solids. In Industrial Applications of Boundary Element Methods. (Banerjee, P.K.; Wilson, R.B., Eds.), Developments in Boundary Element Methods, Elsevier, London, 77-117,1989.
19. Banerjee, P.K.; Butterfield, R.: Boundary Element Methods in Geomechanics. In Finite Elements in Geomechanics. (Gudehus, G., Ed.), London, J. Wiley and Sons, 529-570, 1977.
20. Banerjee, P.K.; Butterfield, R.: Boundary Element Methods in Engineering Science. McGraw Hill, London, 1981.
21. Bathe, K.-J.: Finite Element Procedures in Engineering Analysis. Prentice Hall, Englewood Cliffs, NJ, 1982.
22. Benzine, G.; Gamby, D.: Etude des Mouvements Transitoires de Flexion d'une Plaque par la Methode des Equations Integrales de Frontiere. Journal de Mecanique Appliquee, 1(3),451-466, 1982.
23. Beskos, D. E.: Boundary Element Methods in Dynamic Analysis: Part II (1986-1996). Applied Mechanics Review, 50(3), 149-197, 1997.
24. Beskos, D.E.: Boundary Element Methods in Dynamic Analysis. Applied Mechanics Review, 40(1), 1-23, 1987.
25. Beskos, D.E.: Introduction to Boundary Element Methods. In Boundary Element Methods in Mechanics. (Beskos, D.E., Ed.), Mechanics and Mathematical Methods, NorthHolland, Amsterdam, New York, 1-21, 1987.
26. Beskos, D.E.: Dynamic Analysis of Plates. In Boundary Element Analysis of Plates and Shells. (Beskos, D.E., Ed.), Springer Series in Computational Mechanics, SpringerVerlag, Berlin, Heidelberg, New York, 35-92, 1991.
27. Bettess, P.: Infinite Elements. Penshaw Press, 1992.
28. Biot, M. A: General Theory of Three-Dimensional Consolidation. Journal of Applied Physics, 12,155-164,1941.
29. Biot, M. A: Theory of Elasticity and Consolidation for a Porous Anisotropic Solid. Journal of Applied Physics, 26, 182-185, 1955.
30. Biot, M.A.: Theory of Deformation of a Porous Viscoelastic Anisotropic Solid. Journal of Applied Physics, 27(5), 459-467, 1956.
31. Biot, M.A.: Theory of Propagation of Elastic Waves in a Fluid-Saturated Porous Solid.I. Low-Frequency Range. Journal of the Acoustical Society of America, 28(2), 168-178, 1956.
32. Biot, M. A: Theory of Propagation of Elastic Waves in a Fluid-Saturated Porous Solid. II. Higher Frequency Range. Journal of the Acoustical Society of America, 28(2), 179-191,1956.
33. Birgisson, B.; Siebrits, E.; Peirce, AP.: Elastodynamic Direct Boundary Element Methods with Enhanced Numerical Stability Properties. International Journal for Numerical Methods in Engineering, 46, 871-888,1999.
34. Boltzmann, L.: Zur Theorie der elastischen Nachwirkungen. Sitzungsbericht der Akademie der Wissenschaften (Wien): Mathematisch-Naturwissenschaftlichen Klasse, 70(2),275-300,1874.
35. Bonnet, G.: Basic Singular Solutions for a Poroelastic Medium in the Dynamic Range. Journal of the Acoustical Society of America, 82(5), 1758-1762, 1987.
36. Bonnet, G.; Auriault, J.-L.: Dynamics of Saturated and Deformable Porous Media: Homogenization Theory and Determination of the Solid-Liquid Coupling Coefficients. In Physics of Finely Divided Matter. (Boccara, N.; Daoud, M., Eds.), Springer Verlag, Berlin, 306-316,1985.
37. Bonnet, M.: Shape Differentiation of Regularized BIE: Application to 3D Crack Analysis by the Virtual Crack Extension Approach. In Boundary Elements in Mechanical and Electrical Engineering. (Brebbia, c.A.; Chaudouet, A, Eds.), Springer-Verlag, 1990.
38. Bonnet, M.: On the Use of Geometrical Symmetry in the Boundary Element Method for 3D Elasticity. In Boundary Element Technology VI. (Brebbia, C.A., Ed.), Southampton, Computational Mechanics Publication, 185-201, 1991.
39. Bowen, R.M.: Theory of Mixtures. In Continuum Physics. (Eringen, A.C., Ed.), Vol. III, Acadenic Press, New York, 1-127, 1976.
40. Brebbia, C.A.; Dominguez, J.: Boundary Element Methods for Potential Problems. Applied Mathematical Modeling, 1,372-378, 1977.
41. Brebbia, C.A.; Telles, J.c.F.; Wrobel, L.C.: Boundary Element Techniques. SpringerVerlag, Berlin, New York, 1984.
42. Bronstein, 1. N.; Semendjajew, K. A.: Taschenbuch der Mathematik. HaITi Deutsch Verlag, Thun, Frankfurt/Main, 21. edition, 1984.
43. Caputo, M.: Vibrations of an Infinite Plate with a Frequency Independent Q. Journal of the Acoustical Society of America, 60(3), 634-639, 1976.
44. Carini, A.; Diligenti, M.; Maier, G.: Boundary Integral Equation Analysis in Linear Viscoelasticity: Variational and Saddle Point Formulations. Computational Mechanics, 8, 87-98, 1991.
45. Chen, J.: Time Domain Fundamental Solution to Biot's Complete Equations of Dynamic Poroelasticity. Part I: Two-Dimensional Solution. International Journal of Solids and Structures, 31(10), 1447-1490, 1994.
46. Chen, 1.: Time Domain Fundamental Solution to Biot's Complete Equations of Dynamic Poroelasticity. Part II: Three-Dimensional Solution. International Journal of Solids and Structures, 31(2), 169-202, 1994.
47. Chen, J.; Dargush, G.F.: Boundary Element Method for Dynamic Poroelastic and Thermoelastic Analysis. International Journal of Solids and Structures, 32(15), 2257-2278, 1995.
48. Cheng, A. H.-D.; Badmus, T.; Beskos, D.E.: Integral Equations for Dynamic Poroelasticity in Frequency Domain with BEM Solution. Journal of Engineering Mechanics ASCE, 117(5),1136-1157, 1991.
49. Cheng, A. H.-D.; Detournay, E.: On Singular Integral Equations and Fundamental Solutions of Poroelasticity. International Journal of Solids and Structures, 35(34-35), 4521-4555, 1998.
50. Cheng, A. H.-D.; Ligget, J.A.: Boundary Integral Equation Method for Linear Porouselasticity with Applications to Fracture Propagation. International Journal for Numerical Methods in Engineering, 20(2), 279-296, 1984.
51. Cheng, A. H.-D.; Ligget, J.A.: Boundary Integral Equation Method for Linear Porouselasticity with Applications to Soil Consilidation. International Journal for Numerical Methods in Engineering, 20(2), 255-278, 1984.
52. Cheng, A. H.-D.; Predeleanu, M.: Transient Boundary Element Formulation for Linear Poroelasticity. Journal of Applied Mathematical Modelling, 11, 285-290, 1987.
53. Cheng, A. H.-D.; Sidauruk, P.; Abousleiman, Y.: Approximate Inversion of the Laplace Transform. The Mathematica Journal, 4(2), 76-82, 1994.
54. Cheng, A.H.-D.; Antes, H.: On Free Space Green's Function for High Order Helmholtz Equations. In Boundary Element Methods: Fundamentals and Applications. (Kobayashi, S.; Nishimura, N., Eds.), Berlin, Springer-Verlag, 67-71, 1991.
55. Christensen, R.M.: Theory of Viscoelasticity. Academic Press, New York, 1971.
56. Coda, H.B.; Venturini, W.S.: Three-Dimensional Transient BEM Analysis. Computers & Structures, 56(5), 751-768, 1995.
57. Creus, GJ.: Viscoelasticity-Basic Theory and Applications to Concrete Structures, Vol. 16, Lecture Notes in Engineering. Springer, Berlin, Heidelberg, 1986.
58. Crump, K. S.: Numerical Inversion of Laplace Transforms Using a Fourier Series Approximation. Journal of the Associationfor Computing Machinery, 23(1), 89-96,1976.
59. Cruse, T.A.: A Direct Formulation and Numerical Solution of the General Transient Elastodynamic Problem, II. Journal of Mathematical Analysis and Applications, 22, 341-355, 1968.
60. Cruse, T.A.: Numerical Solutions in Three-Dimensional Elastostatics. International Journal of Solids and Structures, 5, 1259-1274, 1969.
61. Cruse, T.A.; Rizzo, FJ.: A Direct Formulation and Numerical Solution of the General Transient Elastodynamic Problem, I. Journal of Mathematical Analysis and Applications, 22, 244-259, 1968.
62. de Boer, R.: Theory of Porous Media. Springer-Verlag, Berlin, 2000.
63. de Boer, R.; Ehlers, W.: A Historical Review of the Formulation of Porous Media Theories. Acta Mechanica, 74, 1-8, 1988.
64. de Boer, R.; Ehlers, W.: The Development of the Concept of Effective Stresses. Acta Mechanica, 83, 77-92, 1990.
65. de Boer, R.; Ehlers, w.; Liu, Z.: One-Dimensional Transient Wave Propagation in FluidSaturated Incompressible Porous Media. Archive of Applied Mechanics, 63, 59-72, 1993.
66. de Hoop, A.T.: An Elastodynamic Reciprocity Theorem for Linear, Viscoelastic Media. Applied Scientific Research, 16, 39-45, 1966.
67. de Langre, E.; Axisa, E; Guilbaud, D.: Forced Flexural Vibrations of Beams Using a Time-Stepping Boundary Element Method. In Boundary Elements in Mechanical and Electrical Engineering. (Brebbia, c.A.; Chaudouet-Miranda, A., Eds.), Computational Mechanics Publications, Southampton, 139-150, 1990.
68. Debnath, L.: Integral Transform and their Applications. CRC Press, 1995.
69. Detournay, E.; Cheng A. H.-D.: Fundamentals of Poroelasticity, Vol. II, Comprehensive Rock Engineering: Principles, Practice & Projects, Chapter 5, 113-171. Pergamon Press, 1993.
70. Diebels, S.; Ehlers, W.: Dynamic Analysis of a Fully Saturated Porous Medium Accounting for Geometrical and Material Non-Linearities. International Journal for Numerical Methods in Engineering, 39, 81-97, 1996.
71. Doetsch, G.: Anleitung zum praktischen Gebrauch der Laplace-Transformation und der Z-Transformation. R. Oldenbourg Verlag, Miinchen, Wien, 1967.
72. Dominguez, L: Dynamic Stiffness of Rectangular Foundations. Report no. R78-20, Department of Civil Engineering, MIT, Cambridge MA, 1978.
73. Dominguez, l: Response of Embedded Foundations to Traveling Waves. Report no. R78-24, Department of Civil Engineering, MIT, Cambridge MA, 1978.
74. Dominguez, J.: An Integral Formulation for Dynamic Poroelasticity. Journal of Applied Mechanics, ASME, 58, 588-591, 1991.
75. Dominguez, J.: Boundary Element Approach for Dynamic Poroelastic Problems. International Journal for Numerical Methods in Engineering, 35(2),307-324, 1992.
76. Dominguez, l: Boundary Elements in Dynamics. Computational Mechanics Publication, Southampton, 1993.
77. Drozdov, A.D.: Fractional Differential Models in Finite Viscoelasticity. Acta Mechanica, 124,155-180, 1997.
78. Dubner, H.; Abate, l: Numerical Inversion of Laplace Transforms by Relating them to the Finite Fourier Cosine Transform. Journal of the Association for Computing Machinery, 15(1), 115-123, 1968.
79. Durbin, E: Numerical Inversion of Laplace Transforms: an Efficient Improvement to Dubner and Abate's Method. The Computer Journal, 17(4),371-376, 1974.
80. Ehlers, w.: Porase Medien-ein kontinuumsmechanisches Modell auf der Basis der Mischungstheorie. Forschungsbericht aus dem Fachbereich Bauwesen 47, Universitat-GH Essen, 1989.
81. Ehlers, w.: Compressible, Incompressible and Hybrid Two-phase Models in Porous Media Theories. ASME: AMD-Vol., 158, 25-38,1993.
82. Ehlers, w.: Constitutive Equations for Granular Materials in Geomechanical Context. In Continuum Mechanics in Environmental Sciences and Geophysics. (Hutter, K., Ed.), CISM Courses and Lecture Notes, No. 337, Springer-Verlag, Wien, 313-402, 1993.
83. Ehlers, W.; Kubik, 1.: On Finite Dynamic Equations for Fluid-Saturated Porous Media. Acta Mechanica, 105,101-117,1994.
84. Eringen, A. C.; Suhubi, E. S.: Elastodynamics, Vol. II. Academic Press, New York, San Francisco, London, 1975.
85. Fillunger, P.: Der Auftrieb von Talsperren, Teil I-III. Osterr. Wochenschrift for den offentlichen Baudienst, 532-570, 1913.
86. Fliigge, w.: Viscoelasticity. Springer-Verlag, New York, Heidelberg, Berlin, 1975.
87. Fredholm, I.: Sur une Classe d'Equations Fonctionelles. Acta Mathematica, Sweden, 27,365-390, 1903.
88. Gaul, L.; Klein, P.; Kempfle, S.: Damping Description Involving Fractional Operators. Mechanical Systems and Signal Processing, 5(2), 81-88, 1991.
89. Gaul, L.; Klein, P.; Plenge, M.: Dynamic Boundary Element Analysis of Foundation Slabs on Layered Soil. In Boundary Elements X. (Brebbia, C.A., Ed.), Vol. 4, Southampton, Boston, Computational Mechanics Publications, 29-44, 1988.
90. Gaul, L.; Schanz, M.: BEM Formulation in Time Domain for Viscoelastic Media Based on Analytical Time Integration. In Boundary Elements XIV. (Brebbia, c.A.; Dominguez, I.; Paris, E, Eds.), Vol. II, Southampton, Computational Mechanics Publications, 223-234, 1992.
91. Gaul, L.; Schanz, M.: Dynamics of Viscoelastic Solids Treated by Boundary Element Approaches in Time Domain. European Journal of Mechanics AlSolids, 13(4-suppl.), 43-59, 1994.
92. Gaul, L.; Schanz, M.: A Viscoelastic Boundary Element Formulation in Time Domain. Archives of Mechanics, 46(4), 583-594, 1994.
93. Gaul, L.; Schanz, M.: Boundary Element Calculation of Transient Response of Viscoelastic Solids Based on Inverse Transformation. Meccanica, 32(3),171-178, 1997.
94. Gaul, L.; Schanz, M.: A Comparative Study of Three Boundary Element Approaches to Calculate the Transient Response of Viscoelastic Solids with Unbounded Domains. Computer Methods in Applied Mechanics and Engineering, 179(1-2),111-123,1999.
95. Geers, T.L.: IUTAM Symposium on Computational Methods for Unbounded Domains. Kluwer Academic Publishers, Dodrecht, Boston, London, 1997.
96. Gel'fand, I. M.; Shilov, G. E.: Generalized Functions, Vol. I. Academic Press, New York and London, 1964.
97. Giljohann, D.; Bittner, M.: The Three-Dimensional DtN Finite Element Method for Radiation Problems of the Helmholtz Equation. Journal of Sound and Vibration, 212(3), 383-394, 1998.
98. Graff, K. E: Wave Motion in Elastic Solids. Oxford University Press, 1975.
99. Graffi, D.: Uber den Reziprozitatssatz in der Dynamik elastischer Korper. Ingenieur Archiv, 22, 45-46, 1954.
100. Grag, S.K.; Nafeh, A.H.; Good, A.I.: Compressional Waves in Fluid-Saturated Elastic Porous Media. Journal of Applied Physics, 45, 1968-1974, 1974.
101. Guiggiani, M.; Gigante, A.: A General Algorithm for Multidimensional Cauchy Principal Value Integrals in the Boundary Element Method. Journal of Applied Mechanics, ASME, 57,906--915, 1990.
102. Gurtin, M.E.; Sternberg, E.: On the Linear Theory of Viscoelasticity. Archive for Rational Mechanics and Analysis, 11,291-356, 1962.
103. Hairer, E.; Njijrsett, S.P.; Wanner, G.: Solving Ordinary Differential Equations I: Nonstiff Problems. Springer Series in Computational Mathematics. Springer-Verlag, Berlin Heidelberg, 1987.
104. Hairer, E.; Wanner, G.: Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems. Springer Series in Computational Mathematics. Springer-Verlag, Berlin Heidelberg, 1991.
105. Hormander, L.: Linear Partial Differential Operators. Springer-Verlag, 1963.
106. Ihlenburg, E: Finite Element Analysis of Acoustic Scattering. Applied Mathematical Sciences. Springer-Verlag, New York Berlin Heidelberg, 1998.
107. Jawson, M.A.: Integral Equation Methods in Potential Theory: I. Proceedings of the Royal Society of London, 275(A), 23-32,1963.
108. Jonsson, J.: Comments to "Ground Vibration Generated by a Load Moving Along a Railway Track". Journal of Sound and Vibration, 236(2), 359-366, 2000.
109. Karabalis, D.L.; Rizos, D.C.: An Advanced Direct Time Domain Boundary Element Method for 3-D Elastodynamics. In Boundary Elements xv. (Brebbia, c.A.; Renics, J.J., Eds.), Vol. 2, 347-361, 1993.
110. Karabalis, D.L.; Rizos, D.C.: Dynamic Analysis of 3-D Foundations. In Boundary Element Techniques in Geomechanics. (Manolis, G.D.; Davies, T. G, Eds.), London, Elsevier, 1993.
111. Kausel, E.: Thin-Layer Method: Formulation in the Time Domain. International Journalfor Numerical Methods in Engineering, 37(6), 927-941, 1994.
112. Kellogg, O.D.: Foundations of Potential Theory. Springer-Verlag, Berlin, 1929.
113. Khutoryanski, N.M.; Sosa, H.: Dynamic Representation Formulas and Fundamental Solutions for Piezoelectricity. International Journal of Solids and Structures, 32, 3307-3325,1995.
114. Kim, Y.K.; Kingsbury, H.B.: Dynamic Characterization of Poroelastic Materials. Experimental Mechanics, 19,252-258, 1979.
115. Kobayashi, S.; Kawakami, T.: Application of BE-FE Combined Method to Analysis of Dynamic Interactions Between Structures and Viscoelastic Soil. In Boundary Elements VII. (Brebbia, c.A.; Maier, G., Eds.), Vol. I, Berlin, Heidelberg, Springer, 6-3-6-12, 1985.
116. Kupradze, V.D.: Potential Methods in the Theory of Elasticity. Israel Program for Scientific Translations, Jerusalem, 1965.
117. Lakes, R.S.: Viscoelastic Solids. CRC Press, Boca Raton, London, 1999.
118. Lubich, c.: Convolution Quadrature and Discretized Operational Calculus. I. Numerische Mathematik, 52, 129-145, 1988.
119. Lubich, C.: Convolution Quadrature and Discretized Operational Calculus. II. Numerische Mathematik, 52, 413-425, 1988.
120. Lubich, Ch.: On the Multistep Time Discretization of Linear Initial-Boundary Value Problems and their Boundary Integral Equations. Numerische Mathematik, 67, 365-389,1994.
121. Lubich, Ch.; Schneider, R.: Time Discretization of Parabolic Boundary Integral Equations. Numerische Mathematik, 63, 455-481, 1992.
122. Manolis, G.D.: A Comparative Study on Three Boundary Element Method Approaches to Problems in Elastodynamics. International Journal for Numerical Methods in Engineering, 19,73-91, 1983.
123. Manolis, G.D.; Beskos, D.E.: Dynamic Stress Concentration Studies by Boundary Integrals and Laplace Transform. International Journal for Numerical Methods in Engineering, 17, 573-599, 1981.
124. Manolis, G.D.; Beskos, D.E.: Integral Formulation and Fundamental Solutions of Dynamic Poroelasticity and Thermoelasticity. Acta Mechanica, 76, 89-104, 1989. Errata [125]
125. Manolis, G.D.; Beskos, D.E.: Corrections and Additions to the Paper "Integral Formulation and Fundamental Solutions of Dynamic Poroelasticity and Thermoelasticity". Acta Mechanica, 83, 223-226,1990.
126. Mansur, W. 1.: A Time-Stepping Technique to Solve Wave Propagation Problems Using the Boundary Element Method. Phd thesis, University of Southampton, 1983.
127. Mansur, W; Brebbia, C. A: Transient Elastodynamics Using a Time-Stepping Technique. In Boundary Elements. (Brebbia, C. A; Futagami, T.; Tanaka, M., Eds.), Berlin, Springer-Verlag, 677-698, 1983.
128. Mansur, W.J.; Carrer, J. AM.; Siqueira, E.F.N.: Time Discontinuous Linear Traction Approximation in Time-Domain BEM Scalar Wave Propagation. International Journal for Numerical Methods in Engineering, 42(4), 667-683, 1998.
129. Mantic, Y.: A new Formula for the C-matrix in the Somigliana Identity. Journal of Elasticity, 33, 191-201, 1993.
130. Meyer, O.E.: Zur Theorie der inneren Reibung. Journal fur die reine und angewandte Mathematik, 78, 130-135, 1874.
131. Muskhelishvili, N.L.: Singular Integral Equations. Noordhoff Publishing Co., Groningen, 1953.
132. Muskhelishvili, N.L.: Some Basic Problems of the Mathematical Theory of Elasticity. Noordhoff Publishing Co., Groningen, 1953.
133. Narayanan, G.Y.; Beskos, D.E.: Numerical Pperational Methods for Time-Dependent Linear Problems. International Journal for Numerical Methods in Engineering, 18, 1829-1854, 1982.
134. Nardini, D.; Brebbia, C. A: A New Approach to Free Vibration Analysis Using Boundary Elements. In Boundary Element Methods. (Brebbia, C. A, Ed.), Springer-Verlag, Berlin, 312-326, 1982.
135. Norris, AN.: Dynamic Green's Functions in Anisotropic Piezoelectric, Thermoelastic and Poroelastic Solids. Proceedings of the Royal Society of London, 447(A), 175-188, 1994.
136. Nowacki, W: Dynamic Problems of Thermoelasticity. Nordhoff, Leyden, 1975.
137. Oldham, K. B.; Spanier, J.: The Fractional Calculus, Vol. 111, Mathematics in Science and Engineering. Academic Press, New York, London, 1974.
138. Ortner, N.: Die Fundamentallosung des Timoshenko-und des Boussinesq-Operators. Zeitschrift for angewandte Mathematik und Mechanik, 68(11), 547-553, 1988.
139. Pak, R.Y.S.: Asymmetric Wave Propagation in an Elastic Half-Space by a Method of Potentials. Journal of Applied Mechanics, ASME, 54,121-126, 1987.
140. Paris, F.; Cafias, L.: Boundary Element Method: Fundamentals and Applications. Oxford University Press, Oxford New York Tokyo, 1997.
141. Partridge, P. W; Brebbia, C. A; Wrobel, L.c.: The Dual Reciprocity Boundary Element Method. Computational Mechanics Publication, Southampton, 1992.
142. Peirce, A; Siebrits, E.: Stability Analysis and Design of Time-Stepping Schemes for General Elastodynamic Boundary Element Models. International Journal for Numerical Methods in Engineering, 40(2), 319-342,1997.
143. Pekeris, C.L.: The Seismic Surface Pulse. Proc. of the National American Society, 41, 469-480, 1955.
144. Plona, T.J.: Observation of a Second Bulk Compressional Wave in Porous Medium at Ultrasonic Frequencies. Applied Physics Letters, 36(4), 259-261, 1980.
145. Podlubny, L.: Fractional Differential Equations, Vol. 198, Mathematics in Science and Engineering. Academic Press, San Diego, New York, London, 1999.
146. Providakis, C.P.; Beskos, D.E.: Dynamic Analysis of Beams by the Boundary Element Method. Computers & Structures, 22(6), 957-964, 1986.
147. Rayleigh, WS.: On Waves Propagated Along the Plane Surface of an Elastic Solid. Proceedings of the London mathematical Society, 17,4-11, 1887.
148. Rellich, F.: Uber das asymptotische Verhalten der Losungen von flu + ku = 0 in unendlichen Gebieten. Jahresbericht der deutschen Mathematiker Vereinigung, 53, 57-64, 1943.
149. Richards, 11.; Youn, H.K.: Theory of Distributions: A Non-technical Introduction. Cambridge University Press, 1990.
150. Rizos, D.C.; Karabalis, D.L.: An Advanced Direct Time Domain BEM Formulation for General 3-D E1astodynamic Problems. Computational Mechanics, 15,249-269, 1994.
151. Rizzo, EL: An Integral Equation Approach to Boundary Value Problems of Classical Elastostatics. Quarterly of Applied Mathematics, 25,83-95, 1967.
152. Rossikhin, Y. A; Shitikova, M.Y.: Applications of Fractional Calculus to Dynamic Problems of Linear and Nonlinear Hereditary Mechanics of Solids. Applied Mechanics Review, 50(1), 15-67, 1997.
153. Ryshik, I.M.; Gradstein, I.S.: Summen-, Produkte-und Integraltafeln. VEB Deutscher Verlag der Wissenschaften, Berlin, 1963.
154. Saez, A; Dominguez, L: BEM Analysis of Wave Scattering in Transversely Isotropic So lids. International Journal for Numerical Methods in Engineering, 44, 1283-1300, 1999.
155. Schanz, M.: A Time Domain Boundary Element Formulation Based on a Multistep Time Discretization. In Boundary Elements XIX. (Marchetti, M.; Brebbia, C. A; Aliabadi, M.H., Eds.), Southampton, Computational Mechanics Publications, 767-776, 1997.
156. Schanz, M.: Multistep Time Discretization of Boundary Integral Equations in Dynamics. In Modelling and Simulation Based Engineering. (Atluri, S.N.; O'Donoghue, P.E., Eds.), Vol. I, Palmdale, Tech Science Press, 223-228, 1998.
157. Schanz, M.: A Boundary Element Formulation in Time Domain for Viscoelastic Solids. Communications in Numerical Methods in Engineering, 15,799-809, 1999.
158. Schanz, M.: Boundary Element Calculation of Wave Propagation in 3-d Poroelastic Solids. In Advances in Computational Engineering & Sciences. (Atluri, S.N.; Brust, EW, Eds.), Vol. I, Palmdale, Tech Science Press, 118-123,2000.
159. Schanz, M.: Application of 3-d Boundary Element Formulation to Wave Propagation in Poroelastic Solids. Engineering Analysis with Boundary Elements, (in press).
160. Schanz, M.: Dynamic Poroelasticity Treated by a Time Domain Boundary Element Method. IUTAM Symposium on Advanced Mathematical and Computational Mechanic Aspects of the Boundary Element Method. Kluwer Academic Publishers, (in press).
161. Schanz, M.; Antes, H.: Application of 'Operational Quadrature Methods' in Time Domain Boundary Element Methods. Meccanica, 32(3),179-186, 1997.
162. Schanz, M.; Antes, H.: A New Visco-and Elastodynamic Time Domain Boundary Element Formulation. Computational Mechanics, 20(5), 452---459, 1997.
163. Schanz, M.; Cheng, AH.-D.: Dynamic Analysis of a One-Dimensional Poroviscoelastic Column. Journal of Applied Mechanics, ASME, (in press), 2000.
164. Schanz, M.; Cheng, AH.-D.: Transient Wave Propagation in a One-Dimensional Poroelastic Column. Acta Mechanica, 145, 1-18, 2000.
165. Schanz, M.; Gaul, L.: Implementation of Viscoelastic Behaviour in a Time Domain Boundary Element Formulation. Applied Mechanics Review, 46(11, Part 2), S41-S46, 1993.
166. Schanz, M.; Gaul, L.; Antes, H.: Numerical Damping and Instability of a 3-D BEM Time-Stepping Algorithm. Extended Abstracts of IABEM 93, Braunschweig, 1993.
167. Schanz, M.; Gaul, L.; Wenzel, W; Zastrau, B.: A Boundary Element Formulation for Generalized Viscoelastic Solids in Time Domain. In Boundary Element Topics. (Wendland, W., Ed.), Springer, Heidelberg, 31-50, 1997.
168. Schwartz, L.: Theorie des distributions. Herman, Paris, 1966.
169. Sheng, X.; Jones, C.J.C.; Petyt, M.: Ground Vibration Generated by a Load Moving Along a Railway Track. Journal of Sound and Vibration, 228(1),129-156, 1999.
170. Sim, WL; Kwak, B.M.: Linear Viscoelastic Analysis in Time Domain by Boundary Element Method. Computers & Structures, 29(4), 531-539, 1988.
171. Sommerfeld, A.: Partial Differential Equations in Physics. Academic Press, New York, 1949.
172. Spiegel, M. R.: Laplace Transforms. Schaum's Outline. McGraw-Hill Book Company, Dusseldorf, New-York, 1965.
173. Stakgold L.: Green's Functions and Boundary Value Problems. Pure and Applied Mathematics. John Wiley & Sons, 2nd edition, 1998.
174. Suiker, A. SJ; de Borst, R.; Esveld, E.: Critical Behaviour of a Timoshenko Beam-Half Plane System Under a Moving Load. Archive of Applied Mechanics, 68, 158-168, 1998.
175. Tanaka, M.: New Integral Equation Approach to Viscoelastic Problems, Vol. 3: Computational Aspects, Topics in Boundary Element Research, Chapter 2, 25-35. Springer, Berlin, Heidelberg, 1987.
176. Torvik, PJ.; Bagley, R.L.: Fractional Derivatives in the Description of Damping Materials and Phenomena. In The Role of Damping in Vibration and Noise Control. (Rogers, L.; Simonis, J.e., Eds.), The American Society of Mechanical Engineers, 125-l35, 1987. DE-Vol. 5.
177. Triantafyllidis, Th.: 3-D Time Domain BEM Using a Half-Space Green's Functions. Engineering Analysis with Boundary Elements, 8, 115-124, 1991.
178. Truesdell, e.; Toupin, R. A: The Classical Field Theories. In Handbuch der Physik. (Fliigge, S., Ed.), Vol. IIIIl, Springer-Verlag, Berlin, 226--793, 1960.
179. Vardoulakis, I.; Beskos, D.E.: Dynamic Behavior of Nearly Saturated Porous Media. Mechanics of Composite Materials, 5, 87-108,1986.
180. Vgenopoulou, 1.; Beskos, D.E.: Dynamic Behavior of Saturated Poroviscoelastic Media. Acta Mechanica, 95, 185-195, 1992.
181. von Terzaghi, K.: Die Berechnung der DurchHissigkeit des Tones aus dem Verlauf der hydromechanischen Spannungserscheinungen. Sitzungsbericht der Akademie der Wissenschaften (Wien): Mathematisch-Naturwissenschaftlichen Klasse, 132, 125-138, 1923.
182. Wang, e.y.; Achenbach, J.D.: Three-Dimensional Time-Harmonic Elastodynamic Green's Functions for Anisotropic Solids. Proceedings of the Royal Society of London, 449(A),44l-458, 1995.
183. Wang, e.y.; Achenbach, J.D.; Hirose, S.: Two-Dimensional Time Domain BEM for Scattering of Elastic Waves in Solids of General Anisotropy. International Journal of Solids and Structures, 33(26), 3843-3864, 1996.
184. Wiebe, Th.; Antes, H.: A Time Domain Integral Formulation of Dynamic Poroelasticity. Acta Mechanica, 90,125-137,1991.
185. Wolf, P.; Dabre, G.R.: Time-Domain Boundary Element Method in Viscoelasticity with Application to a Spherical Cavity. Soil Dynamics and Earthquake Engineering, 5, 138-148,1986.
186. Yu, G.; Mansur, W.J.; Carrer, AM.: A Linear e for 2-D Elastodynamic BE Analysis. Computational Mechanics, 24,82-89,1999.
187. Yu, G.; Mansur, W.J.; Carrer, I. AM.; Gong, L.: A Linear e Method Applied to 2D Time Domain BEM. Communications in Numerical Methods in Engineering, 14(12), 1171-1179,1998.
188. Yu, G.; Mansur, W.J.; Carrer, A.M.; Gong, L.: Time Weighting in Time Domain BEM. Engineering Analysis with Boundary Elements, 22(3), 175-181, 1998.
189. Yu, G.; Mansur, w.J.; Carrer, AM.; Gong, L.: Stability of Galerkin and Collocation Time Domain Boundary Element Methods as Applied to the Scalar Wave Equation. Computers & Structures, 74(4), 495-506,2000.
190. Zienkiewicz, O.e.: The Finite Element Method. McGraw-Hill Book Company, 1977.
191. Zienkiewicz, O.C.; Paul, D.K.; Chan, AH.E.: Unconditionally Stable Staggered Solution Procedure for Soil-Pore Fluid Interaction Problems. International Journal for Numerical Methods in Engineering, 26, 1039-1055, 1988.
192. Zienkiewicz, O.C.; Shiomi, T.: Dynamic Behaviour of Saturated Porous Media; The Generalized Biot Formulation and its Numerical Solution. International Journal for Numerical and Analytical Methods in Geomechanics, 8, 71-96,1984.