Boundary value problems of holomorphic vector functions and applications to anisotropic elasticity
Authors:
M. Z. Wang and G. P. Yan
Journal:
Quart. Appl. Math. 55 (1997), 231-241
MSC:
Primary 73B40; Secondary 73V35
DOI:
https://doi.org/10.1090/qam/1447576
MathSciNet review:
MR1447576
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Abstract: Using Strohβs formalism, plane problems of anisotropic elasticity are turned into the boundary value problems of holomorphic functions. A general method is presented for solving the boundary value problems. The displacement and the stress boundary value problems of an anisotropic body in an elliptical region are solved.
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D. M. Barnett and J. Lothe, Synthesis of the sextic and the integral formalism for dislocations, Greenβs function and surface waves in anisotropic elastic solids, Phys. Norv. 7, 13β19 (1973)
D. M. Barnett and J. Lothe, An image force theorem for dislocations in anisotropic bicrystals, J. Phys. Fluids 4, 1618β1635 (1974)
D. M. Barnett and J. Lothe, Line force loadings on anisotropic half-spaces and wedges, Phys. Norv. 8, 13β22 (1985)
- D. M. Barnett and J. Lothe, Free surface (Rayleigh) waves in anisotropic elastic half-spaces: the surface impedance method, Proc. Roy. Soc. London Ser. A 402 (1985), no. 1822, 135β152. MR 819916
R. J. Asaro, J. P. Hirth, D. M. Barnett, and J. Lothe, A further synthesis of sextic and integral theories for dislocations and line forces in anisotropic media, Phys. Status Solidi B 60, 261β271 (1973)
P. Chadwick and G. D. Smith, Foundations of the theory of surface waves in anisotropic elastic materials, Adv. Appl. Mech. 17, 303β376 (1977)
H. O. K. Kirchner and J. Lothe, Displacements and tractions along interfaces, Philos. Mag. A 56, 583β594 (1987)
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T. C. T. Ting, Line forces and dislocations in anisotropic elastic composite wedges and spaces, Phys. Status Solidi B 146, 81β90 (1988)
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Qianqian Li and T. C. T. Ting, Line inclusions in anisotropic elastic solids, J. Appl. Mech. 56, 556β563 (1989)
Jianmin Qu and Qianqian Li, Interfacial dislocation and its application to interface crack in anisotropic materials, J. Elasticity 26, 169β195 (1991)
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T. C. T. Ting and M. Z. Wang, Generalized Stroh formalism for anisotropic elasticity for general boundary conditions, Acta Mech. Sinica 8, 193β207 (1992)
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S. G. Lekhnitskii, Anisotropic Plate, Gordon and Breach Science Publishers, 1968
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J. D. Eshelby, W. T. Read, and W. Shockley, Anisotropic elasticity with applications to dislocation theory, Acta Metallurgica 1, 251β259 (1953)
A. N. Stroh, Dislocations and cracks in anisotropic elasticity, Philos. Mag. 3, 625β646 (1958)
A. N. Stroh, Steady state problems in anisotropic elasticity, J. Math. Phys. 41, 77β103 (1962)
D. M. Barnett and J. Lothe, Synthesis of the sextic and the integral formalism for dislocations, Greenβs function and surface waves in anisotropic elastic solids, Phys. Norv. 7, 13β19 (1973)
D. M. Barnett and J. Lothe, An image force theorem for dislocations in anisotropic bicrystals, J. Phys. Fluids 4, 1618β1635 (1974)
D. M. Barnett and J. Lothe, Line force loadings on anisotropic half-spaces and wedges, Phys. Norv. 8, 13β22 (1985)
D. M. Barnett and J. Lothe, Free surface (Rayleigh) waves in anisotropic elastic half-spaces: The surface impedance method, Proc. Royal Soc. London Ser. A 402, 135β152 (1985)
R. J. Asaro, J. P. Hirth, D. M. Barnett, and J. Lothe, A further synthesis of sextic and integral theories for dislocations and line forces in anisotropic media, Phys. Status Solidi B 60, 261β271 (1973)
P. Chadwick and G. D. Smith, Foundations of the theory of surface waves in anisotropic elastic materials, Adv. Appl. Mech. 17, 303β376 (1977)
H. O. K. Kirchner and J. Lothe, Displacements and tractions along interfaces, Philos. Mag. A 56, 583β594 (1987)
T. C. T. Ting, Explicit solution and invariance of the singularities at an interface crack in anisotropic composites, Internat. Solids Structures 22, 965β983 (1986)
T. C. T. Ting, Line forces and dislocations in anisotropic elastic composite wedges and spaces, Phys. Status Solidi B 146, 81β90 (1988)
T. C. T. Ting, The anisotropic elastic wedge under a concentrated couple, Quart. J. Mech. Appl. Math. 41, 562β578 (1988)
R. Chadwick, Wave propagation in transversely isotropic elastic media. I. Homogeneous plane waves. II. Surface waves. III. The special case ${a_s} = 0$ and the inextensible limit, Proc. Roy. Soc. London Ser. A 422, 23β121 (1989)
Chyanbin Hwu and T. C. T. Ting, Two-dimensional problems of the anisotropic elastic solids with an elliptic inclusion, Quart. J. Mech. Appl. Math. 42, 553β572 (1989)
Qianqian Li and T. C. T. Ting, Line inclusions in anisotropic elastic solids, J. Appl. Mech. 56, 556β563 (1989)
Jianmin Qu and Qianqian Li, Interfacial dislocation and its application to interface crack in anisotropic materials, J. Elasticity 26, 169β195 (1991)
Zhigang Suo, Singularities, interfaces and cracks in dissimilar anisotropic media, Proc. Roy. Soc. London Ser. A 427, 331β358 (1991)
T. C. T. Ting, Some identities and the structure of ${N_i}$ in the Stroh formalism of anisotropic elasticity, Quart. Appl. Math. 46, 109β120 (1988)
T. C. T. Ting, Effects of change of reference coordinates on the stress analyses of anisotropic elastic materials, Internat. J. Solids Structures 18, 139β152 (1982)
T. C. T. Ting and Chyanbin Hwu, Sextic formalism in anisotropic elasticity for almost non-semisimple matrix N, Internat. J. Solids Structures 24, 65β76 (1988)
T. C. T. Ting, On the orthogonal, Hermitian and positive definite properties of the matrices $i{B^{ - 1}}\bar B$ and $- i{A^{ - 1}}\bar A$ in anisotropic elasticity, J. Elasticity 30, 277β284 (1993)
T. C. T. Ting, Barnett-Lothe tensors and their associated tensors for monoclinic materials with the symmetry plane at ${x_3} = 0$, J. Elasticity 27, 143β165 (1992)
T. C. T. Ting and G. P. Yan, The anisotropic elastic solid with an elliptic hole or rigid inclusion, Internat. J. Solids Structures 27, 1879β1894 (1991)
T. C. T. Ting and M. Z. Wang, Generalized Stroh formalism for anisotropic elasticity for general boundary conditions, Acta Mech. Sinica 8, 193β207 (1992)
M. Z. Wang, T. C. T. Ting, and G. P. Yan, The anisotropic elastic semi-infinite strip, Quart. Appl. Math. 51, 283β297 (1993)
S. G. Lekhnitskii, Anisotropic Plate, Gordon and Breach Science Publishers, 1968
N. I. Muskhelishvili, Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff, 1963
H. J. Gao, Stress of holes in anisotropic elastic solids: conformal mapping and boundary perturbation, Quart. J. Mech. Appl. Math. 45, 149β168 (1992)
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Article copyright:
© Copyright 1997
American Mathematical Society