Two displacement methods for in-plane deformations of orthotropic linear elastic materials

Zeitschrift fur Angewandte Mathematik und Physik

Volumn 52, Issue 5, 2001, Pages 810-822

  Gao, Xin Lin ^a  

^a Michigan Technological University   (United States)

Author keywords

Airy's stress function; Analytic function theory; Displacement formulation; Eigenvalue problems; Green's theorem; Lekhnitskii's method; Orthotropic and anisotropic materials; Partial differential equations; Plane elasticity

Indexed keywords

EID: 0035538121     PISSN: 00442275     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00001575     Document Type: Article

References (13)

1. R. M. Jones, Mechanics of Composite Materials. Hemisphere, New York 1975.
2. S. G. Lekhnitskii, Theory of Elasticity of an Anisotropic Elastic Body. Holden-Day, San Francisco 1963.
3. S. G. Lekhnitskii, Anisotropic Plates. Gordon and Breach, New York 1968.
4. J. D. Eshelby, W. T. Read and W. Shockley, Anisotropic elasticity with applications to dislocation theory, Acta Metall. 1 (1953), 251-259.
5. X.-L. Gao, A mathematical analysis of the elasto-plastic plane stress problem of a power-law material, IMA J. Appl. Math. 60 (1998), 139-149.
6. X.-L. Gao, Alternative derivation of Marguerre's displacement solution in plane isotropic elasticity, ASME J. Appl. Mech. 67 (2000), 419-421.
7. A. E. Green and W. Zerna, Theoretical Elasticity. Oxford University Press, Oxford 1968.
8. P. P. Teodorescu, One hundred years of investigations in the plane problem of the theory of elasticity, Appl. Mech. Rev. 17 (1964), 175-186.
9. P. C. Chou and N. J. Pagano, Elasticity: Tensor, Dyadic, and Engineering Approaches. Van Nostrand, Princeton, New Jersey 1967.
10. X.-L. Gao and S. Mall, Variational solution for a cracked mosaic model of woven fabric composites, Int. J. Solids Struct. 38 (2001), 855-874.
11. Von K. Marguerre, Ebenes und achsensymmetrisches Problem der Elastizitats theorie, ZAMM 13 (1933), 437-438.
12. X.-L Gao, An exact elasto-plastic solution for the plane wedge problem of an elastic linear-hardening material, Math. Mech. Solids 4 (1999), 289-306.
13. R. W. Little, Elasticity. Prentice-Hall, Englewood Cliffs, New Jersey 1973.