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A mathematical theory of elastic orthotropic plates in plane strain and axi-symmetric deformations

University of British Columbia

We present an elastic orthotropic plate theory in plane strain and axisym-metric deformations by first developing their uniform asymptotic expansions of the exact solutions for the basic governing boundary value problems. Then, the establishment of the necessary conditions for decaying states, both explicitly and asymptotically, enables us to determine the outer solution without reference to the inner solution and clarify the precise meaning of the well known St.Venant's principle under the circumstances considered here. The possible existence of corner stress singularities was examined by establishing and solving three transcendental governing equations. By developing a generalized Cauchy type singular integral equation for the plane strain deformation and an integral equation of the second kind for the axi-symmetric deformation and taking the corner stress singularities into consideration, we obtained accurate numerical solutions for all canonical boundary value problems which are needed in the asymptotic necessary conditions for decaying states. Finally, the accuracy of the numerical solutions of canonical boundary value problems and the efficiency of the plate theory were confirmed through the applications of solving two physical problems and comparing with the existing results.

Text

2010-08-16

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http://hdl.handle.net/2429/27436

Mathematics

University of British Columbia

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