Study of stress-strain state of the transversely isotropic plates using the refined theory

Abstract

The fundamental solution of statics equations of transversely isotropic plate was obtained using the two-dimensional Fourier integral transform and the inversion technic based on the special G-function. Such method allows reducing the system of resolving differential equations, which describe static state of flat plate or shell, to a system of algebraic equations. Then, the inverse Fourier transform restores the fundamental solution. Numerical studies, which were carried out, have detected the behavior patterns of stress-strain state components in dependence on material elastic constants. This approach demonstrates development of refined theory of plates and shells based on the three-dimensional elasticity theory.