High-precision modeling of deformation of laminated structures

Abstract

Precise three-dimensional solutions for homogeneous, two- and three-layer plates of symmetric and nonsymmetric structure over their thickness with orthotropic layers in transverse symmetric and antisymmetric loading normal to the surface of the plates are given. It is shown that the character of stressed states under flexural (antisymmetric) and nonflexural (symmetric transverse compression) loading differs greatly. It is noted that the known refined continual models, which take into account the transverse shear and compression, are all essentially flexural and therefore cannot describe the nonflexural deformations well. In particular, continual shear models in symmetric pressure loading lead to zero solutions. A refined nonflexural continual model of deformation of sandwich plates in bilateral symmetric compression is constructed. The general order of resolving differential equations for continual models does not depend on the number of layers. Approximation functions of the transverse coordinate are obtained with the help of well-founded hypotheses. A high-accuracy variant of the flexural continual model is proposed for antisymmetric loading with account of shear and transverse normal strains, as well as a version combining both models mentioned. A method of precise satisfation of all the constitutive relations for the layers, including the conditions of their contact, is proposed, whereas in the known continual models the dependence between the transverse normal stress and strain is satisfied only integrally, or else the Poisson effect is neglected.