On an approach to numerical solution of stress-strain state problems for nonthin plates and shells

Numerical solution of elastic equilibrium problems for nonthin plates and shells of constant and variable thickness is based on using a curvilinear-mesh method in combination with the Vekua method — reduction of three-dimensional elastic equations to a recurrent sequence of boundary problems in a two-dimensional region. Coefficients of the first and second quadratic forms for a conditional mediane surface are calculated by means of a metric of boundary faces without any derivatives with respect to their local bases. Specific examples of numerical solution of the test problems for a thick plate bending case, for which the exact and approximate solutions can be also found by other methods, have proven the proposed numerical approach to be efficient (in terms of a rapid convergence and accuracy). A numerical solution has been obtained for a problem of bending for a nonthin plate of constant and variable thickness made of an orthotropic material and for a shell with a circular recess under axial compression.