To the Solution of Three-Dimensional Problems of Oscillations in the Theory of Elasticity in Thick Plates of Variable Thickness

Abstract

A technique for solving the three-dimensional problem of bending in the theory of elasticity in orthotropic plates of variable thickness is developed in the paper. On the basis of the method of expansion of displacements into an infinite series, the problem has been reduced to the solutions of two independent problems, which are described by two independent systems of two-dimensional infinite equations.

Dynamic methods of spatial calculation of structures based on a plate model

“…This article proposes a method for calculating the structures for seismic resistance on the basis of a continuum plate model developed in the framework of the bimoment theory [8][9][10][11][12][13][14][15][16][17], taking into account the spatial stress-strain state. If to consider the law of nonlinearity of displacements distribution in the cross-sections of the plate, then in addition to tensile and shear forces, bending and torsional moments, there appear the additional force factors, called the bimoments.…”