Refined dynamic theory of multilayer shells and plates. Report 1. Initial hypotheses and relationships of the model

Abstract

The problem of constructing a refined theory of multilayer shells and plates on the basis of hypotheses that account for the effect of inertial forces is formulated. The hypotheses are obtained by integrating equations of motion of a three-dimensional medium for assigned tangential components of the stress tensor of the classical theory of multilayer shells. Relationships of a model of the stress-strain state of the refined dynamic theory are derived in conformity with the hypotheses: the components of the displacement vector and the stress and strain tensors. All components take into account the effect of inertial forces; this distinguishes them from components obtained in cases where the same hypotheses as those for the theory of statics are introduced a priori for construction of refined theories of the dynamics of shells.