Geometrically nonlinear problem of longitudinal and transverse bending of a sandwich plate with transversally soft core

I. B. Badriev ; M. V. Makarov ; V. N. Paimushin

Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 158 (2016) no. 4, pp. 453-468

Résumé

The problem of determining the stress-strain state a sandwich plate with a transversally soft core in one-dimensional geometrically nonlinear formulation has been considered. It has been assumed that in the right end section the edges of the carrier layers are rigidly clamped and there is no adhesive bond between the core and the support element, and in the left end section the edges of the carrier layers of the plate are hinged on an absolutely stiff in the transverse direction diaphragm glued to the end section of the core, the load is applied in the middle surface of the first carrier layer from the left side. On the basis of the generalized Lagrange principle, a general formulation has been created in the form of an operator equation in the Sobolev space. The properties of the operator have been established, i.e., its pseudo-monotonicity and coercivity.Thus, a theorem on the existence of a solution has been established. A two-layer iterative method has been suggested for solving the problem. Considering additional properties of the operator, i.e., its quasipotentiality and bounded Lipschitz continuity, convergence of the method has been investigated. The variation limits of the iteration parameter ensuring the method convergence have been established. A software package has been developed, with the help of which subsequent numerical experiments for the model problem of longitudinal-transverse bending of a sandwich plate have been carried out. Tabulation of both longitudinal and transverse loads has been carried out. The obtained results show that, in terms of weight perfection, the sandwich plate of an asymmetric structure with unequal thicknesses of the carrier layers is the most rational and equally stressed one under the considered loading.

Détail

Keywords: sandwich plate, transversely soft core, generalized statement, solvability theorem, iterative method, convergence theorem, numerical experiment.