Transforming Calculated Schemes in Geometrically Non-linear Mechanics Problems of the Sandwich Plates with Contour Reinforcing Beams

Abstract

A numerical study of the geometrically nonlinear problem of deforming the cylindrical shape of a sandwich plate with a transversally soft core, supported in the end sections of absolutely rigid bodies, according to transforming calculation schemes as it is loaded, has been carried out. It is shown that such a transformation is necessary after the delamination of the adhesive layer connecting the end section of the core with the contour reinforcing beam, designed to ensure the transfer of external load on the carrier layers. The previously obtained equations were used, which are based on introducing into consideration, as unknown contact forces, the interaction of the outer layers with a core, as well as the external layers and the core with reinforcing bodies at all points of their interface surfaces. The problem under study required the sequential formulation and solving of two problems: on the stress-strain state of the structure until the beginning of the destruction of the adhesive layer between the core and the reinforcing beam and about determining the increments of the parameters of the stress-strain state after delamination. To simulate the delamination process, a method based on the parameter continuation method is proposed. This method provides for zeroing the tangential stresses formed in the adhesive layer at the first loading stage, by choosing the incremental tangent stresses specified above as the loading parameter. Numerical methods for solving the formulated problems were developed. They are based on a preliminary reduction of the initial problems to systems of integro-algebraic equations and the construction of their solutions by the finite sum method. To resolve the geometric nonlinearity, a two-layer iterative process is used.