Finite element method in determining the destructive load on the perforated shell under short-term forces

Abstract

Stress-strain state of cylindrical shells with periodic system of openings is considered. It is supposed that the shell moves under the influence of short-term intense load. The method of determining destructive loads in case of short-term force effects on a perforated cylindrical shell is proposed. The problem of determining the shell motion is considered in the elastic-plastic formulation. It is supposed that when the equivalent loads are equal to or exceed the yield strength; plastic deformations begin to develop in the elastic body. The zone of plastic deformations is specified at each step of loading. The total deformation is presented as the sum of elastic and plastic components. Elastic deformations are expressed through elastic displacements with Cauchy ratios. Equilibrium conditions are applied in stresses. The elastic component results in to Lamé equations in displacements, unknown plastic stresses take the form of additional loads and are taken into account in the right part of the differential equations of motion. The theories of small elastic-plastic deformations and plastic flows are applied. The law of plastic flow is chosen, a multi-linear or bilinear tensile diagram characterizing the zone of plastic flow is given, and it is assumed that components of plastic deviator deformations are directly proportional to the components of the stress deviator. The finite element method is used to solve the system of differential equations of motion. Spatial 20-nodes finite elements with quadratic approximation of unknown motion inside elements are used. Studying the convergence of the method depending on the number of elements has been performed. The estimation of the moment of the beginning of destruction is obtained.