Abstract
A method for analyzing the nonlinear dynamic response of deformable solids, subjected to time and space dependent thermal and mechanical loads, is developed. The nonlinearities considered in this analysis are due to the nonlinear character of the strain displacement relations and the equations of motion and to the nonlinear constitutive relations which describe the physical behavior of the material. In this investigation, elastic-plastic relations of the incremental (Prandtl-Reuss) type were chosen for material description. A displacement-type finite element method is applied to reduce the governing partial differential equations to a set of simultaneous nonlinear ordinary differential equations of motion of a lumped mass system connected by three-dimensional elements. These equations are solved by applying a step-by-step numerical technique in conjunction with the constitutive relations. The analysis is specifically applied to plane strain problems. Two plane wave propagation problems and two large deformation problems of shells and beams under blast loading were investigated. Comparison of analytical or experimental results with numerical calculations indicates good agreement.
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