SUMMARYA nonlinear, large deflection, elasto-plastic finite element code (EPSA) has been developed for the analysis of shells C n an acoustic medium subjected to dynamic loadings. The nonlinear equations of shells are discretized with the aid of a finite differencejfinite element method based upon the principle of virtual work. The resulting system of equations contains the nodal displacements as the generalized co-ordinates of the problem. The integration in time of the equations of motion is done explicitly via a central difference scheme.Shell strain-displacement relations are established by a two-dimensional finite difference scheme. The shell constitutive equations are formulated in terms of the shell stress resultants and the shell strains and curvatures. The fluid-structure interaction is accounted for by means of the doubly asymptotic approximation (DAA) expressed in terms of orthogonal fluid expansion functions. The analytically produced results satisfactorily reproduce available experimental data for dynamically loaded shells.
A viscoplastic shell model is formulated that utilizes the shell membrane strains and curvatures as the kinematic variables and the shell stress resultants (membrane forces and moments) as the dynamic variables. The viscoplastic shell model combines the concepts of Perzyna’s viscoplastic constitutive equations with Bieniek’s shell stress resultant formulation. The model is incorporated into the Elastoplastic Shell Analysis code (EPSA) for the analysis of shells in an acoustic medium subjected to dynamic loadings that produce moderately large elastoviscoplastic deformations in the shell. An example is presented to demonstrate the effect of material rate dependence on structural response.
The "EPSA" (Elasto-Plastic Shell Analysis) code has been developed for the analysis of shells in an acoustic medium subjected to dynamic loadings which produce large elasto-plastic deformations in the shell. The analysis includes the modeling of significant internal structures, which produce hard spots on the shell. In addition, the effects of ambient pressure are considered. This report presents the theoretical development for the "EPSA" code and a description of the code itself. A users manual for "EPSA" is planned for the future.
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