Program Shell of Analysis of One-dimensional and Two-dimensional Problems of Nonlinear Elasticity Theory

Abstract

Within the framework of the computer algebra system Maple, an interactive program shell for analysis of nonlinear problems of elasticity has been developed. The set of algorithms of automatic generation of boundary-value problems of equilibrium, both in Cartesian as well as in orthogonal curvilinear coordinate systems, was implemented. The integration of numerical tools embedded in the Maple system with resources of the finite-element modeling environment FlexPDE was realized to perform the numerical analysis of nonlinear partial differential equations. Some model problems demonstrating the main abilities of the program shell to solve direct and inverse problems of nonlinear elasticity theory are presented. The developed system allows, in particular, solving the simplest inverse problems of selecting or determining one scalar characteristic (geometric, material or force parameter) of the system under consideration.