Symbolic computations for the solution of inverse/design problems with Maple

Abstract

Symbolic computations during the solution of applied mechanics problems permit the derivation of results of general validity with respect to the parameter(s) used. Here this approach is generalized to the cases when, beyond possible linear equations, nonlinear polynomial equations appear also in the exact/approximate methods used. The cases of three elementary inverse/design torsion problems in classical isotropic elasticity, where the dimensions of the cross-section of the bar should be determined if the torque and the maximum shear stress are known in advance, are used for the illustration of the method, which leads to a polynomial equation with respect to the fundamental unknown variable. The computer algebra system Maple V and the Gröbner bases method are used for the derivation of the present results. Finally, several serious factors influencing the computations in the present method, which generally requires a large amount of symbolic computations, are considered in some detail.