The solution of multi-parameter systems of equations with application to problems in nonlinear elasticity
Systems of nonlinear equations governed by more than one parameter are discussed with particular attention to bifurcation behaviour. The procedure adopted is to add to the original system of n equations (m-1) further equations, in the case of m parameters, and to seek solution curves in \({\mathbb{R}}^{n+m}\) to this augmented system. Two types of additional equations are considered: one describes a piecewise linear path in the space of parameters, and the second constrains the solution curve to be a locus of singular points. These ideas are all subsequently applied to the systems of equations arising from finite element approximations of boundary value problems in nonlinear elasticity. The behaviour of a nonlinear elastic thick-walled cylinder subjected to internal pressure and axial extension is discussed.
scientific article; zbMATH DE number 3945427
scientific article