Reduced degree displacement functions for instability and nonlinear structural analysis

A procedure for simplifying the derivation of stiffness matrices used in the finite element analysis of instability and nonlinear structural problems is presented. The displacement functions assumed to derive the nonlinear components of element stiffness matrices provide inter-element continuity of displacement derivatives of order one less than appear in the energy functional and therefore comply with established convergence criteria for finite element analysis. For the class of problems discussed, this implies the use of linear polynomial displacement functions, which simplifies the derivation considerably and avoids the need for complex numerical integration. A number of practical examples are discussed to illustrate the effectiveness of this procedure.