An energy balancing strategy for solution of combined geometrical and material nonlinearity problems

Abstract

This paper describes an energy based line-search technique for large displacement and nonlinear stability analysis of planar truss and frame structures which, in addition to geometric non-linearities, simultaneously exhibit nonlinear material behavior. To improve the convergence characteristics of incremental-iterative procedures, a line search seeks a scalar factor which, at fixed load level, scales the displacement vector in such a way that the fundamental energy identity is satisfied. Furthermore, this factor can also be used for guiding the load incrementation. Aiming at computational simplicity and economy, efficient “section-type” beam elements are introduced. Using the total Lagrangian formulation, consideration of geometric nonlinearities yields, however, stiffness matrices which are linear and quadratic functions of the displacements. The material nonlinearity is treated by bilinear laws. The inelastic behavior is defined for several cross sections: thus, by forming the element stiffness matrices for bending the resulting variable stiffness must be accounted for. The effectiveness of the simple solution procedure has been tested using planar truss, beam, and cable-beam-type structures with known analytical and/or alternative solutions. Good agreement with these existing solutions demonstrates the applicability of the proposed method for routine engineering analysis.