A novel approach to elasto-plastic finite element analysis of beam structures using the concept of incremental secant stiffness

This paper presents an incremental secant stiffness formulation for materially non-linear analysis of planar beam structures under monotonically increasing external loads. To describe the elasto-plastic behaviour of a typical beam member, a set of non-dimensional plasticity coefficients are introduced to progressively deteriorate the elastic stiffness properties over an incremental load history. The proposed method is developed to provide the accuracy of distributed plasticity approaches, while maintaining the computational effectiveness of plastic hinge methods. By enforcing individual members to maintain equilibrium during plastic deformation, the spread-of-plasticity effects are automatically taken into account. It should be noted that the element stiffness matrix in present study is explicitly formulated, which renders numerical integrations unnecessary. In order to improve the efficiency of solution process, a direct iteration scheme based on the incremental secant stiffness is proposed as an alternative to the commonly used Newton–Raphson methods. The solution procedure is found to converge rapidly when casting into an incremental-iterative analysis. The present method has been implemented into a finite element computer program using FORTRAN. Results of numerical examples have demonstrated that the present approach appears to be robust and efficient in predicting the inelastic response of planar beam structures.