Simplified method based on the deformation theory for structural limit analysis—I. Theory and formulation

Abstract

Based on the deformation theory of linear hardening materials, a simplified finite element analysis method is proposed to calculate the limit load of structures. Compared with the general elasto-plastic incremental finite element analysis, the proposed method can avoid the incremental iteration of nodal displacements and the constitutive equation integration at each Gauss integral point. Compared with the mathematical programming method combined with finite element analysis, the proposed method shows theoretical simplicity and avoids bringing in complex mathematical theories. It is also easy to put into code. Compared with some current limit analysis methods, such as the GLOSS R-Node method and the elastic compensation method, the present method gives a remarkably accurate estimation of limit loads instead of just a simple lower or upper bound. Numerical examples have demonstrated that it is effective and the computational results are accurate enough to meet the need of engineering practice.