ANALYSIS OF BEAM STRUCTURES WITH NONLINEAR MATERIALS BY TOTAL COMPLEMENTARY ENERGY MINIMIZATION

A new analysis method for straight and continuous beam structures with nonlinear materials is proposed on the basis of the principle of minimum complementary energy and mathematical programming algorithm. The bending moment distribution of a continuous beam structure is expressed in terms of the unknown redundant bending moments acting at the supports and the analysis problem is formulated as an unconstrained total complementary energy minimization problem, Then the redundant bending moments are determined by solving the energy minimization problem with the aid of a sequential quadratic approximation algorithm. In the process of the energy minimization, pre-arranged bending moment-complementary energy relations for the cross-sections of beam elements made of given nonlinear materials are used very effectively for calculations of the total complementary energy and the sensitivities of beam structure. The problem formulation and analysis algorithm of the proposed method are quite simple and applicable for any types of linear and nonlinear material beam problems. The reliability and efficiency of the method are confirmed by comparing the results obtained with those by the finite element method for several statically indeterminate continuous beams with linear and three types of nonlinear materials.