Non-linear analysis of reinforced concrete cross-sections by non-linear optimisation

摘要

A new approach to the non-linear analysis of cross-sections loaded by normal forces and bending moments is presented in the paper. The mechanical model is based on the LAGRANGE principle of minimum of total potential energy. Deformations and stresses are directly obtained by solving a nonlinear optimisation problem without constraints. The mathematical model is independent of the specifics of material. Thus cracks in concrete, non-linearity of material etc. can be taken into account without basic modification of the numerical algorithm. Numerical solutions of the non-linear optimisation problems can be found by application of standard software. Thus the analysis of reinforced concrete cross-sections or more general composite cross-sections with non-linear behaviour of material is as simple as in the case of linear elasticity. The application of the method is demonstrated for polygonal cross-sections. Pre-stresses or pre-strains can easily be included in the mathematical model.