Determination of the reinforced concrete slabs ultimate load using finite element method and mathematical programming

Abstract

In the present paper, the ultimate load of the reinforced concrete slabs [16] is determined using the finite element method and mathematical programming. The acting efforts and displacements in the slab are obtained by a perfect elasto-plastic analysis developed by finite element method. In the perfect elasto-plastic analysis the Newton-Raphson method [20] is used to solve the equilibrium equations at the global level of the structure. The relations of the plasticity theory [18] are resolved at local level. The return mapping problem in the perfect elasto-plastic analysis is formulated as a problem of mathematical programming [12]. The Feasible Arch Interior Points Algorithm proposed by Herskovits [8] is used as a return mapping algorithm in the perfect elasto-plastic analysis. The proposed algorithm uses Newton's method for solving nonlinear equations obtained from the Karush-Kuhn-Tucker conditions [11] of the mathematical programming problem. At the end of this paper, it is analyzed six reinforced concrete slabs and the results are compared with available ones in literature.

Keywords

• optimization
• Finite Element Method
• plates theory
• reinforced concrete