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

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.