Resumen

MONT'ALVERNE, A.M.; DEUS, E.P.; OLIVEIRA JUNIOR, S.C.  y  MOURA, A.S.. Determination of the reinforced concrete slabs ultimate load using finite element method and mathematical programming. Lat. Am. j. solids struct. [online]. 2012, vol.9, n.1, pp. 69-93. ISSN 1679-7825.  http://dx.doi.org/10.1590/S1679-78252012000100004.

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.

Palabras llave : optimization; Finite Element Method; plates theory; reinforced concrete.