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Latin American Journal of Solids and Structures
On-line version ISSN 1679-7825
MONT'ALVERNE, A.M.; DEUS, E.P.; OLIVEIRA JUNIOR, S.C. and 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  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  is used to solve the equilibrium equations at the global level of the structure. The relations of the plasticity theory  are resolved at local level. The return mapping problem in the perfect elasto-plastic analysis is formulated as a problem of mathematical programming . The Feasible Arch Interior Points Algorithm proposed by Herskovits  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  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.