Dynamic response simulation for reinforced concrete slabs

Present investigation comprises development of a new finite element numerical formulation for nonlinear transient dynamic analysis of reinforced concrete slab structures. Depending on many experimental data, new material constitutive relationships for concrete material have been formulated. A regression analysis of available experimental data in the SPSS-statistical program has been employed for formulating the proposed material finite element models, and the appropriateness of the models are confirmed through the histograms and measured indices of determination. Concrete slab structures were analyzed using eight-node serendipity degenerated plate elements. The constitutive models of the nonlinear materials are introduced to take into account the nonlinear stress–strain relationships of concrete. For studying the stress profile of the concrete slab through its thickness, a layered approach is adopted. Elastic perfectly plastic and strain hardening plasticity approaches have been employed to model the compressive behavior of concrete. Assumptions for strain rate effect were included in dynamic analysis by supposing the dynamic yield function as a function of the strain rate, in addition to be the total plastic strain. The yield condition is formulated in terms of the first two stress invariants. Geometrical nonlinearity was considered in analysis as a mathematical model based on the total lagrangian approach taking into account Von Karman assumptions. Implicit Newmark with corrector–predictor algorithm was used for time integration solution of the equation of the motion for slab structures. An incremental and iterative procedure is adopted to trace the entire response of the structure; a displacement convergence criterion is adopted in the present study. A computer program coded in FORTRAN has been developed and used for the dynamic analysis of reinforced concrete slabs. The numerical results show good agreement with other published studies’ results which include deflections.