Time integration procedures for finite element analysis of blast-resistant reinforced concrete structures

Abstract

This paper is concerned with solution procedures for the nonlinear dynamic finite element analysis of above-ground reinforced concrete structures under airblast loading conditions. The equations of motion due to airblast loading and airblast-induced ground excitations are derived using the principle of virtual displacements using a total Langrangian approach. The kinematic equations for the spatial discretization of concrete and steel are used in accordance with isoparametric formulations. A modified form of the explicit central difference time integration scheme is proposed for the semi-discretized dynamic equilibrium equations including damping forces defined in explicit terms, to advance the nodal displacements, velocities and accelerations in time. For numerical stability, limiting time steps postulated by previous workers are considered. To limit the effects of discretization errors in the numerical solution, considerations such as energy balance check and control of spurious oscillations are discussed. The Euler explicit integration scheme is adopted for the time rate dependent constitutive equations of contrete and steel to advance viscoplastic strains in time. A priori stability criteria based on theoretical and experimental considerations are derived for the calculation of time increment. A computational algorithm for the explicit schemes is described as part of a comprehensive computer program, FEABRS, for linear and nonlinear dynamic problems. As illustration, the solution of some dynamic problems, a beam and a circular slab, are presented and a comparison is made with results from other sources.