Nonlinear finite element analysis of reinforced concrete structures subjected to blast loading
This thesis is concerned with the development of finite element techniques for nonlinear dynamic analysis of planar and axisymmetric reinforced concrete structures subjected to blast loading. The main aspects of numerical modelling process to simulate blast loads, structural geometries and material behaviour are addressed. Major attention has been focused on the development of appropriate history and rate dependent constitutive models for concrete and steel where several material nonlinearities are considered in tension and compression as well as the strain rate effects. Computational algorithms and modified solution procedures have been also developed and coded, which are applied to various structural problems under severe dynamic loading conditions. The basic characteristics of the explosion and blast wave phenomena are presented along with a discussion of the modelling of blast pressures in the free-field due to unconfined and confined explosions. Predictions methods are considered which allow an estimation to be made of the associated internal or external airbiast loads on above-ground structures. The dynamic equilibrium equations for a blast-loaded structure are derived using the principle of virtual work in total Lagrangian approach. The finite element discretization of the equations of motion in space is adopted in accordance with isoparametric formulations. The steel reinforcement is modelled by bar or membrane elements embedded within the basic 8-node isoparametric concrete element. Perfect bond is assumed between steel and surrounding concrete. The integrals, which define the element matrices and vectors are obtained numerically by use of Gaussian quadrature. Hinton's lumping scheme has been employed to generate the lumped mass matrix from the consistent mass matrix for both concrete and steel. The compressive behaviour of concrete is modelled as a strain rate sensitive elasto-viscoplastic material. The onset of viscoplastic behaviour and the softening regime are defined by rate dependent yield and failure surfaces. Based on Kupfer's results, four different functions are developed for the representation of these surfaces in the principal stress space. In the pre-peak range, a history and rate dependent hardening rule is developed to control the expansion of the loading surfaces with the increase of viscoplastic strain. Strain hardening function is derived to fit quasi-static experimental results and is extended for dynamic problems by including the strain rate effects upon the concrete compressive strength and the corresponding strain. In the post-fracture range, the contraction of the loading surface is controlled by a rate dependent softening rule which is described as a function of the post-failure viscoplastic dissipated energy and strain rate until crushing occurs, according to proposed strain controlled crushing conditions. The viscoplastic strain rate is calculated by a rate dependent associated flow rule in which the fluidity parameter is derived as a function of the effective strain rate. In tension, concrete is modelled as a linear elastic strain softening material where crack initiation is controlled by a rate dependent strain criterion. The smeared crack approach is employed to simulate cracks, post-cracking behaviour is governed by an objective nonlinear softening rule based on concrete fracture energy and crack characteristic length. Shear transfer across the cracks is considered by a suitable simple model. The strain rate-induced anisotropy is introduced by employing different rate sensitivity functions for tension and compression. Steel is modelled as a uniaxial strain rate dependent elasto-viscoplastic material in tension and compression in which the yield stress and the fluidity parameter are strain rate sensitive. The identification of model parameters of concrete and steel are performed using some standard experimental results. A modified explicit central difference scheme based on the Newmark- method is proposed to advance the nodal displacements, velocities and accelerations in time. Numerical stability has been controlled using appropriate time increments and energy balance check. The details of an explicit Euler scheme for time integration of time rate constitutive equations of concrete and steel are described in which a semi-empirical a prior stability criterion for the definition of time step length is proposed.' To implement the proposed models and schemes, a versatile and comprehensive computer program, FEABRS, has been developed for the finite element linear and nonlinear dynamic analysis of two-dimensional reinforced concrete structures. Using the program, several reinforced concrete structures are analysed and reported in detail, with the results obtained being compared with those from other numerical and experimental sources. A good agreement is obtained and it is shown that many aspects of the structural behaviour can be well presented by the proposed analysis.