Damage analysis of concrete structures using polynomial wavelets

Abstract

This paper presents and discusses a hybrid-mixed stress finite element model based on the use of polynomial wavelets for the physically non-linear analysis of concrete structures. The effective stress and the displacement fields in the domain of each element and the displacements on the static boundary are independently approximated. As none of the fundamental equations is locally enforced a priori, the hybrid-mixed stress formulation enables the use of a wide range of functions. In the numerical model reported here, all approximations are defined using complete sets of polynomial wavelets. These bases present some important features. In one hand, the functions are orthogonal, which is an important issue when implementing hybrid-mixed stress elements as it ensures high levels of sparsity. On the other hand, the polynomial wavelet basis is defined through linear combinations of Legendre polynomials. This fact enables the use of closed-form solutions for the computation of the integrations involved in the definition of all linear structural operators. A simple isotropic damage model is adopted and a non-local integral formulation where the strain energy release rate is taken as the non-local variable is considered. The numerical model is both incremental and iterative and is solved with a modified Newton–Raphson method that uses the secant matrix. Classical benchmark tests are chosen to illustrate the use of the model under discussion and to assess its numerical performance.