The non-conventional finite element model adopted is developed from first-principles of Mechanics, namely, equilibrium, compatibility and constitutive relations [1]. The fundamental principles of Mechanics are imposed in a weighted residual form, assuring that the discrete numerical model embodies all the relevant properties of the continuum model it represents. What caracterises the hybrid-displacement Trefftz model used in this work is the fact that the approximation functions used to model the displacements in the domain are extracted from the solution of the system of differential equations that governs the problem being modelled [2]. In the model presented here, the approximation functions for the displacements are obtained from the differential equation considering a material with linear elastic behavior, but the behavior of the material concrete is nonlinear. While the material's behavior is linear elastic, a pure hybrid-displacement Trefftz formulation is adopted. From the point where concrete assumes a nonlinear behavior, this formulation degenerates into a hybrid displacement formulation.

The local constitutive equation adopted for the concrete is an isotropic damage model with one scalar damage variable [3]. This model is simple to implement and quite convenient to describe damage evolution in structures subjected to tension. Following [3], the present work adopts a nonlocal integral model where the strain energy release rate is adopted as the nonlocal variable.

The numerical model is both incremental and iterative. A set of numerical examples are presented to illustrate and to validate the use of such numerical technique. The performance of the model is assessed by comparison with other numerical techniques presented in the literature and with experimental results.

1

J.A.T. Freitas, J.P.M. Almeida, and E.M.B.R. Pereira. "Non-conventional formulations for the finite element method", Computational Mechanics, 23:488-501, 1999. doi:10.1007/s004660050428

2

C. Cismasiu, "The Hybrid-Trefftz Displacement Element for Static and Dynamic Structural Analysis Problems", PhD thesis, Instituto Superior Técnico, Universidade Técnica de Lisboa, Lisboa, 2000.

3

C. Comi and U. Perego. "Symmetric and non-symmetric non-local damage formulations: an assessment of merits", In European Conference on Computational Mechanics, 2001.

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £135 +P&P)