The hybrid-mixed stress model used is based on the direct and independent approximation of the stress and displacement fields in the domain of each element. The displacements on the static boundary, which includes the boundaries shared by two elements, are also approximated independently [1,2]. None of the fundamental relations are locally enforced a priori. All field equations are imposed in a weighted residual form ensuring that the discrete numerical model embodies all the relevant properties of the continuum field it represents.

This finite element formulation is defined as a stress model since the equilibrium conditions on the boundary are used to enforce on average the continuity conditions between elements. From a structural engineering point of view, the main advantage of this numerical model when applied to the analysis of concrete structures is that quasi-equilibrated solutions are locally obtained.

All approximations are defined as linear combinations of complete sets of orthogonal Legendre polynomials [3]. The properties of such functions enable the use of analytical solutions for the integrations involved in the computation of almost all structural matrices. In fact, the use of numerical integration schemes can be avoided except for the computation of the elastic operator, since the behaviour of the material is non-linear.

The constitutive relationship adopted is the Mazars isotropic damage model [4] which is simple to implement and quite convenient to describe damage evolution in structures subjected to monotonically increasing loads.

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 results obtained using other numerical schemes presented in the literature and with some experimental results.

1

JAT Freitas, JP Moitinho de Almeida and EMBR Pereira, "Non-conventional formulations for the finite element method", Computational Mechanics, 23, pp. 488-501, 1999; doi:10.1007/s004660050428

2

LMS Castro, "Wavelets e Séries de Walsh em Elementos Finitos", PhD thesis, Technical University of Lisbon, 1996;

3

EMBR Pereira and JAT Freitas, "Numerical Implementation of a Hybrid-Mixed Finite Element Model for Reissner-Mindlin Plates", Computers and Structures, 74(3), 323-334, 2000; doi:10.1016/S0045-7949(98)00291-0

4

J Mazars, "Application de la mécanique de l'endommagement au comportement non linéaire et à la rupture du béton de structure", PhD thesis, Université Paris 6, 1984;

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