O. J. B. Almeida Pereira

A SET OF HYBRID EQUILIBRIUM FINITE ELEMENT MODELS FOR THE ANALYSIS OF THREE-DIMENSIONAL SOLIDS

In this paper an approach to the formulation of equilibrium elements for the analysis of three-dimensional elasticity problems is presented. This formulation is an extension of the approach previously proposed for the analysis of two-dimensional elasticity problems. The general aspects of the formulation remain unchanged when applied to the new problem, but new points are considered, namely the way to perform volume integrations for general elements and the techniques used to obtain the self-equilibrated three-dimensional stress approximation functions. The numerical behaviour of such elements is presented and discussed.

Adaptive methods for hybrid equilibrium finite element models

This paper presents initial results of work directed at the development of practical adaptive methods for equilibrium finite element models of elastostatic problems in solid mechanics. The formulation of hybrid elements is reviewed, with particular emphasis on recent developments for equilibrium elements. Compatibility defaults for 3D and 2D models are proposed, together with an explicit expression for an error indicator based on such defaults. Two further error indicators are defined which are based on the availability of dual conforming displacement solutions. These solutions are derived from two forms of dual analysis. The one may be considered as being in parallel, the other as being sequential with conforming displacements recovered locally from an equilibrium solution. The two latter error indicators provide upper bounds to the global error. A self-adaptive strategy is proposed to exploit any of these error indicators and estimators, and numerical results are presented and compared for a simple plane stress problem.

Direct evaluation of Cauchy-principal-value integrals in boundary elements for infinite and semi-infinite three-dimensional domains

Abstract Algorithms for the direct numerical evaluation of Cauchy-principal-value integrals in three-dimensional problems have recently been implemented. An application of one of these algorithms to infinite boundary elements and to semi-infinite special fundamental solutions is discussed.

Automatic drawing of stress trajectories in plane systems

Abstract An approximate method for plotting the principal stress trajectories in plane systems, using a computer and knowing the stress tensor at every point of a finite element mesh, is described. This method can be used to plot any second-order tensor field in a plane system.