Affiliation:
1. Department of Civil Engineering, Architecture and Georesources Instituto Superior Técnico, University of Lisbon Portugal
2. Laboratori de Calcul Numeric (LaCaN), E.T.S. de Ingenieria de Caminos, Canales y Puertos Universitat Politecnica de Catalunya Barcelona Spain
Abstract
AbstractWe present a methodology for the definition of the matrices involved in stress based finite element approximations in three‐dimensional problems. In order to handle the increased complexity of the 3D case, a rotation of the global reference frame is used, which greatly simplifies the expressions involved. This rotation is also applicable to the 2D case. The main focus of this work concerns the matrices used in the implementation of the hybrid equilibrium approach. However, a similar complementary methodology (displacement based) is also presented, allowing for an efficient definition of the matrices required for dual analysis, wherein bounds of the solution error are obtained from pairs of complementary solutions, one compatible and the other equilibrated.
Funder
European Education and Culture Executive Agency
Subject
Applied Mathematics,General Engineering,Numerical Analysis