SUMMARYA simple algorithm is developed for adaptive and automatic h refinement of two-dimensional triangular finite element meshes. The algorithm is based on a n element refinement ratio that can be calculated from an a posteriori error indicator. The element subdivision algorithm is robust and recursive. Smooth transition between large and small elements is achieved without significant degradation of the aspect ratio of the elements in the mesh. Several example problems are presented to illustrate the utility of the approach.
SUMMARYThe validity of the Ziekiewicz-Zhu u posteriori error estimator for elasticity problems involving more than one material is examined. A simple modification to the estimation process is suggested to obtain acceptable error indicators and error estimator values for problems involving multiple materials.
SUMMARYClosed form expressions for the stiffness matrix and a simple error estimator and error indicator are derived for plane straight sided triangular finite elements in elasticity problems. The calculation of the error estimator is performed on an element by element basis, and is found to be very accurate and efficient. In general, the solutions for benchmark problems using the error indicators for selective refinement of the regions show accelerated convergence when compared to the convergence rate of solutions using uniform mesh refinement. Evaluation of the stiffness matrices and error estimators using explicit formulations is found to be several times faster than numerical integration.
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