No abstract

No abstract

SUMMARYThis paper proposes an energy measure of discretization error and examines its use for finite element mesh refinement in the analysis of structural continua.The measure is based on the strain energy contributions by the admissible displacement response modes of an element. A n element energy differential is obtained by separating the energy contribution due to the higher displacement modes. This measure is suitable for use with all element types based on the direct stiffness method.The paper presents results of membrane, plate and shell analyses using the measure. It compares sequences of analysis with successively improved meshes to explore the quality of the measure. It concludes that the element energy difference provides a quantitative measure of the efficiency of a given mesh and a qualitative measure which is useful for selecting further mesh refinements, when necessary.

No abstract

SUMMARYNew requirements for finite element model convergence are defined. It is shown that the presence of constant strain states in an element is not sufficient to guarantee convergence.Numerical tests are proposed to assess convergence, direction of convergence, monotonicity of convergence, convergence rate and monotonicity of convergence rate. The proposed tests are mathematically stronger and more general than existing tests.