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An adaptive mesh refinement procedure is used in static plate bending finite element analysis to study the edge effects in Mindlin—Reissner plates.

The concepts of solution error and optimal mesh in adaptive finite element analysis are revisited. It is shown that the correct evaluation of the convergence rate of the error norms involved in the error measure and the optimal mesh criteria chosen are essential to avoid oscillations in the refinement process. Two mesh optimality criteria based on: (a) the equal distribution of global error, and (b) the specific error over the elements are studied and compared in detail through some examples of application.

Gives a bibliographical review of the error estimates and adaptive finite element methods from the theoretical as well as the application point of view. The bibliography at the end contains 2,177 references to papers, conference proceedings and theses/dissertations dealing with the subjects that were published in 1990‐2000.

The goal of structural optimization is to find the best possible configuration that minimizes the objective function and satisfies a set of constraints. Here we present a method based on the evolutionary structural optimization method, where the quality of the solution is improved by avoiding the chain‐like sets of elements which are sources of potential kinematic instabilities, and by including local error estimators. Both of these enhancements are employed to activate refining the mesh so as to obtain accurate and stable solutions as the volume removal proceeds. Several related contributions of Professor E. Hinton are cited.