A simple p-adaptive refinement procedure for structural shape optimization

A methodology is developed in this paper to perform adaptive finite element analysis using the p-method. The method is based on the use of local error indicators which measure the error in traction across the elements and residual inside the elements. A refinement procedure is coupled with the error estimator for local polynomial escalation. The method is used to solve problems in two-dimensional elasticity and its performance is examined. The adaptive procedure of this type is very useful in many practical applications where it is necessary to evaluate the response as accurately as possible. The application of the above p-adaptive analysis to the problem of shape optimization of structures is discussed. The benefits of using adaptive analysis for shape optimization are demonstrated in the examples.