DYNAMIC ANALYSIS OF PLANE STRESS PROBLEMS BY THE HIERARCHICAL FINITE ELEMENT METHOD WITH THE USE OF ERROR INDICATORS FOR SELECTIVE MESH ENRICHMENTS

Resumo

The search for optimized projects has led to the design of leaner and lighter structures, which
are more susceptible to dynamic effects. These must be thoroughly analyzed in order to avoid excessive
displacements, structural damage and to guarantee user comfort. However, the analytic solution of
dynamic problems tends to present great difficulties and, in some cases, cannot be obtained. Therefore,
researchers developed approximated methods. The most used approximated method is the Finite
Element Method (FEM). As a well-established method, the main focus of FEM studies has shifted from
the development of the method to the improvement of its results. In this context two lines of research
have proven to greatly influence the accuracy and efficiency of the method, the study of refinements
and the study of error indicators. Even though refinements improve the accuracy of solutions they can
lead to greater computational efforts and complexity. A way to balance these drawbacks is to combine
them with error indicators. These allow the engineer to specify which mesh elements have greater
influence on the results and apply refinements selectively. The present study focuses on precisely these

characteristics and evaluates the use of the Friberg Error Indicator in the dynamic analyses of two-
dimensional structures as a mean to the application of a selective p-refinement. Numerical examples,

considering plane stress state, are computationally modeled with the use of Lobatto’s hierarchical shape
functions and trigonometrical enrichments. The results of eigenvalues for the enrichment of different
elements are compared with those present in past literature.