AN OBJECT-ORIENTED CLASS ORGANIZATION FOR GLOBAL-LOCAL GENERALIZED FINITE ELEMENT METHOD

Abstract

THIS PAPER SHOWS AND DISCUSSES A GENERIC IMPLEMENTATION OF THE GLOBAL-LOCAL ANALYSIS TOWARD GENERALIZED FINITE ELEMENT METHOD (GFEMGL). THIS IMPLEMENTATION, PERFORMED INTO AN ACADEMIC COMPU-TATIONAL PLATFORM, FOLLOWS THE OBJECT-ORIENTED APPROACH PRESENTED BY THE AUTHORS IN A PREVIOUS WORK FOR THE STANDARD VERSION OF GFEM IN WHICH THE SHAPE FUNCTIONS OF FINITE ELEMENTS ARE HIERARCHICALLY ENRICHED BY ANALYTICAL FUNCTIONS, ACCORDING TO THE PROBLEM BEHAVIOR. IN GLOBAL-LOCAL GFEM, HOWEVER, THE ENRICHMENT FUNCTIONS ARE CONSTRUCTED NUMERICALLY FROM THE SOLUTION OF A LOCAL PROBLEM. THIS STRATEGY ALLOWS THE USE OF A COARSE MESH EVEN WHEN THE PROBLEM PRODUCES COMPLEX STRESS DISTRIBUTIONS. ON THE OTHER HAND, A LOCAL PROBLEM IS DEFINED WHERE THE STRESS FIELD PRESENTS HIGH GRADIENTS AND IT IS DISCRETIZED USING A LARGE NUMBER OF ELEMENTS. THE RESULTS OF THE LOCAL PROBLEM ARE USED TO ENRICH THE GLOBAL PROBLEM WHICH IMPROVES THE APPROXIMATE SOLUTION. THE GREAT ADVANTAGE IS ALLOWING A WELL-REFINED DESCRIPTION OF THE LOCAL PROBLEM, WHEN NECESSARY, AVOIDING AN OVERBURDEN FOR THE COMPUTATION OF THE GLOBAL SOLUTION. DETAILS OF THE IMPLEMENTATION ARE PRESENTED AND IMPORTANT ASPECTS OF USING THIS STRATEGY ARE HIGHLIGHTED IN THE NUMERICAL EXAMPLES.