Application of Scale-Free and Dimensionless Finite Elements

摘要

The finite element method is used to generate highly refined finite elements numerically. These elements are directly applicable to the analysis of general structures or for use in modeling special structures such as stress concentrations. Side-free and dimensionally independent finite elements are developed including general rectangular, triangular, and three-dimensional elements. Recursively generated square composite elements and the four-node quadrilateral element generated from the assembly of four scale-free triangular elements also are developed. Various characteristics of scale-free refined elements and standard finite elements are compared to highlight the relative merits of these elements. Developments used in generating scale-free refined stress concentration elements are described. Also, generation of a refined element for the case of a square shear panel with a central circular hole is illustrated. This refined element is used in a larger structure to illustrate its use and effectiveness. Advantages of the highly-refined stress concentration elements are noted.