The AMORE paradigm for finite element analysis. (April 2019) - Bathe, Klaus-Jürgen
Highlights: We review and give insight into a novel paradigm for finite element analysis. The approach enables much easier meshing than is usually performed. The paradigm is focusing on the automatic meshing of any given geometry. The geometry may be given by use of a CAD program or a digitized scan. Effective traditional and new "overlapping" finite elements are used. Abstract: The objective in this paper is to largely review, but also give new insight into, the recent development of a novel paradigm for finite element analysis. The approach enables much easier meshing than usually performed for finite element analysis and then the computationally efficient solution of the finite element model. The important aspects of the paradigm are the automatic meshing on any given geometry (typically given by use of a CAD program or a computerized scan) with the use of overlapping and regular finite elements – hence the acronym AMORE forA utomaticM eshing withO verlapping andR egularE lements. We summarize the basic steps used in the paradigm, give the basic equations to formulate the overlapping elements, discuss specific attributes, give some applications and conjecture on the further development and use of the solution scheme. Our discussion is based on previously published work with a focus on simplifying the formulation of the overlapping elements, providing novel insight, and suggesting a notation. The paradigm has so far only been applied in the linear analyses of solids, however embodies significant potential for general and wide use in computer-aided engineering.