Abstract
ABSTRACT The finite element method is widely used in design engineering for modeling and analyzing structural systems. Two approaches have been developed: the force-based method that exploits the equilibrium of forces and moments at nodal joints of the mesh to formulate the assembly of element-level matrices into master mass and stiffness matrices and its dual counterpart, the flexibility-based method. An alternative formulation of stiffness-based finite element assembly is proposed that decomposes element-level matrices even further into strain mode contributions. This decomposition (referred to as finite element disassembly here) allows the derivation of an efficient numerical solver. It is shown that a single matrix factorization is required for analyzing all models characterized by the same topology. This makes finite element disassembly and the associated inverse solver ideal in cases where multiple design analyzes are performed. In the first part, this publication derives a framework for an alternat...
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