Statics and inverse dynamics solvers based on strain-mode disassembly
Keywords:
disassembly, finite element method, numerical method, fast reanalysisAbstract
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 momellts at nodal joillts 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 alternative finite element assembly of mass and stiffness matrices in the colltext of linear elasticity. Basically, disassembly consists ofrepresentingfinite element matrices as a matrix product where topology contributions are isolated from constitutive law or inertia law contributions. Application examples are discussed to illustrate the advantages and limitations of this formulation using various meshes typically encountered in the automotive and aerospace industries. The second area of application discussed in the second part of this publication is the correlation between finite element models and test data. It is shown that numerical models can be updated for improving their correlation with measured frequency responsefimctions with minimum computational cost when the model is disassembled.
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