Equivalent model construction for a non-linear dynamic system based on an element-wise stiffness evaluation procedure and reduced analysis of the equivalent system

• Published in: Computational mechanics Vol. 60; no. 5; pp. 709 - 724
• Main Authors: Kim, Euiyoung, Cho, Maenghyo
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2017; Springer; Springer Nature B.V
• Subjects: Classical and Continuum Physics; Computational Science and Engineering; Design parameters; Engineering; Equivalence; Finite element method; Formulations; Mathematical models; Matrix methods; Nonlinear analysis; Nonlinear systems; Order parameters; Original Paper; Reduced order models; Stiffness; Theoretical and Applied Mechanics; Structural dynamics; Geometric non-linearities; Reduced-order models; Equivalent model construction; Stiffness evaluation; Material non-linearities
• ISSN: 0178-7675; 1432-0924
• DOI: 10.1007/s00466-017-1435-y

In most non-linear analyses, the construction of a system matrix uses a large amount of computation time, comparable to the computation time required by the solving process. If the process for computing non-linear internal force matrices is substituted with an effective equivalent model that enables the bypass of numerical integrations and assembly processes used in matrix construction, efficiency can be greatly enhanced. A stiffness evaluation procedure (STEP) establishes non-linear internal force models using polynomial formulations of displacements. To efficiently identify an equivalent model, the method has evolved such that it is based on a reduced-order system. The reduction process, however, makes the equivalent model difficult to parameterize, which significantly affects the efficiency of the optimization process. In this paper, therefore, a new STEP, E-STEP, is proposed. Based on the element-wise nature of the finite element model, the stiffness evaluation is carried out element-by-element in the full domain. Since the unit of computation for the stiffness evaluation is restricted by element size, and since the computation is independent, the equivalent model can be constructed efficiently in parallel, even in the full domain. Due to the element-wise nature of the construction procedure, the equivalent E-STEP model is easily characterized by design parameters. Various reduced-order modeling techniques can be applied to the equivalent system in a manner similar to how they are applied in the original system. The reduced-order model based on E-STEP is successfully demonstrated for the dynamic analyses of non-linear structural finite element systems under varying design parameters.