The difference-based equivalent static load method: an improvement of the ESL method’s nonlinear approximation quality

Abstract Nonlinear dynamic structural optimization is a real challenge, in particular for problems that require the use of explicit solvers, e.g., crash. Here, number design variables typically very limited. A way to overcome this drawback linear auxiliary load cases which are derived from nonlinear analysis results order enable application static response optimization. The equivalent method (ESLM) provides well-defined procedure create such cases. main idea here after selection representative time steps, set loads (ESLs) computed each step resulting displacement field identical respective analysis. Each ESLs defines an case, used crucial point finite element (FE)-model case describes undeformed initial geometry. This can lead insufficient approximation quality system highly problems. To drawback, difference-based extension ESL called DiESL has been developed FE-model deformed geometry at time, and corresponding only leading state subsequent step. Consequently, responses (corresponding step) as accumulated sum previous Furthermore, problem consists not one but n T FE-models where selected steps. Such multi-model (MMO) be solved with commercial FE solvers. It turns out approach leads significant improvement faster convergence optimum when compared standard ESLM. will demonstrated discussed based on test examples.