The design optimization capability in LS-OPT is based on response surface methodology and design of experiments. The D-optimality criterion is used to distribute sampling points for effective generalization of the design response. A successive response surface method leads to convergence of the design response, while neural networks update a global approximation that is gradually built up and refined locally during the iterative process. A space filling sampling scheme updates the sampling set by maximizing the minimum distances among new and existing sampling points.
LS-OPT combines multiple disciplines and/or cases to improve a unique design. Multiple criteria can be specified and analysis results can be combined arbitrarily using mathematical expressions.
Response Surface Methodology
Response surface methodology (RSM) is a collection of statistical and mathematical techniques useful for developing, improving and optimizing the design process. RSM encompasses a point selection method which has important applications in the design, development and formulation of new products, as well as in the improvement of existing product designs.
In LS-OPT, RSM is used both in optimization and probabilistic analysis to reduce the number of simulations. In the latter procedure, RSM is also used to distinguish deterministic effects from random ones.
With LS-OPT, you can investigate stochastic effects using Monte Carlo simulation involving either direct finite element analysis or analysis of surrogate models such as RSM or neural networks. As an input distribution, any statistical distribution — normal, uniform, beta, Weibull or user-defined — can be specified. Latin hypercube sampling efficiently implements the input distribution. Histograms and influence plots are available through the postprocessor (Version 2.2).
Instability/Noise/Outlier Investigations (Version 2.2)
Some structural problems may not be well-behaved (i.e., a small change in an input parameter may cause a large change in results).
LS-OPT computes various statistics of the displacement and history data for viewing in the LS-DYNA finite element model postprocessor (LS-PrePost). The methodology differentiates between changes in results due to design variable changes and those due to structural instabilities (buckling) and numerical instabilities (lack of convergence or round-off). By viewing these results in LS-Pre-Post, you can pinpoint the source of instability for any chosen response and address instabilities which adversely affect the predictability of the results.
A trade-off study lets you interactively study the effect of changes in the design constraints on the optimum design. For example, you may want to change the safety factor for maximum stress in a beam to see how this change affects the optimal thickness and displacement of the beam.
For each response, the relative importance of all variables can be viewed on a bar chart together with their confidence intervals. Variables of lesser importance can be removed from the optimization, thereby saving time while having little effect on the final result.