The Optimization capability in LS-OPT is based on Response Surface Methodology and Design of Experiments. The D-Optimality Criterion is used for the effective distribution of sampling points for effective generalization of the design response. A Successive Response Surface Method allows convergence of the design response. Neural Networks provide an updateable global approximation that is gradually built up and refined locally during the iterative process. A Space Filling sampling scheme is used to update the sampling set by maximizing the minimum distances amongst new and existing sampling points.

LS-OPT allows the combination of multiple disciplines and/­or cases for the improvement of a unique design. Multiple criteria can be specified and analysis results can be combined arbitrarily using C or FORTRAN type 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 (also referred to as Design of Experiments, Approximation methods and Design Optimization to determine optimal settings of the design dimensions. RSM 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, Response Surface Methodology 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 effects.

  • Probabilistic Analysis
  • LS-OPT enables the investigation of stochastic effects using Monte Carlo simulation involving either direct FE Analysis or analysis of surrogate models such as Response Surface Methodology or neural networks. As an input distribution, any of a series of statistical distributions such as Normal, Uniform, Beta, Weibull or User-defined can be specified. Latin Hypercube sampling provides an efficient way of implementing 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 FE 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). Viewing these results in LS-PrePost allows the engineer to pinpoint the source of instability for any chosen response and therefore to address instabilities which adversely affect predictability of the results.

  • Tradeoff
  • A trade­off study enables the designer to interactively study the effect of changes in the design constraints on the optimum design. E.g., the safety factor for maximum stress in a beam is changed and the designer wants to know how this change affects the optimal thickness and displacement of the beam.

  • Variable Screening
  • For each response, the relative importance of all variables can be viewed on a bar chart together with their confidence intervals. This feature enables the user to identify variables of lesser importance that can be removed from the optimization, thereby contributing to time saving while having little effect on the result.

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