# LS-OPT - Optimization & Robustness

## Introduction and Optimization (2 days)

LS-OPT is an independent, comprehensive optimization program from LSTC. It is ideal for solving strongly non-linear optimization problems and is thus highly suitable for use in combination with LS-DYNA. However, LS-OPT can also be combined with any other solver. LS-OPT functions on the basis of a special, highly effective response surface method. The program also includes stochastic methods for assessing the robustness of FE models and illustrating dependencies between optimization variables and desired values. Input from the user is supported by a comfortable graphical user interface.

The seminar gives an introduction to the program LS-OPT. General theory aspects of the Response Surface Method are discussed and the possibilities of applying this method in LS-OPT are especially explained. In particular, the application of LS-OPT in combination with non-linear FE solvers will be discussed in more detail. Seminar participants will be given the chance to implement their newly-gained knowledge by working on practice examples.

#### Contents:

• Overview of optimization methods for strongly non-linear problems
• Formulation of an optimality problem (objective function, constraints, design variables, etc.)
• DOE (Design of Experiments)
• Theory of the Response Surface Method (RSM)
• LS-OPT graphical user interface
• Interpretation of approximation errors
• Multidisciplinary Optimization (MDO)
• Sensitivity analysis (ANOVA, Sobol)
• Parameter Identification (all contents of the seminar Parameter Identification with LS-OPT are covered)
• Visualization of optimization results in LS-OPT
• Application examples

## Robust Design (1 day)

In recent years, methods for stochastic analysis and assessing the robustness of FE models have been implemented in LS-OPT. These features allow to answer questions such as:

• What is the probability of a specific failure limit being exceeded?
• Is my solution robust or does a minor alteration to my input variables lead to a completely different result?
• Is the dependence between input variables and the answer (solution) chaotic or predictable?

The aim of this course is to give participants a comprehensive overview of the practical application of stochastic methods and robustness analysis using LS-OPT. Additionally, basic knowledge of statistics and probability will be given and the methods implemented in LS-OPT are discussed.

To attend the module “Robust Design”, prior attendance at the module “Introduction and Optimization” is recommended.

Dates
Dates Duration/days Calendar Registration Referee Language Location Fee
14.02.2024, 09:00 - 17:00 3 days (2+1) Add to calendar Katharina Liebold, Nikolay Lazarov English Stuttgart (GER) 1575 €
15.10.2024, 09:00 - 17:00 3 days (2+1) Add to calendar Registration Katharina Liebold, Nikolay Lazarov English Stuttgart (GER) 1575 €

## Lecturers

### Katharina Liebold

Dipl.-Math.

Area of expertise:
Optimization