This presentation was made at the NAFEMS European Conference on Simulation-Based Optimisation held on the 15th of October in London.

Optimisation has become a key ingredient in many engineering disciplines and has experienced rapid growth in recent years due to innovations in optimisation algorithms and techniques, coupled with developments in computer hardware and software capabilities. The growing popularity of optimisation in engineering applications is driven by ever-increasing competition pressure, where optimised products and processes can offer improved performance and cost-effectiveness which would not be possible using traditional design approaches. However, there are still many hurdles to be overcome before optimisation is used routinely for engineering applications.

The NAFEMS European Conference on Simulation-Based Optimisation brings together practitioners and academics from all relevant disciplines to share their knowledge and experience, and discuss problems and challenges, in order to facilitate further improvements in optimisation techniques.

Resource Abstract

The advent of additive manufacturing (AM) processes at industrial scale have opened new design space possibilities. The increasing maturity of these processes make their widespread adoption in series production imminent, including in safety-critical sectors such as aerospace. A novel generation of structural topology optimization is presented, which includes stochastic distributions of input data to represent real-life variability of material properties and fluctuations in applied forces. A phase field approach is used to describe the distribution of material in order to allow for arbitrary topological changes during the optimization iterations. The state equation is assumed to be a high-dimensional PDE parametrized in a (truncated finite) set of random variables. The current case employs linearized elasticity with a parametric elasticity tensor.



It is of significant industry interest that, instead of an optimization with respect to the ideal material properties and ideal applied load conditions, the designed structures should in particular be robust with respect to unlikely but possibly critical off-design events. For this, as a common risk measure, the Conditional Value at Risk (CVaR), is introduced to the cost functional of the minimization procedure. Industry-relevant examples, based on Monte Carlo sampling for different risk values, are compared with the result of a classical deterministic formulation.



The resulting designs are dependent on the risk parameter of the functional and thus, stochastically optimized designs can be significantly different from those obtained from a deterministic approach. It is shown that a stochastically optimized design has lower and narrower distributions of both mechanical stress across its domain and displacements at its load point(s) under fluctuating loads, as well as higher survivability probabilities during off-design conditions. Since these safety factors are quantified and available to the engineers, they can have confidence in the robustness of their designs.



Including information about real-life variability during optimization represents a step-change in the usability of topology optimization because the final designs’ safety factors are known and can be constrained as needed. Additionally, given a required safety level, it is possible to deduce the required material property quality bounds for manufacturing. Hence, stochastic topology optimization is of particular value for high-performance and safety-critical sectors, including but not limited to high-speed machinery, aerospace, automotive, motorsports, and ceramics. The proposed paper will discuss the stochastic mathematical theory approach, breakthroughs in computational performance of numerical algorithms, as well as case-studies developed with industry partners. In addition, R&D work for introducing additional “Design-for-AM” or “Design-for-Casting” constraints to the above formulation will be presented.



Rafinex is a spin-out company from the Weierstrass Institute for Applied Analysis and Stochastics in Berlin. Its novel algorithms use AI-acceleration to reduce the computational time required for stochastic topology optimization of industrial problem statements from several days to a few hours. This significantly enhances its usability in industry, and Rafinex enables widespread access to its benefits, particularly for small-to-medium enterprises, through its cloud portal where the advanced algorithms, high-performance-computing hardware and human expertise requirements are bundled, ready to be used by everyone.