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Stochastic topology optimization for robust design

Stochastic modelling represents real-life variability in loads and material properties. Considering this variability during topology optimization is critically important and enables you to automatically create robust designs that behave safely, even in off-design conditions. Because they are optimized for thousands of real-life loading scenarios at the same time, you can have confidence in your lightweight product designs.

Including load variabilities in particular is critical for obtaining a robust design with topology optimization.

Unlike currently available commercial solutions, Rafinex’s stochastic topology optimization accounts for thousands of real-life conditions simultaneously. It overcomes classical limitations by representing real-life variability in load directions and material properties. Considering all these uncertainty sources at the same time is what makes this next-generation technique so powerful.

Robust designs ready-for-manufacture

High-resolutions meshes are ready-for-manufacturing without manual input

You will generate designs which are proven to be more robust and safer, even in off-design conditions. Additionally, you obtain one single optimized design which meets all your requirements, rather than having to manually combine several design solutions, each individually optimized for one load case only. This saves you months of valuable engineering time. Furthermore, Rafinex’s adaptive meshing is high-resolutions, making the optimized design ready for immediate manufacturing – no time lost doing a manual redesign.

Designs proven to be safer and more robust

Robust, safe and predictable lightweight designs are obtained because uncertainties in applied loads and material properties are considered concurrently. The resulting designs exhibit much lower maximum displacements, von Mises stress and compliance sensitivities – proving your designs to be more robust, safer and more reliable. Stochastic topology optimization not only gives you one single optimal design but also computes quantifiable safety levels, such as survivability probabilities. You obtain optima you can trust.

A reduction in maximum displacement is obtained for designs which are optimized with a stochastic approach. Across all load scenarios the stochastic design has both a lower displacement and narrower variability when compared to the three classically optimized designs. This robustness and predictable behaviour during off-design load scenarios are vital for safe leightweighting.

Robust designs perform their function more reliably in real-life service.

Robust design have consistently lower maximum stress during in-service scenarios.

Reduced maximum von Mises stresses are observed in robust designs. Our robust design not only has the consistently lowest maximum von Mises stress state, but these stress states are predictably contained within a narrower range.

Your lightweight designs can be optimized while you know them to be safe during reallife service conditions.

Finally, robust designs also have lower fluctuations in maximum von Mises stresses across all load conditions, making them safer for fatigue.

Be confident in your designs because you have quantified thier limits and made sure that they are safe – without having to compromise on performance. The robust aircraft bracket, shown above, not only has the best displacement and von Mises stress characteristics, but it also exhibits the lowest mean, and variability of, compliance at the primary load point.

Robust designs exhibit lower mean and variabilites in their key behavioural metrics.

“Stochastically optimized designs are robust, safe and predictable in performing their function.”

Design to your desired risk tolerance

Classically optimized geometries can become unsafe quite quickle during off-design load conditions.

Classical topology optimization, using a deterministic approach to loads and material properties, result in designs which are each optimized for one specific load scenario. These designs can quickly become unsafe when applied loads are off-design.

The Conditional Value at Risk (CVaR) for the von Mises stress, shown to the right, quantifies your design’s weak points and limitations.

Robust designs have consistently lower risk everywhere in their domain. Stochastic topology optimization yields designs which have lower and more uniform Conditional Value at Risk for the von Mises stress, shown here for the worst 10% of load scenarios.
You are free to choose different cut-off percentages for your CVaR to match your design safety philosophy, material failure criteria and product quality control requirements.

Robust designs exhibit very uniform stress distributions across their domains.
Different risk metrics can be used during the stochastic topology optimization.

Conditional Value at Risk indicates the average of a quantity’s most extreme fraction of loading scenarios, such as the worst 10%. This cut-off is freely choosable, so you can set more stringent requirements for the von Mises stress.

The CVaR quantifies your risk and answers questions such as “What happens in the most extreme cases?” allowing to quantify your material property limits and adapt your safety requirements.

Design-for-Manufacturability constraints

Topology optimization has recently become rather synonemous with additive manufacturing. However, despite rapid progress in additive manufacturing process and equipment, classical manufacturing processes still have the upper hand when it comes to unit cost of parts when it comes to mid- to large-sized series production. Hence, Rafinex has developed a range of manufacturability constraints that directly act during the stochastic topology optimization in order to determine designs that are both robust and directly comply with the chosen manufacturing process, such as casting.

Stochastic (bottom) vs. Classical (top) topology optimzations for a cantilever design wihout any manufacturiability constraints (left) and with a castability constraint (right).

Didn’t stochastic topology optimization used to take weeks of computational time?

Indeed, stochastic topology optimization is a computationally demanding technique. However, with recent breakthroughs in numerical methods and high-performance-computing hardware in the cloud, Rafinex is able to perform stochastic topology optimization at an industry-relevant scale within minutes – a task which used to take weeks of computational efforts.