Topology optimization

The conventional topology optimization formulation uses a finite element method (FEM) to evaluate the design performance.

Topology optimization has a wide range of applications in aerospace, mechanical, bio-chemical and civil engineering.

Currently, engineers mostly use topology optimization at the concept level of a design process.

Due to the free forms that naturally occur, the result is often difficult to manufacture.

Adding constraints to the formulation in order to increase the manufacturability is an active field of research.

Large numbers of finite elements increases the attainable topological complexity, but come at a cost.

Secondly, algorithms that can handle a large number (several thousands of elements is not uncommon) of discrete variables with multiple constraints are unavailable.

[2] The earlier stated complexities with solving topology optimization problems using binary variables has caused the community to search for other options.

Gradient based algorithms that handle large amounts of continuous variables and multiple constraints are available.

One of the most implemented interpolation methodologies is the Solid Isotropic Material with Penalisation method (SIMP).

A global measure of the displacements is the strain energy (also called compliance) of the structure under the prescribed boundary conditions.

Although it seemed like this was purely a heuristic approach for a long time, theoretical connections to nonlocal elasticity have been made to support the physical sense of these methods.

[11] Fluid-structure-interaction is a strongly coupled phenomenon and concerns the interaction between a stationary or moving fluid and an elastic structure.

Topology optimisation for fluid structure interaction problems has been studied in e.g. references[12][13][14] and.

Thermoelectricity is a multi-physic problem which concerns the interaction and coupling between electric and thermal energy in semi conducting materials.

Topology optimization combined with 3D printing can result in less weight, improved structural performance and shortened design-to-manufacturing cycle.

Monolithic[22] as well as staggerede approaches,[19][23] which are more common in topology optimization, have been used to create various design with internal contact.

Recently, thermal contact has been included in the TMC topology optmization framework.

Sketch of the well-known wall problem. The objective of the design problem is to minimize the structural compliance.

Design evolution for a fluid-structure-interaction problem from reference. ^{[

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]} The objective of the design problem is to minimize the structural compliance. The fluid-structure-interaction problem is modelled with Navier-Cauchy and Navier-Stokes equations.

A sketch of the design problem. The aim of the design problem is to spatially distribute two materials, Material A and Material B, to maximise a performance measure such as cooling power or electric power output

Design evolution for an off-diagonal thermoelectric generator. The design solution of an optimisation problem solved for electric power output. The performance of the device has been optimised by distributing Skutterudite (yellow) and bismuth telluride (blue) with a density-based topology optimisation methodology. The aim of the optimisation problem is to maximise the electric power output of the thermoelectric generator.

Design evolution for a thermoelectric cooler. The aim of the design problem is to maximise the cooling power of the thermoelectric cooler.

3D Topology Optimization with Internal Contact for a hook mechanism.