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Topology optimization


Topology optimization (TO) is a mathematical method that optimizes material layout within a given design space, for a given set of loads, boundary conditions and constraints with the goal of maximising the performance of the system. TO is different from shape optimization in the sense that the design can attain any shape within the design space, instead of dealing with predefined configurations.

The conventional TO formulation uses a finite element method to evaluate the design performance. The design is optimised using nonlinear programming techniques such as the method of moving asymptotes, genetic algorithms, optimality criteria method. Another method of solving TO is the use of level sets, and topological derivatives.

Topology optimization is used by engineers at the concept level of the design process to arrive at a design proposal that is then fine tuned for performance and manufacturability. This replaces time consuming and costly design iterations while improving design performance.

In some cases, results from a topology optimization, although optimised, may be expensive or infeasible to manufacture. These challenges can be overcome through the use of manufacturing constraints in the problem formulation. Using manufacturing constraints, the method yields engineering designs that would satisfy practical manufacturing requirements. In some cases results from topology optimization can be directly manufactured using additive manufacturing.

A topology optimisation problem can be written in the general form of an optimization problem as

subject to

The problem statement includes the following:

Evaluating often includes solving a differential equation. This is most commonly done using the finite element method since these equations do not have a, known, analytical solution.


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