Editing Topology optimization (section)

{{short description|Mathematical method for optimizing material layout under given conditions}}

'''Topology optimization''' is a mathematical method that optimizes material layout within a given design space, for a given set of [[Structural load|loads]], [[boundary conditions]] and [[Constraint (mathematics)|constraints]] with the goal of maximizing the performance of the system. Topology optimization is different from [[shape optimization]] and sizing optimization in the sense that the design can attain any shape within the design space, instead of dealing with predefined configurations.

The conventional topology optimization formulation uses a [[finite element method]] (FEM) to evaluate the design performance. The design is optimized using either gradient-based [[mathematical programming]] techniques such as the optimality criteria algorithm and the [[method of moving asymptotes]] or non gradient-based algorithms such as [[genetic algorithms]].

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 [[Engineering design process|design process]]. Due to the free forms that naturally occur, the result is often difficult to manufacture. For that reason the result emerging from topology optimization is often fine-tuned for manufacturability. Adding constraints to the formulation in order to [[design for manufacturability|increase the manufacturability]] is an active field of research. In some cases results from topology optimization can be directly manufactured using [[additive manufacturing]]; topology optimization is thus a key part of [[design for additive manufacturing]].