Topology Optimization - Problem Statement

Problem Statement

Mathematically one can pose a generic problem as follows:

subject to:

Design Constraints

Governing Differential Equation

The problem statement includes the following

a. Objective functional : This is the goal of the optimization study which is to be minimised over the selection field. For example, one would want to minimise the compliance of a structure to increase structural stiffness.

b. Design space : Design space is the allowable volume within which the design can exist. Assembly and packaging requirements, human and tool accessibility are some of the factors that need to be considered in identifying this space . With the definition of the design space, regions or components in the model that cannot be modified during the course of the optimisation are considered as non-design regions.

c. The Discrete Selection Field: This is the field over which the discrete optimisation is to be performed. It selects or deselects a point on the design space to further the design objective. By selection it has to take the value and by de-selection it has to take the tvalue .

d. Design constraints: These are design criteria that need to satisfied. These could include material availability constraints, displacement constraints, etc.

e. Governing Differential Equation: This is the one that governs the physics of the structure to be built. For example the elasticity equation in the case of stiff structures would be the governing differential equation.