Topology optimization and boundary elements—a preliminary implementation for linear heat transfer

A design of an optimal shape of domain described by NURBS curves using the topological derivative and boundary element method

“…The idea of the topological derivative is based on determining the sensitivity of a given cost function (total potential energy) when the size of this hole is changed. The local value of the D T is defined as follows [1][2][3][4] K. Freus, S. Freus…”

“…In the opening, the Neumann condition is taken into account. The topological-shape sensitivity method is utilized as a procedure to calculate the topological derivative taking the total potential energy as a cost function [1][2][3][4]. The boundary of the domain is described by the NURBS curves which are commonly used for representing and designing a shape in numerical implementation.…”

“…On the top of the domain (Γ 6 ), the Robin condition is considered where the heat transfer coefficient is α = 10 W/ (m 2 K) and the ambient temperature is T ∞ = 20°C. On the boundary 2 Γ the temperature T b = 500°C is accepted while on 4 Γ , T b = 200°C is given. On the remaining parts of the boundary the Neumann condition q b = 0 is prescribed.…”

Applying the topological derivative and the boundary element method to design of shape of the heat exchanger

“…The concept of the topological derivative T D * is based on establishing the sensitivity of a given cost function (total potential energy) when the size of this hole is changed. The local value of the T D * is obtained by [1][2][3][4] …”

“…In this way, wherever this sensitivity is low enough (or high enough), depending on the problem, material is progressively removed. The topological derivative is often used for solving the topology design of several engineering problems (for example, design of heat conductors or heat exchanger) [1][2][3]. In this paper, we adopt a new approach called the topological--shape sensitivity method, which is based on classical shape sensitivity analysis.…”