Abstract
A continuum structure in cooperating physical fields is described by a distributed parameter system using partial differential equations. A shape optimization problem of the structure is usually modelled by minimizing an objective function with shape parameters subject to the governing field equations and several constraints. The problem can be reformulated as a variational problem introducing their adjoint system. The two or three dimensional problem is essentially nonlinear with respect to the shape parameters, even if the governing equations are linear to the fields. It is therefore difficult to solve the problem analytically.
In the presented paper, an iterative optimization procedure is proposed to solve the nonlinear variational problem numerically with the aid of the finite element discretization technique combined with the multiplier method. The procedure is applied, for a numerical example, to a shape optimization problem of an internally finned tube, which is used to improve the heat transfer efficiency. The results show that the proposed scheme can readily be implemented to obtain the optimal shape under several cooperating physical fields.
