Abstract
A design optimization problem in continuum structure is usually characterized by minimizing an objective function with shape parameters subject to a governing field equation and several constraints. The problem can be reformulated as a variational problem, introducing its adjoint system. If the problem is nonlinear with respect to the shape parameters, it is in general difficult to solve the problem analytically.
This paper proposes a practical method to solve the nonlinear variational problem numerically with the aid of the finite element discretization technic combined with the multiplier method. For numerical examples of an application, shape optimization problems of a fin, which is used to promote the heat exchanger efficiency, are considered herein to show the validity of the proposed scheme.
