A simple boundary element formulation for shape optimization of 2D continuous structures

For the design of nuclear equipment like pressure vessels, steam generators, and pipelines, among others, it is very important to optimize the shape of the structural systems to withstand prescribed loads such as internal pressures and prescribed or limiting referential values such as stress or strain. In the literature, shape optimization of frame structural systems is commonly found but the same is not true for continuous structural systems. In this work, the Boundary Element Method (BEM) is applied to simple problems of shape optimization of 2D continuous structural systems. The proposed formulation is based on the BEM and on deterministic optimization methods of zero and first order such as Powell's, Conjugate Gradient, and BFGS methods. Optimal characterization for the geometric configuration of 2D structure is obtained with the minimization of an objective function. Such function is written in terms of referential values (such as loads, stresses, strains or deformations) prescribed at few points inside or at the boundary of the structure. The use of the BEM for shape optimization of continuous structures is attractive compared to other methods that discretized the whole continuous. Several numerical examples of the application of the proposed formulation to simple engineering problems are presented. (authors)