In most shape optimization problems, the optimal solution does not belong to the set of genuine shapes but is a composite structure. The homogenization method consists in relaxing the original problem thereby extending the set of admissible structures to composite shapes. From the numerical viewpoint, an important asset of the homogenization method with respect to traditional geometrical optimi...

Topology optimization searches for an optimal distribution of material and void without any restrictions on the structure of the design geometry. Shape optimization tunes the shape of the geometry, while the topology is fixed. In this paper we proceed sequentially with the optimal topology and shape design so that a coarsely optimized topology is the initial guess for the following shape optimi...

In this paper, we present a mathematical model for determining the optimal radius of the iron pole shape in spoke-type permanent-magnet (PM) machines (STPMM) in order to minimize the pulsating torque components. The proposed method is based on the formal resolution of the Laplace’s and Poisson’s equations in a Cartesian pseudo-coordinate system with respect to the relative permeability effect o...

In this article, the problem of determining the shape of a thin wing for minimum drag has been examined. In order to determine the optimal shape, we have extended a measure theory-based method. Using an embedding procedure, the problem of finding the optimal shape is reduced to one consisting of minimizing a linear form over a set of positive measures. The resulting problem can be approximated ...

Nowadays, lightweight automotive component design, regarding fuel consumption, environmental pollutants and manufacturing costs, is one of the main issues in the automotive societies. In addition, considering safety reasons, the durability of the automotive components, as one of the most important design requirements should be guaranteed. In this paper, a two-step optimization process including...