The classical level set method, which represents the boundary of the unknown geometry as the zero-level set of a function, has been shown to be very effective in solving shape optimization problems. The present work addresses the issue of using a level set representation when there are simple geometrical and topological constraints. We propose a logarithmic barrier penalty which acts to enforce...

We consider the optimal distribution of several elastic materials in a fixed working domain. In order to optimize both the geometry and topology of the mixture we rely on the level set method for the description of the interfaces between the different phases. We discuss various approaches, based on Hadamard method of boundary variations, for computing shape derivatives which are the key ingredi...

Level set methods are a popular way to solve the image segmentation problem in computer image analysis. A contour is implicitly represented by the zero level of a signed distance function, and evolved according to a motion equation in order to minimize a cost function. This function defines the objective of the segmentation problem and also includes regularization constraints. Gradient descent ...

We propose a product design optimization method that maximizes the integrated satisfaction level for evaluative factors. Product designs include many evaluative factors that have complex interrelationships. To cope with such circumstances, we construct strategies and a practical method to obtain optimum design solutions. First, the evaluative items for the product are listed and each item is de...

In this paper, the conventional level set methods are extended as an effective approach for shape and topology optimization by the introduction of the radial basis functions (RBFs). The RBF multiquadric splines are used to construct the implicit level set function with a high level of accuracy and smoothness and to discretize the original initial value problem into an interpolation problem. The...

During the last 20 years, structural optimization has become one of the most important topics of engineering applications. Design optimization of structure has been an interesting area of research in the field of engineering design for its ability to short the design cycle and to enhance product quality. Significant research activity has occurred in the area of structural optimization in the la...

0045-7949/$ see front matter Crown Copyright 2 doi:10.1016/j.compstruc.2010.11.003 ⇑ Corresponding author. Tel.: +82 32 860 7310; fax E-mail addresses: [email protected], jhp@h [email protected] (H.G. Beom), [email protected] (Y. W (S. Lin), [email protected] (B. Liu). This paper proposes an evolutionary accelerated computational level set algorithm for structure topology optimization. It integ...

1. Abstract A novel strategy for handling the molding constraint for cast parts is presented. In a first step, a simple projection method for the velocity field is applied. If the optimized shape violates thickness constraints, this projection method is no longer sufficient and a general molding constraint is applied at the same time with thickness control. We apply an augmented Lagrangian meth...

We intend to propose a framework to handle the problem of mesh deformation in the context of shape optimization. The main idea is to combine the level set method with meshing tools specialized to deal with implicitly-defined geometries. The proposed method is then as well a topology optimization as a geometric optimization method.