We study some shape optimization problems related to sums and quotients of Dirichlet Laplacian eigenvalues kn for planar domains. We show how to minimize a sum ðkk þ kkþ1ÞjXj; k 1⁄4 1;2; . . . when the minimizing domain is disconnected. In particular, we prove that the optimizers in the cases k 1⁄4 1 and k 1⁄4 2 are connected. We develop a numerical method for solving shape optimization eigenva...

In this paper, we present an optimization framework for automating the shape customization of human-centric products, which can be mounted on or embedded in human body (such as exoskeletal devices and implants). This kind of products needs to be customized to fit the body shapes of users. At present, the design customization for freeform objects is often taken in an interactive manner that is i...

A. The paper can be considered as a complement to previous papers of the authors. An insight into applied asymptotic analysis of boundary value problems in singularly perturbed domains is presented. As a result, the asymptotic expansions of eigenvalues are obtained and discussed in terms of integral attributes of the geometrical perturbations including the virtual mass tensor, polarizati...

It's not surprisingly when entering this site to get the book. One of the popular books now is the variational methods in shape optimization problems. You may be confused because you can't find the book in the book store around your city. Commonly, the popular book will be sold quickly. And when you have found the store to buy the book, it will be so hurt when you run out of it. This is why, se...

In the framework of structural optimization via a level-set method, we develop an approach to handle the directional molding constraint for cast parts. A novel molding condition is formulated and a penalization method is used to enforce the constraint. A first advantage of our new approach is that it does not require to start from a feasible initialization, but it guarantees the convergence to ...

Shape is an important consideration in green building design due to its significant impact on energy performance and construction costs. This paper presents a methodology to optimize building shapes in plan using the genetic algorithm. The building footprint is represented by a multi-sided polygon. Different geometrical representations for a polygon are considered and evaluated in terms of thei...

We propose methods that allow the investigation of local modifications of aerodynamic design data represented by discrete unstructured surface meshes. A displacement measure is suggested to evaluate local differences between the shapes. The displacement measure provides information on the amount and direction of surface modifications. Using the displacement measure in conjunction with statistic...

This article establishes a new model for estimating the peak indentation force of the edge chipping of rocks when using a conical or a pyramidal point-attack pick. The investigation points out that the existing formulation in the literature is based on an inappropriate stress assumption and equilibrium, and hence leads to incorrect cutting force estimations. The new model developed in this stud...

A non convex minimum problem on a square arising in shape optimization is studied. Conditions are discussed for the existence or the non existence of solutions.

The transform relation between the meshing position and rotation angle of a cylindrical gear pair is firstly derived according to the theory of gear meshing. Then the technique of building the assembly model of a cylindrical gear pair at specified meshing position in ANSYS is researched. On this basis, a new method to perform static contact analysis of cylindrical gear at any meshing location i...