Hideyuki AZEGAMI

For optimization problems of domains in which elliptic boundary value problems are defined a solution is proposed. The treated problems are those to determine the domain that minimizes an objective functional of the state functions under the conditions that the coefficient functions of the partial differential equations and the boundary value functions in the elliptic boundary value problems have smoothness and a one-to-one correspondence with domain variation and that the volumes of the domains

This paper presents an improved version of the traction method that was proposed as a solution to shape optimization problems of domain boundaries in which boundary value problems of partial differential equations are defined. The principle of the traction method is presented based on the theory of the gradient method in Hilbert space. Based on this principle, a new method is proposed by selecting another bounded coercive bilinear form from the previous method. The proposed method obtains domain

We present a numerical analysis and results using the traction method for optimizing domains in terms of which linear elastic problems are defined. In this paper we consider the application of the traction method, which was proposed as a solution to domain optimization problems in elliptic boundary value problems. The minimization of the mean compliance is considered. Using the Lagrange multiplier method, we obtain the shape gradient functions for these domain optimization problems from the opti

Shape optimization problems of linear elastic bodies, flow fields, magnetic fields, etc. for equilibrium types can be generalized as optimization problems of domains in which elliptic boundary value problems are defined. This paper shows that ordinary domain optimization problems do not have sufficient regularity and proposes a technique to overcome this irregularity. It briefly describes the derivation of the shape gradient functions for a self-adjoint shape optimization problem, and shape iden

A review of the literature on the mechanical aspects of the etiology for idiopathic scoliosis reveals that the buckling hypothesis has been presented as a purely mechanical phenomenon. In an attempt to confirm the buckling hypothesis, a numerical simulation of growth and the resulting buckling phenomena was done by means of finite element analysis. It previously was observed that growth was induced in the T4 to T10 vertebrae. Only the sacrum was assumed to be stationary. From the growth analysis

The present paper describes a numerical solution to topology optimization problems of domains in which boundary value problems of partial differential equations are defined. Density raised to a power is used instead of the characteristic function of the domain. A design variable is set by a function on a fixed domain which is converted to the density by a sigmoidal function. Evaluation of derivatives of cost functions with respect to the design variable appear as stationary conditions of the Lag

We present a numerical analysis method and results using the traction method for optimization problems of domains in which linear elastic problems are defined. In this paper we consider the application of the traction method which was proposed as a solution to domain optimization problems in elliptic boundary value problems. The minimization problems of the mean compliance were treated. Using the Lagrange multiplier method, we obtain the shape gradient functions for these domain optimization pro

A numerical analysis technique is presented for solving optimization problems of geometrical domains in which elliptic boundary value problems are defined. Domain variation is formulated with a one-to-one mapping and its infinitesimal variation with a speed field as advocated by Zolesio. * The sensitivity functions, which we call the shape gradient functions, of domain variation are derived using the Lagrange multiplier method or the adjoint method. 3 By applying the gradient method in functiona

A simple method for analysis of uniform-strength shape is newly proposed. In this paper, the most fundamental case of a static elastic body is considered. The idea of the present method came from the growth behavior of living organisms by which they changed their own shapes to adapt themselves to the mechanical living environment. The scheme consists of the iteration of the two analytical steps : (1) conventional elastic analysis for evaluation of stress distribution, and (2) incremental growth

This paper presents analytic solutions of the shape derivatives (Fréchet derivatives with respect to domain variation) for singular points of cost functions in shape-optimization problems for the domain in which the boundary value problem of a partial differential equation is defined. A design variable is given by a domain mapping. Cost functions are defined as functionals of the design variable and the solution to the boundary value problem. The analytic solutions for singular points such as cr