This paper is a survey of structural shape optimization with an emphasis on techniques dealing with shape optimization of the boundaries of two- and three-dimensional bodies. Attention is focused on the special problems of structural shape optimization which are due to a finite element model which must change during the optimization process. These problems include the requirement for sophisticated automated mesh generation techniques and careful choice of design variables. They also include special problems in obtaining sufficiently accurate sensitivity derivatives.

Structural shape optimization — a survey

A model of consumer buying behavior is used to identify household characteristics that should affect deal proneness. The model treats household purchasing and inventory decisions like those of a firm. In other words, the household's purchasing decisions are assumed to be based on such factors as transaction costs, holding costs, and stockout costs in addition to product price. Household characteristics then are related to these cost parameters to identify households that are likely to be deal prone. The predictions are tested empirically by use of panel data for five frequently purchased products. The empirical results indicate that deal prone households can be identified and that the key variables affecting deal proneness are household resource variables such as home ownership and automobile ownership.

Identifying the Deal Prone Segment

This paper is a survey of structural shape optimization with an emphasis on techniques dealing with shape optimization of the boundaries of two and three dimensional bodies. Attention is focused on the special problems of structural shape optimization which are due to a finite element model which must change during the optimization process. These problems include the requirement for sophisticated automated mesh generation techniques and careful choice of design variables. They also include special problems in obtaining sufficiently accurate sensitivity derivatives.

Structural shape optimization - A survey

A review of structural shape optimization

General solutions for thermopiezoelectrics with various holes under thermal loading

: This paper presents optimized hole shapes in plates of finite width subjected to uniaxial load for a large range of hole to plate widths (D/W) ratios. The stress concentration factor for the optimized holes decreased by as much as 44% when compared to circular holes. Simultaneously, the area covered by the optimized hole increased by as much as 26% compared to the circular hole. Coefficients of efficiency between 0.91 and 0.96 are achieved. The geometries of the optimized holes for the D/W ratios considered are presented in a form suitable for use by designers. It is also suggested that the developed geometries may be applicable. to cases of rectangular holes and to the tip of a crack. This information may be of interest in fracture mechanics. (Auhtor)

Optimum hole shapes in finite plates under uniaxial load

Minimizing the stress concentration around holes in uniaxially loaded finite plates is an important consideration in engineering design. One method for reducing the stress concentration around a central circular hole in a uniaxially loaded plate is to introduce smaller auxiliary holes on either side of the original hole to help smooth the flow of the tensile principal-stress trajectories past the original hole. This method has been demonstrated by Heywood and systematically studied by Erickson and Riley. Erickson and Riley show that for a central-hole diameter-to-plate width ratio of 0.222, the maximum stress reduction is up to 16 percent. In recent work, Durelliet al. show that the stress concentrations around holes in uniaxially loaded plates can be minimized by changing the hole shape itself till an optimum hole profile with constant stress values respectively on the tensile and compressive segments of the hole boundary is reached. By this technique the maximum stress reduction obtained for the above case is up to 20 percent.

Hole-shape optimization in a finite plate in the presence of auxiliary holes

A new method has been developed that permits the direct design of shapes of two-dimensional structures and structural components, loaded in their plane, within specified design constraints and exhibiting optimum distribution of stresses. The method uses photoelasticity and requires a large field diffused light polariscope. Several problems of optimisation related to the presence of holes in finite and infinite plates, subjected to uniaxial and biaxial loadings, are solved parametrically. Some unexpected results have been found: 1) the optimum shape of a large hole in a bar of finite width, subjected to uniaxial load, is "quasi" square, but the transverse boundary has the configuration of "hat"; 2) for the small hole in the large plate, a "barrel" shape has a lower s.c.f. than the circular hole and appreciably higher coefficient of efficiency; 3) the optimum shape of a tube, subjected to diametral compression, has small "hinges" and is much lighter and stronger than the circular tube. Applications are also shown to the design of dove-tails and slots in turbine blades and rotors.

K. Rajaiah

Papers

Optimum hole shapes in finite plates under uniaxial load

Hole-shape optimization in a finite plate in the presence of auxiliary holes

Lighter and stronger

Collocation Solution for Point-Supported Square Plates

Optimum hole shape determination in infinite orthotropic plates under inplane loading by conformal transformation