Novel Method for Shape and Topology Optimization of Heat Conductive Objects—Volume-of-Solid Method

Abstract

The aim of this thesis is to develop a novel computational approach which is based on a non-constrained formulation with a volume-of-solid (VOS) function equation for topology design of heat conductive solid paths between constant-temperature objects In the first step of the approach the distributions of the VOS function and the temperature in the original design domain are carried out by simultaneously solving the VOS function equation and the heat conduction equation Secondly the shape outline of the heat conduction path leading to a maximum heat transfer rate per unit solid mass is determined by selecting a cut-off value of the VOS function Validity and capability of the VOS method are investigated and tested by several different cases However it is found that with this method one needs to carry out the grid generation repeatedly during the evolution of the shape of the heat conduction paths Thus the design process is rather time-consuming In this regard the VOS method is improved by introducing the simplified conjugate-gradient method (SCGM) and grid image visualization into the topology design process This improved approach VOS+SCGM is applied to the two-dimensional test cases with various thermal boundary configurations Results show that the optimal shapes of the heat conduction paths can be more efficiently predicted by using the VOS+SCGM method In the VOS+SCGM method the grid generation is no longer required and instead the grid image visualization is used to portray the shape of the objects Furthermore the VOS method is applied to optimize the conduction path in laminated metallic materials between unequal isothermal surfaces Three-layer laminated metallic composite materials which are made of copper aluminum stainless steel or iron are considered in this study Two possible orientations of the composite materials vertical and horizontal are investigated Optimal shapes of the thermal conduction path between different temperature objects are determined toward minimization of the objective function This approach is able to reach optimal shape corresponding to different objective functions It implies that the selection of the objective function becomes more flexible By using this approach optimal thermal conduction paths leading to maximum heat transfer rate per unit mass (Q/m) maximum heat transfer rate per unit volume (Q/V) or maximum heat transfer rate per unit cost (Q/USD) can be readily yielded

Date of Award	2016 Jul 21
Original language	English
Supervisor	Chin-Hsiang Cheng (Supervisor)