Optimal material tailoring of 2D heterogeneous cylinder for a prescribed temperature field in transient heat conduction

Abstract

In this paper, optimization of volume fraction distribution in a finite length thick hollow cylinder made of heterogeneous material is considered. The cylinder has two-directional functionally graded constituent and subjected to transient thermal loading. Two-dimensional heat conduction in the cylinder is considered and variation of temperature with time as well as temperature distribution through the cylinder is investigated. A graded finite element method combined with direct time integration method is used to model the structure and solve time-dependent equations. Volume fractions of constituent materials on a finite number of design points are taken as design variables and the volume fractions at any arbitrary point in the cylinder are obtained via cubic spline interpolation functions. The objective is to minimize the difference between the actual distribution of the temperature through the structure and a desired target distribution after a prescribed time while the total mass of the structure is also minimized. Multi-objective Genetic Algorithm jointed with interior penalty-function method for implementing constraints is effectively employed to find the global solution of the optimization problem. Obtained results indicate that by using the uniform distribution of temperature and minimum mass as objective functions, considerably more effective usage of materials can be achieved compared with the common power law volume fraction distribution. The proposed methodology provides a framework for designing functionally graded structures with optimum material tailoring for a prescribed field variable problem.

Keywords

2D FGM volume fraction optimization transient heat conduction genetic algorithm

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