Abstract
In this paper, an efficient meshless local B-spline based finite difference (FD) method for analysis of functionally graded materials (FGMs) subjected to temperature-dependent heat sources is presented. The favourable properties of B-spline basis functions in having arbitrary degree for resolution of solution, partition of unity and the Kronecker delta properties are combined with high accuracy and low computational effort of differential quadrature method in approximating shape functions and their derivatives. In this study, the FGMs are assumed to have temperature-dependent materials properties that vary as a function of radial distance. The homogenized properties are evaluated with power-law mixture rule. The nonlinearities from material properties and heat source terms are handled by the predictor-corrector method along with the Crank-Nicolson scheme for time integration. Case of nonlinear 2D heat conduction in FGM due to temperature dependentheat sources is examined. The method is shown to be accurate and efficient for complex thermal analysis of FGMs taking into account temperature dependency of material properties and heat sources.
Highlights
Devising more accurate and efficient numerical schemes for thermal analysis of functionally graded materials (FGM) is of great interest
An efficient meshless local B-spline based finite difference (FD) method for analysis of FGMs subjected to temperature-dependent heat sources is presented
Case of FGM made of zirconium oxide (ZrO2) and titanium alloy (Ti-6Al-4V) due to with temperature dependent heat source is considered in this study
Summary
Devising more accurate and efficient numerical schemes for thermal analysis of functionally graded materials (FGM) is of great interest. The distinct feature of meshless methods is that the problems of discrete material property and discontinuity of solution are not encountered in the meshless methods due to the absence of mesh. Such an interesting feature is beneficial in handling material variation/gradation or in capturing thermal shock in the materials. The motivation and objective of the present work is to develop and present an efficient and effective meshless collocation approach for thermal analysis of FGMs taking into account temperature dependency of material properties heat sources. An efficient meshless local B-spline based finite difference (FD) method for analysis of FGMs subjected to temperature-dependent heat sources is presented. The nonlinearities from the temperature-dependent material properties and heat source terms are handled by using the predictor-corrector method along with the Crank-Nicolson implicit scheme for time integration
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