Analysis Two Dimension Heat Conduction in Functionally Graded Materials Using Finite Element Methods

Rezza Ruzuqi

doi:10.54783/ijsoc.v2i2.96

Rezza Ruzuqi Sorong Marine and Fisheries Polytechnic, Indonesia

DOI: https://doi.org/10.54783/ijsoc.v2i2.96

Keywords: FGMs, Heat Conduction, Finite Element Methods (FEM), ANSYS

Abstract

Along with the progress of the industrial world, both the aviation industry, the health industry, the chemical industry, the electronics industry, and so on, the need for composite materials is increasing to meet market demand. Functionally Graded Materials (FGMs) are an advanced material class of composite materials that have material properties that vary from one point to another. In this study, two-dimensional heat conduction analysis will be conducted in FGM using the Finite Element Method (FEM). Three models gradation FGMs properties examined in the study, namely polynomial, Trigonometry, and Exponential. The response temperature of FGMs using gradation three models compared and analyzed. The optimum temperature distribution of four models built with the ANSYS software. The result is that heat conduction in trigonometric variations is very good, resulting in low-temperature values when compared to both of them. Then, the performance and efficiency obtained using FEM to analyze two-dimensional heat conductivity in FGMs is also very good.

References

Birman, V. (1995). Stability of functionally graded hybrid composite plates. Composites Engineering, 5(7), 913-921.

Birman, V. (1997). Stability of functionally graded shape memory alloy sandwich panels. Smart Materials and Structures, 6(3), 278-286.

Yin, H. M., Sun, L. Z., & Paulino, G. H. (2004). Micromechanics-based elastic model for functionally graded materials with particle interactions. Acta Materialia, 52(12), 3535-3543.

Vel, S. S., & Batra, R. C. (2002). Exact solution for thermoelastic deformations of functionally graded thick rectangular plates. AIAA journal, 40(7), 1421-1433.

Kaysser, W. A., & Ilschner, B. (1995). FGM research activities in Europe. Mrs Bulletin, 20(1), 22-26.

Jin, Z. H. (2002). An asymptotic solution of temperature field in a strip a functionally graded material. International communications in heat and mass transfer, 29(7), 887-895.

Ootao, Y., & Tanigawa, Y. (2004). Transient thermoelastic problem of functionally graded thick strip due to nonuniform heat supply. Composite Structures, 63(2), 139-146.

Sladek, J., Sladek, V., & Zhang, C. (2003). Transient heat conduction analysis in functionally graded materials by the meshless local boundary integral equation method. Computational Materials Science, 28(3-4), 494-504.

Sutradhar, A., & Paulino, G. H. (2004). The simple boundary element method for transient heat conduction in functionally graded materials. Computer Methods in Applied Mechanics and Engineering, 193(42-44), 4511-4539.

Sutradhar, A., Paulino, G. H., & Gray, L. J. (2005). On hypersingular surface integrals in the symmetric Galerkin boundary element method: application to heat conduction in exponentially graded materials. International Journal for Numerical Methods in Engineering, 62(1), 122-157.

Abreu, A. I., Canelas, A., & Mansur, W. J. (2013). A CQM-based BEM for transient heat conduction problems in homogeneous materials and FGMs. Applied Mathematical Modelling, 37(3), 776-792.

Ochiai, Y. (2004). Two-dimensional steady heat conduction in functionally gradient materials by triple-reciprocity boundary element method. Engineering analysis with boundary elements, 28(12), 1445-1453.

Chen, J., Liu, Z., & Zou, Z. (2002). Transient internal crack problem for a nonhomogeneous orthotropic strip (Mode I). International Journal of Engineering Science, 40(15), 1761-1774.

Yao, W., Yu, B., Gao, X., & Gao, Q. (2014). A precise integration boundary element method for solving transient heat conduction problems. International Journal of Heat and Mass Transfer, 78, 883-891.

Bruch Jr, J. C., & Zyvoloski, G. (1973). A finite element weighted residual solution to one‐dimensional field problems. International Journal for Numerical Methods in Engineering, 6(4), 577-585.

Bruch Jr, J. C., & Zyvoloski, G. (1974). Transient two‐dimensional heat conduction problems solved by the finite element method. International Journal for Numerical Methods in Engineering, 8(3), 481-494.

Wang, B. L., & Mai, Y. W. (2005). Transient one-dimensional heat conduction problems solved by finite element. International Journal of Mechanical Sciences, 47(2), 303-317.

Wang, B. L., & Tian, Z. H. (2005). Application of finite element–finite difference method to the determination of transient temperature field in functionally graded materials. Finite elements in analysis and design, 41(4), 335-349.

Haghighi, M. G., Eghtesad, M., & Malekzadeh, P. (2008). Coupled DQ–FE methods for two dimensional transient heat transfer analysis of functionally graded material. Energy conversion and management, 49(5), 995-1001.

Malekzadeh, P., Golbahar Haghighi, M. R., & Heydarpour, Y. (2012). Heat transfer analysis of functionally graded hollow cylinders subjected to an axisymmetric moving boundary heat flux. Numerical Heat Transfer, Part A: Applications, 61(8), 614-632.

Chen, B., & Tong, L. (2004). Sensitivity analysis of heat conduction for functionally graded materials. Materials & design, 25(8), 663-672.

Santos, H., Soares, C. M. M., Soares, C. A. M., & Reddy, J. N. (2008). A semi-analytical finite element model for the analysis of cylindrical shells made of functionally graded materials under thermal shock. Composite Structures, 86(1-3), 10-21.

Asgari, M., & Akhlaghi, M. (2009). Transient heat conduction in two-dimensional functionally graded hollow cylinder with finite length. Heat and Mass Transfer, 45(11), 1383-1392.

Babaei, M. H., & Chen, Z. (2010). Transient hyperbolic heat conduction in a functionally graded hollow cylinder. Journal of Thermophysics and Heat Transfer, 24(2), 325-330.

Gao, X. W. (2006). A meshless BEM for isotropic heat conduction problems with heat generation and spatially varying conductivity. International journal for numerical methods in engineering, 66(9), 1411-1431.

Zhang, X., Zhang, P., & Zhang, L. (2013). An improved meshless method with almost interpolation property for isotropic heat conduction problems. Engineering Analysis with Boundary Elements, 37(5), 850-859.

De Boor, C. (1972). On calculating with B-splines. Journal of Approximation theory, 6(1), 50-62.

Hidayat, M. I. P., Wahjoedi, B. A., Parman, S., & Yusoff, P. S. M. (2014). Meshless local B-spline-FD method and its application for 2D heat conduction problems with spatially varying thermal conductivity. Applied Mathematics and Computation, 242, 236-254.

Zhang, H. H., Han, S. Y., & Fan, L. F. (2017). Modeling 2D transient heat conduction problems by the numerical manifold method on Wachspress polygonal elements. Applied Mathematical Modelling, 48, 607-620.

Hosseini, S. M., Akhlaghi, M., & Shakeri, M. (2007). Transient heat conduction in functionally graded thick hollow cylinders by analytical method. Heat and Mass Transfer, 43(7), 669-675.

Wang, H. M. (2013). An effective approach for transient thermal analysis in a functionally graded hollow cylinder. International Journal of Heat and Mass Transfer, 67, 499-505.

Daneshjou, K., Bakhtiari, M., Alibakhshi, R., & Fakoor, M. (2015). Transient thermal analysis in 2D orthotropic FG hollow cylinder with heat source. International Journal of Heat and Mass Transfer, 89, 977-984.