Abstract—Novel polyhedral elements termed as virtual node polyhedral element (VPHE) have been formulated based on virtual node method. The VPHEs are able to take arbitrary forms with arbitrary number of nodes and sides. Formulation of the VPHE is provided in this work, together with three examples that demonstrate utilization of the new element in carrying out numerical analyses. The first and second examples involve determination of steady-state temperature distribution (heat transfer phenomena) for two different geometries while the third example involves determination of Young’s modulus for carbon nanotubes (solid mechanics). Three different meshes with increasing number of finite elements (VPHEs) are utilized in examples 1 and 2. Example 3 is simulated by representing each cell of a carbon nanotube with a VPHE element. This is done for two different configurations of carbon nanotube (Armchair and Zigzag). Simulation results show that the VPHEs are able to produce converging solutions towards the analytical or experimental solutions for all three cases considered in this work.

Index Terms—Finite element method, polyhedral finite element, virtual node method, numerical analysis.

The authors are with Faculty of Engineering and Technology, Multimedia University, Jalan Ayer Keroh Lama, Bukit Beruang, 75450 Melaka, Malaysia.

Cite:Logah Perumal, C. P. Tso, Lim Thong Leng, "Novel Polyhedral Finite Elements for Numerical Analysis," International Journal of Computer and Electrical Engineering vol. 9, no. 2, pp. 492-501, 2017.