zbMATH — the first resource for mathematics

Numerical integration to obtain moment of inertia of nonhomogeneous material. (English) Zbl 1464.74308
Summary: The moment of inertia of a continuous object with an arbitrary shape made of a nonhomogeneous material is usually calculated by dividing it into small domains. However, it is a burdensome process to specify the density of the small domains. When the Monte Carlo method is used in the case of an arbitrary shape, the computation time increases. In this paper, a technique of easily calculating the moment of inertia of a 3D nonhomogeneous material using boundary integral equations is proposed. It is also shown how to calculate the mass, primary moment, and center of mass of an arbitrary object made of a nonhomogeneous material. A technique employed in the triple-reciprocity boundary element method is used to evaluate integral. In this paper, a formulization of the boundary element method is utilized, and a technique for the direct numerical integration of the three-dimensional domain using a three-dimensional interpolation method without carrying out domain division is proposed. To investigate the efficiency of this technique, several numerical examples are given.

74S15 Boundary element methods applied to problems in solid mechanics
65D30 Numerical integration
74E05 Inhomogeneity in solid mechanics
Full Text: DOI
[1] Rizwan, U. Z.K.; Sarda, A., Finite element analysis of concave thickness FGM rotating disk subject to thermo-mechanical load, Int J Eng Manag Res, 6, 3, 261-265, (2016)
[2] Mazzei, A. J.J., On the effect of functionally graded materials on resonances of rotating beams, Shock Vib, 19, 1315-1326, (2012)
[3] Davis, P.; Rabinowitz, P., Methods of numerical integration, 341-417, (1984), Academic Press
[4] Cheng, S. W.; Dey, T. K.; Shewchuk, J. R., Delaunay mesh generation, 301-332, (2013), CRC Press
[5] Gao, X. W., The radial integration method for evaluation of domain integrals with boundary-only discretization, Eng Anal Bound Elem, 26, 905-916, (2002) · Zbl 1130.74461
[6] Mohammadi, M.; Hematiyan, M. R.; Aliabadi, M. H., Boundary element analysis of thermo-elastic problems with non-uniform heat sources, Strain Anal, 45, 606-627, (2010)
[7] Krishnan, R. H.; Devanandh, V.; Brahma, A. K., Estimation of mass moment of inertia of human body, when bending forward, for the design of a self-transfer robotic facility, J Eng Technol, 11, 2, 166-176, (2016)
[8] Brebbia, C. A.; Telles, J. C.F.; Wrobel, L. C., Boundary element techniques −theory and applications in engineering, 46-70, (1984), Springer-Verlag · Zbl 0556.73086
[9] Ochiai, Y.; Sekiya, T., Steady heat conduction analysis by improved multiple-reciprocity boundary element method, Eng Anal Bound Elem, 18, 111-117, (1996) · Zbl 0867.65051
[10] Ochiai, Y., Steady heat conduction analysis in orthotropic bodies by triple-reciprocity BEM, Comput Model Eng Sci, 2, 4, 435-445, (2001) · Zbl 0995.80007
[11] Ochiai, Y., Multidimensional numerical integration for meshless BEM, Eng Anal Bound Elem, 27, 3, 241-249, (2003) · Zbl 1033.65109
[12] Ochiai, Y.; Sladek, V., Numerical treatment of domain integrals without internal cells in three-dimensional BIEM formulations, CMES(Comput Model Eng Sci), 6, 6, 525-536, (2005) · Zbl 1103.65123
[13] Ochiai, Y., Meshless large plastic deformation analysis considering with a friction coefficient by triple-reciprocity boundary element method, J Comput Mech Exp Measur, 6, 6, 989-999, (2018)
[14] Ochiai, Y., Three-dimensional heat conduction analysis of inhomogeneous materials by triple-reciprocity boundary element method, Eng Anal Bound Elem, 51, 1, 101-108, (2015) · Zbl 1403.74205
[15] Ochiai, Y.; Sekiya, T., Generation of free-form surface in CAD for dies, Adv Eng Softw, 22, 113-118, (1995)
[16] Juvinall, R. C.; Marshek, K. M., Fundamentals of machine component design, (2006), Wiley
[17] Micchelli, C. A., Interpolation of scattered data, Construct Approx, 2, 12-22, (1986)
[18] Dyn N. Interpolation of scattered data by radial functions, In: Topics in multivariate approximation, editors. Chui C. K., Schumaker L. L. and Utreras F. I., pp. 47-61, (1987), Academic Press, London.
[19] Kroese, D. P.; Taimre, T.; Botev, Z. I., Handbook of Monte Carlo methods, (2011), Wiley · Zbl 1213.65001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.