Numerical integration to obtain moment of inertia of nonhomogeneous material

Abstract

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.