The second moment of inertia of a continuous axisymmetric 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. In this paper, a technique of easily calculating the second moment of inertia of an axisymmetric nonhomogeneous material using boundary integral equations is proposed. The calculations of the mass, primary moment, and center of mass of an arbitrarily shaped object made of a nonhomogeneous material are also shown. A formulization of the boundary element method is utilized, and a technique for the direct numerical integration of the axisymmetric domain using an axisymmetric interpolation method without the need to carry out domain division is proposed. Heterogeneous materials include laminated material composites, in which the density distribution is discontinuous. Axisymmetric interpolation using harmonic and biharmonic functions has a weak point that can be easily overcome using a scale method.

由非均质材料制成的具有任意形状的连续轴对称物体的第二惯性矩通常通过将其划分为小域来计算。然而，指定小域的密度是一个繁重的过程。在本文中，提出了一种使用边界积分方程轻松计算轴对称非均匀材料的二阶惯性矩的技术。还显示了由非均质材料制成的任意形状物体的质量、初级力矩和质心的计算。利用边界元法的公式化，提出了使用轴对称插值法对轴对称域进行直接数值积分而不需要进行域划分的技术。异质材料包括层压材料复合材料，其中密度分布是不连续的。使用谐波和双谐波函数的轴对称插值有一个弱点，可以使用标度方法轻松克服。