【摘要】 本文讨论的对角化质量矩阵是在动能积分的公式中将积分点取在有限单元的结点上而得到的,本文给出了用这种矩阵时,固有频率、固有振型和对应的应力的对角化误差与动能积分的代数精确度、插值位移场的多项式的阶次、应变能中导数的最高阶数的关系,利用这些关系和多个算例讨论了对角化质量矩阵的应用性问题。更多还原

【Abstract】 In the present paper the model of diagonalization for mass matrix is used. In the formula of integration for kinetic energy, the integration points are coincident with finite element nodes so that a diagonal mass matrix is obtained and an algebraic eigenvalue problem is constructed. This paper shows how the error estimates of natural frequencies, natural modes and corresponding stresses by using such diagonal mass matrix depends upon the algebraic accuracy of the integration formula for kinetic energy, the number of order of polynomial for interpolation of displacements and the number of highest order of derivative of displace-ments in strain energy. The applicability of diagonal mass matrix is discussed.更多还原