METHOD AND SYSTEM FOR FINDING NATURAL FREQUENCY AND MODE OF VIBRATION FOR STRUCTURE BY FINITE ELEMENT METHOD WHILE USING HIGHER-ORDER ELEMENT

摘要

PROBLEM TO BE SOLVED: To provide a method and a system for finite element analysis for calculating a solution with a comparatively little computational complexity or memory capacity while using a concentrated mass matrix even when a higher-order element is used.;SOLUTION: A rigid matrix and a concentrated mass matrix are generated from the analytic model of a structure by the routine procedure of a finite element method. A general peculiar value question expressed with these rigid matrix and concentrated mass matrix is converted to a standard peculiar value question Ay=λy (A is a matrix for applying a peculiar value question, λ is a peculiar value and (y) is a peculiar vector). When the concentrated mass matrix contains a negative component (namely, when the concentrated mass matrix is not a regular value matrix), a matrix T={hij} is provided by shading A according to an Arnoldi method of repetition and at such a time, however, by setting an initial vector to be a real number corresponding to a component (h), with which the component of the correspondent concentrated mass matrix is positive, or to be a pure imaginary number corresponding to a component (h), with which the component of such a matrix is negative, the matrix A is converted to a real Hessenberg matrix T. The peculiar value of the standard peculiar value question applied by this Hessenbarg matrix T is found by a QR method. The peculiar vector can be found similarly to the case that the concentrated mass matrix is the regular value matrix.;COPYRIGHT: (C)2001,JPO