The classical 3D beam element has been modified and developed as a new finite element for vibration analysis of frame structures with flexible connections and cracked mem hers. The mass and stiffness matrices of the modified elements are established basing on a new form of shape functions, which are obtained in investigating a beam with flexible supports and crack modeled through equivalent springs. | Vietnam Journal of Mechanics, NCNST of Vietnam T. XX, 1998, No 1 (29 - 46) MODAL ANALYSIS OF DAMAGED STRUCTURES BY THE MODIFIED FINITE ELEMENT METHOD NGUYEN CAO MENH, NGUYEN TIEN KHIEM, DAO NHU MAI, NGU'(EN VIET KHOA Institute of Mechanics, 224 Doican, Hanoi, Vietnam ABSTRACT. The classical 3D beam element has been modified and developed as a new finite element for vibration analysis of frame structures with flexible connections and cracked mem hers. The mass and stiffness matrices of the modified elements are established basing on a new form of shape functions, which are obtained in investigating a beam with flexible supports and crack modeled through equivalent springs. These shape functions remain the cubic polynomial form and contain flexible connection (or crack) parameters. They do not change standard procedure of the finite element method (FEM). Therefore, the presented method is easy for engineers in application and allows to analyze eigen-parameters of structures as functions of the connection (or crack) parameters. The proposed approach has been applied to calculate natural frequencies and mode shape of typical frame structures in presented examples. 1. Introduction The frame structures with semi-rigid (or flexible) connection have been studied in series of papers by Lui and Chen [2-4], Shi and Atluri [5], Kawashima and Fujimoto [6). However, the methods proposed in their studies are limited either by the application for only some individual cases or by the difficulty for engineers in application. Chan and Ho [7] have suggested a new approach for calculating the mass and stiffness matrices of element basing on specific shape functions derived from solving the equilibrium equations of beam. The advantage of the method is keeping the cubic form (but with coeffiCients depending on connection parameters) of shape functions and the same as well known procedure of FEM. Some analytical aspects of the dynamic problem for beam-column with flexible supports .
