A mass-matrix solution based frequency-domain finite-element method

2010 ◽  
Author(s):  
Jianfang Zhu ◽  
Dan Jiao
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Frequency Domain ◽  
Mass Matrix ◽  
Matrix Solution ◽  
Element Method

Nonlinear Random Responses of Shell Structures With Spatial Uncertainties

2002 ◽  
Author(s):  
C. W. S. To
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Large Deformation ◽  
Mass Matrix ◽  
Spatial Uncertainty ◽  
Shell Structures ◽  
Time Step ◽  
Central Difference ◽  
Approximation Techniques ◽  
Element Method

A novel procedure for large deformation nonstationary random response computation of shell structures with spatial uncertainty is presented. The procedure is free from the limitations associated with those employing perturbation approximation techniques, such as the so-called stochastic finite element method and probabilistic finite element method, for systems with spatial uncertainties. In addition, the procedure has several important and excellent features. Chief among these are: (a) ability to deal with large deformation problems of finite strain and finite rotation; (b) application of explicit linear and nonlinear element stiffness matrices, mass matrix, and load vectors reduces computation time drastically; (c) application of the averaged deterministic central difference scheme for the updating of co-ordinates and element matrices at every time step makes it extremely efficient compared with those employing the Monte Carlo simulation and the conventional central difference algorithm; and (d) application of the time co-ordinate transformation enables one to study highly stiff structural systems.

Study on the Mixed Method of Transfer Matrix Method and Finite Element Method for Vibration of Multibody System

2019 ◽  
Author(s):  
Hanjing Lu ◽  
Xiaoting Rui ◽  
Jianshu Zhang ◽  
Yuanyuan Ding
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Transfer Matrix ◽  
Mixed Method ◽  
Transfer Matrix Method ◽  
Transfer Equation ◽  
Matrix Method ◽  
Multibody System ◽  
Mass Matrix ◽  
Element Method

Abstract The mixed method of Transfer Matrix Method for Multibody System (MSTMM) and Finite Element Method (FEM) is introduced in this paper. The transfer matrix and transfer equation of multi-rigid-body subsystem are deduced by MSTMM. The mass matrix and stiffness matrix of flexible subsystem are calculated by FEM and then its dynamics equation is established. The connection point relations among subsystems are deduced and the overall transfer matrix and transfer equation of multi-rigid-flexible system are established. The vibration characteristics of the system are obtained by solving the system frequency equation. The computational results of two numerical examples show that the proposed method have good agreements with MSTMM and FEM. Multi-rigid-flexible-body system with multi-end beam can be solved by proposed method, which extends the application field of MSTMM and provides a theoretical basis for calculating complex systems with multi input end flexible bodies of arbitrary shape.

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