Finite Element Method of Flexible Multibody Dynamics Based on a New Kind of Floating Frame

1991 ◽  
Author(s):  
You-Fang Lu ◽  
Zhao-Hui Qi ◽  
Bin Wang ◽  
Guan-Min Feng
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Analysis ◽  
Multibody Dynamics ◽  
Equations Of Motion ◽  
Flexible Multibody Dynamics ◽  
Flexible Multibody ◽  
Floating Frame ◽  
Element Method

Abstract A new kind of floating frame whose parameters do not appear in equations of motion as additional unknowns is defined. Numerical analysis of flexible multibody dynamics is much facilitated by using finite-element iteration of the corresponding equations based on this concept.

A New Approach to the Rigid Finite Element Method in Modeling Spatial Slender Systems

2018 ◽  
Vol 18 (02) ◽  
pp. 1850017 ◽  
Author(s):  
Iwona Adamiec-Wójcik ◽  
Łukasz Drąg ◽  
Stanisław Wojciech
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Dynamic Analysis ◽  
Equations Of Motion ◽  
Nonlinear Dynamic Analysis ◽  
New Approach ◽  
Static And Dynamic Analysis ◽  
Rigid Finite Element Method ◽  
Longitudinal Flexibility ◽  
Element Method

The static and dynamic analysis of slender systems, which in this paper comprise lines and flexible links of manipulators, requires large deformations to be taken into consideration. This paper presents a modification of the rigid finite element method which enables modeling of such systems to include bending, torsional and longitudinal flexibility. In the formulation used, the elements into which the link is divided have seven DOFs. These describe the position of a chosen point, the extension of the element, and its orientation by means of the Euler angles Z[Formula: see text]Y[Formula: see text]X[Formula: see text]. Elements are connected by means of geometrical constraint equations. A compact algorithm for formulating and integrating the equations of motion is given. Models and programs are verified by comparing the results to those obtained by analytical solution and those from the finite element method. Finally, they are used to solve a benchmark problem encountered in nonlinear dynamic analysis of multibody systems.

NUMERICAL ANALYSIS OF THE FINITE ELEMENT METHOD APPLIED TO THE BOLTZMANN-POISSON SYSTEM

1995 ◽  
Vol 05 (03) ◽  
pp. 351-365 ◽  
Author(s):  
V. SHUTYAEV ◽  
O. TRUFANOV
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Analysis ◽  
Semiconductor Device ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Poisson System ◽  
The Finite Element Method ◽  
Initial Boundary Value ◽  
Element Method

This paper is concerned with the numerical analysis of the mathematical model for a semiconductor device with the use of the Boltzmann equation. A mixed initial-boundary value problem for nonstationary Boltzmann-Poisson system in the case of one spatial variable is considered. A numerical algorithm for solving this problem is constructed and justified. The algorithm is based on an iterative process and the finite element method. A numerical example is presented.

Finite Element Method-based geomechanical risk assessment of underground laboratory located in the deep copper mine

2021 ◽  
Author(s):  
Krzysztof Fulawka ◽  
Witold Pytel ◽  
Piotr Mertuszka ◽  
Marcin Szumny
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Analysis ◽  
New Technologies ◽  
Radiation Detection ◽  
Underground Laboratory ◽  
Design Stage ◽  
Copper Mine ◽  
Geophysical Surveys ◽  
Element Method

<p>Underground laboratories provide a unique environment for various industries and are a suitable place for developing new technologies for mining, geophysical surveys, radiation detection, as well as many other studies and measurements. Unfortunately, any operation in underground excavations is associated with exposure to many hazards not necessarily encountered in surface laboratories. One of the most dangerous events observed in underground conditions is the dynamic manifestation of rock mass pressure in form of rockburst, roof falls and mining tremors. Therefore, proper evaluation of geomechanical risk is a key element ensuring the safety of work in underground conditions. Finite Element Method-based numerical analysis is one of the tools which allow conducting a detailed geomechanical hazard assessment already at the object design stage. The results of such calculations may be the basis for the implementation of preventive measures before running up the underground facility.</p><p>Within this paper, the three-dimensional FEM-based numerical analysis of large-scale underground laboratory located in deep Polish copper mine was presented. The calculations were made with GTS NX software, which allowed determining the changes in the safety factor in surrounding of the analyzed area. Finally, the possibility of underground laboratory establishment, with respect to predicted stress and strain conditions, were determined.</p>

Flexible Multibody Dynamics Formulation by Hamilton’s Equations

2010 ◽  
Author(s):  
Martin M. Tong
Keyword(s):  
Multibody Dynamics ◽  
Multibody System ◽  
Mass Matrix ◽  
Equations Of Motion ◽  
Flexible Multibody Dynamics ◽  
Flexible Body ◽  
Flexible Multibody System ◽  
Generalized Coordinates ◽  
Flexible Multibody ◽  
The Matrix

Numerical solution of the dynamics equations of a flexible multibody system as represented by Hamilton’s canonical equations requires that its generalized velocities q˙ be solved from the generalized momenta p. The relation between them is p = J(q)q˙, where J is the system mass matrix and q is the generalized coordinates. This paper presents the dynamics equations for a generic flexible multibody system as represented by p˙ and gives emphasis to a systematic way of constructing the matrix J for solving q˙. The mass matrix is shown to be separable into four submatrices Jrr, Jrf, Jfr and Jff relating the joint momenta and flexible body mementa to the joint coordinate rates and the flexible body deformation coordinate rates. Explicit formulas are given for these submatrices. The equations of motion presented here lend insight to the structure of the flexible multibody dynamics equations. They are also a versatile alternative to the acceleration-based dynamics equations for modeling mechanical systems.

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