Finite element method in nonlinear dynamic analysis of axisymmetric shells: theory and computer program. [LMFBR]

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.

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Dynamic Analysis of Bolted Cantilever Beam with Finite Element Method Considering Thread Relation

Applied Sciences ◽

10.3390/app10207036 ◽

2020 ◽

Vol 10 (20) ◽

pp. 7036

Author(s):

Chao Cao ◽

Xueyan Zhao ◽

Zhenghe Song

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Dynamic Response ◽

Dynamic Analysis ◽

Cantilever Beam ◽

Nonlinear Dynamic ◽

Beam Model ◽

Nonlinear Phenomenon ◽

Bolted Joint ◽

Element Method

There are complex nonlinear behaviors and mechanisms in the bolted joint interface. Thus, the bolted joint is crucial to the complex nonlinear dynamic response of the structure. However, in the traditional structural dynamic analysis, the screw connection is usually neglected, which makes it challenging to analyze and study the nonlinear dynamic behavior of bolted structures. Hence, based on the Timoshenko beam theory and finite element method, this paper introduces a model considering thread connection to analyze the dynamic response under different excitation. Eventually, the results indicate that owing to the local nonlinearity of bolts, the whole bolted cantilever beam shows hardening-type characteristics. In addition, the frequency response curve also depicts the typical nonlinear phenomenon of instability and uncertainty, namely bifurcation, which preliminarily verifies the correctness and accuracy of the bolted cantilever beam model.

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Stochastic Finite Element Method for Nonlinear Dynamic Problem with Random Parameters

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.189-193.1348 ◽

2011 ◽

Vol 189-193 ◽

pp. 1348-1357

Author(s):

Qing Wang ◽

Yang Cao

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Nonlinear Dynamic ◽

Dynamic Problem ◽

Nonlinear Dynamic Analysis ◽

Stochastic Finite Element Method ◽

Random Parameters ◽

Stochastic Finite Element ◽

Nonlinear Dynamic Problem ◽

Element Method

Several algorithms were proposed relating to the development of a framework of the perturbation-based stochastic finite element method (PSFEM) for nonlinear dynamic problem with random parameters, for this purpose, based on the stochastic virtual work principle , some algorithms and a framework related to SFEM have been studied. An interpolation method was used to discretize the random fields, which is based on representing the random field in terms of an interpolation rule involving a set of deterministic shape functions. Direct integration Wilson- Method in conjunction with Newton-Raphson scheme was adopted to solve finite element equations. Numerical examples were compared with Monte-Carlo simulation method to show that the approaches proposed herein are accurate and effective for the nonlinear dynamic analysis of structures with random parameters

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