A New Formulation of Finite Element Equations of Motion for Geometrically Nonlinear Dynamics Analysis

1988 ◽  
pp. 1101-1104
Author(s):  
Nobutoshi Masuda ◽  
Takeo Nishiwaki ◽  
Masaru Minagawa
Keyword(s):  
Nonlinear Dynamics ◽  
Finite Element ◽  
Equations Of Motion ◽  
Dynamics Analysis ◽  
Geometrically Nonlinear ◽  
New Formulation

Nonlinear Dynamics Analysis of a Printed Wiring Board With Simple and Clamped Boundary Conditions

2001 ◽  
Author(s):  
Xiaoling He
Keyword(s):  
Nonlinear Dynamics ◽  
Boundary Conditions ◽  
Equations Of Motion ◽  
Nonlinear Resonance ◽  
Failure Criteria ◽  
Dynamics Analysis ◽  
Printed Wiring Board ◽  
Resonance Behavior ◽  
Condition Effect ◽  
Wiring Board

Abstract Dynamic response of a printed wiring board (PWB) is analyzed in nonlinear dynamics approach. Equations of motion for the simply supported PWB and the clamped PWB are obtained by the Galerkin’s method. A 2-layer plastic PWB made of isotropic laminates is studied for its boundary condition effect on the vibratory behavior in deflection and stresses. Failure due to plane stress interaction is estimated based on the composite failure criteria. It is found that nonlinear resonance occurs almost periodically in both frequency and temporal domain. Load frequency and magnitude affect the deflection response under different boundary conditions. Resonance behavior is critical in PWB failure prediction based on the stress analysis. The analytical results can be extended to the nonlinear dynamics analysis of the thin laminated plate.

The Influence of Loading Position in A Priori High Stress Detection using Mode Superposition

2020 ◽  
Vol 1 (1) ◽  
pp. 93-102
Author(s):  
Carsten Strzalka ◽  
◽  
Manfred Zehn ◽  
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
A Priori ◽  
High Stress ◽  
Von Mises Stress ◽  
Detailed Knowledge ◽  
Variable Loading ◽  
Numerical Effort ◽  
Von Mises

For the analysis of structural components, the finite element method (FEM) has become the most widely applied tool for numerical stress- and subsequent durability analyses. In industrial application advanced FE-models result in high numbers of degrees of freedom, making dynamic analyses time-consuming and expensive. As detailed finite element models are necessary for accurate stress results, the resulting data and connected numerical effort from dynamic stress analysis can be high. For the reduction of that effort, sophisticated methods have been developed to limit numerical calculations and processing of data to only small fractions of the global model. Therefore, detailed knowledge of the position of a component’s highly stressed areas is of great advantage for any present or subsequent analysis steps. In this paper an efficient method for the a priori detection of highly stressed areas of force-excited components is presented, based on modal stress superposition. As the component’s dynamic response and corresponding stress is always a function of its excitation, special attention is paid to the influence of the loading position. Based on the frequency domain solution of the modally decoupled equations of motion, a coefficient for a priori weighted superposition of modal von Mises stress fields is developed and validated on a simply supported cantilever beam structure with variable loading positions. The proposed approach is then applied to a simplified industrial model of a twist beam rear axle.

Modeling and nonlinear dynamics analysis of a rotating beam with dry friction support boundary conditions

2021 ◽  
Vol 498 ◽  
pp. 115978
Author(s):  
Chaofeng Li ◽  
Xiaowen Liu ◽  
Qiansheng Tang ◽  
Zilin Chen
Keyword(s):  
Nonlinear Dynamics ◽  
Boundary Conditions ◽  
Dry Friction ◽  
Dynamics Analysis ◽  
Rotating Beam

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.

Topology Synthesis of Compliant Mechanisms for Nonlinear Force-Deflection and Curved Path Specifications

1999 ◽  
Vol 123 (1) ◽  
pp. 33-42 ◽  
Author(s):  
A. Saxena ◽  
G. K. Ananthasuresh
Keyword(s):  
Finite Element ◽  
Linear Models ◽  
Compliant Mechanisms ◽  
Synthesis Method ◽  
Design Sensitivity ◽  
Finite Element Models ◽  
Geometrically Nonlinear ◽  
Linear Elastic ◽  
Nonlinear Design ◽  
Nonlinear Force

Optimal design methods that use continuum mechanics models are capable of generating suitable topology, shape, and dimensions of compliant mechanisms for desired specifications. Synthesis procedures that use linear elastic finite element models are not quantitatively accurate for large displacement situations. Also, design specifications involving nonlinear force-deflection characteristics and generation of a curved path for the output port cannot be realized with linear models. In this paper, the synthesis of compliant mechanisms is performed using geometrically nonlinear finite element models that appropriately account for large displacements. Frame elements are chosen because of ease of implementation of the general approach and their ability to capture bending deformations. A method for nonlinear design sensitivity analysis is described. Examples are included to illustrate the usefulness of the synthesis method.

Combined finite element and multi-body dynamics analysis of effects of hydraulic cylinder movement on ploughshare of Horizontally Reversible Plough

2016 ◽  
Vol 163 ◽  
pp. 168-175 ◽  
Author(s):  
Lin Zhu ◽  
Shuang-Shuang Peng ◽  
Xi Cheng ◽  
Yin-Yin Qi ◽  
Jia-Ru Ge ◽  
...  
Keyword(s):  
Finite Element ◽  
Hydraulic Cylinder ◽  
Dynamics Analysis ◽  
Body Dynamics ◽  
Multi Body
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