A Finite Element Geometrically Nonlinear Dynamic Formulation of Flexible Multibody Systems Using a New Displacements Representation

1997 ◽  
Vol 119 (4) ◽  
pp. 573-581 ◽  
Author(s):  
J. Mayo ◽  
J. Domi´nguez
Keyword(s):  
Finite Element ◽  
Multibody Systems ◽  
Strain Energy ◽  
Degrees Of Freedom ◽  
Synthesis Method ◽  
Geometrically Nonlinear ◽  
Motion Equations ◽  
Constant Stiffness ◽  
Elastic Nonlinearity ◽  
External Forces

In previous work (Mayo, 1993), the authors developed two geometrically nonlinear formulations of beams inflexible multibody systems. One, like most related methods, includes geometric elastic nonlinearity in the motion equations via the stiffness terms (Mayo and Domi´nguez, 1995), but preserving terms, in the expression for the strain energy, of a higher-order than most available formulations. The other formulation relies on distinguishing the contribution of the foreshortening effect from that of strain in modelling the displacement of a point. While including exactly the same nonlinear terms in the expression for the strain energy, the stiffness terms in the motion equations generated by this formulation are exclusively limited to the constant stiffness matrix for the linear analysis because the terms arising from geometric elastic nonlinearity are moved from elastic forces to inertial, reactive and external forces, which are originally nonlinear. This formulation was reported in a previous paper (Mayo et al, 1995) and used in conjunction with the assumed-modes method. The aim of the present work is to implement this second formulation on the basis of the finite-element method. If, in addition, the component mode synthesis method is applied to reduce the number of degrees of freedom, the proposed formulation takes account of the effect of geometric elastic nonlinearity on the transverse displacements occurring during bending without the need to include any axial vibration modes. This makes the formulation particularly efficient in computational terms and numerically more stable than alternative geometrically nonlinear formulations based on lower-order terms.

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.

Dynamic Analysis of a Mobile Mechanical System with Deformable Elements

2012 ◽  
Vol 463-464 ◽  
pp. 1242-1245 ◽  
Author(s):  
Nicolae Dumitru ◽  
Raluca Malciu ◽  
Madalina Calbureanu ◽  
Sorin Dumitru ◽  
Gabriel Cătălin Marinescu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Elements ◽  
Multibody Systems ◽  
Degrees Of Freedom ◽  
System Modeling ◽  
Rigid Motion ◽  
Elastic Solid ◽  
Constant Matrix ◽  
Lagrange Formulation

The paper presents a method for studying mechanisms with deformable elements, based on overlapping the solid rigid motion over the elastic solid one, in order to identify the dynamic response of the system. Modeling was based on finite element method, so the cinematic elements were meshed in bar type finite elements and the degrees of freedom per node were settled according to the motion character (planar or spatial). A Lagrange formulation of the finite element was adopted for the deformable elements connected in multibody systems. In order to define the joints constraints, the conditions for compatibility between elements were defined using a Boolean constant matrix. Computer processed results were verified by an experimental model.

Non-Linear FE Approach for Flexible Multibody Simulation of Mechanism Dynamics

1998 ◽  
Author(s):  
Ole Ivar Sivertsen
Keyword(s):  
Finite Element ◽  
Multibody Systems ◽  
Nonlinear Finite Element ◽  
Component Mode Synthesis ◽  
Simulation Approach ◽  
Multibody Simulation ◽  
Non Linear ◽  
Flexible Multibody ◽  
External Forces

Abstract The simulation approach presented in this paper is based on a nonlinear Finite Element (FE) formulation for modelling of multibody systems (MBS). This formulation is developed to include a comprehensive library of MBS elements as links, joints, springs, dampers and external forces. The links are modelled as FE substructures and reduced to super elements by component mode synthesis (CMS). Super nodes are used for modelling of the mechanism elements referred to above.

scholarly journals Finite Element Modelling and Simulating Effects of Hairiness Performance on Hairiness Entanglement During Fabric Pilling

2021 ◽  
Author(s):  
Qi Xiao ◽  
Rui Wang ◽  
Hongyu Sun ◽  
Jingru Wang
Keyword(s):  
Finite Element ◽  
Finite Element Simulation ◽  
Strain Energy ◽  
Dissipation Energy ◽  
Motion Equations ◽  
Dynamic Motion ◽  
Element Simulation ◽  
Frictional Dissipation ◽  
Simulation Results ◽  
Good Agreement

Abstract For analyzing behaviors of hairiness entanglement during fabric pilling, nonlinear dynamic motion equations are deduced based on the elastic thin rod element, combined with the moving characteristics of hairiness, which follow the principles of mechanical equilibrium and energy conservation. The finite element simulation model of the effects of hairiness performance on behaviors of hairiness entanglement was established by ABAQUS. The analysis solution values of nonlinear dynamics were compared with the finite element simulation results. The results showed that hairiness elastic modulus, hairiness friction coefficient and hairiness diameter have significant effects on frictional dissipation energy, strain energy and kinetic energy produced by hairiness entanglement during pilling. Compared the finite element simulation results with analysis solution values, they are in good agreement. The fitness is greater than 0.96, which verifies the validity of finite element method.

A Simplified Strain Energy Function to Represent the Mechanical Behavior of the Annulus Fibrosus

2009 ◽  
Author(s):  
Jose J. García ◽  
Christian Puttlitz
Keyword(s):  
Finite Element ◽  
Mechanical Behavior ◽  
Energy Function ◽  
Annulus Fibrosus ◽  
Strain Energy ◽  
Degrees Of Freedom ◽  
Strain Energy Function ◽  
Efficient Simulation ◽  
Matrix Interactions ◽  
Complex Functions

Models to represent the mechanical behavior of the annulus fibrosus are important tools to understand the biomechanics of the spine. Many hyperelastic constitutive equations have been proposed to simulate the mechanical behavior of the annulus that incorporate the anisotropic nature of the tissue. Recent approaches [1,2] have included terms into the energy function which take into account fiber-fiber and fiber-matrix interactions, leading to complex functions that cannot be readily implemented into commercial finite element codes for an efficient simulation of nonlinear realistic models of the spine (which are generally composed of 100,000+ degrees of freedom). An effort is undertaken here to test the capability of a relatively simple strain energy function [3] for the description of the annulus fibrosus. This function has already been shown to successfully represent the mechanical behavior of the arterial tissue and can be readily implemented into existing finite element codes.

Component Mode Synthesis of a Vehicle System Model Using the Fictitious Mass Method

2006 ◽  
Vol 129 (1) ◽  
pp. 73-83 ◽  
Author(s):  
M. Karpel ◽  
B. Moulin ◽  
V. Feldgun
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Structural Model ◽  
Synthesis Method ◽  
Normal Modes ◽  
Low Frequency ◽  
Component Mode Synthesis ◽  
Response Analysis ◽  
Element Analysis ◽  
Local Boundary

A new procedure for dynamic analysis of complex structures, based on the fictitious-mass component mode synthesis method, is presented. Normal modes of separate components are calculated by finite-element analysis with the interface coordinates loaded with fictitious masses that generate local boundary deformations in the low-frequency modes. The original fictitious-mass method is extended to include three types of component interconnections: displacement constraints, connection elements, and structural links. The connection elements allow the introduction of springs and dampers between the interface points without adding structural degrees of freedom. The structural links facilitate the inclusion the discrete finite-element representation of typically small components in the coupling equations. This allows a convenient treatment of loose elements and the introduction of nonlinear effects and parametric studies in subsequent analyses. The new procedure is demonstrated with the structural model of a typical vehicle with four major substructures and a relatively large number of interface coordinates. High accuracy is obtained in calculating the natural frequencies and modes of the assembled structure and the separate components with the fictitious masses removed. Dynamic response analysis of the vehicle travelling over a rough road, performed by modal coupling, is in excellent agreement with that performed for the full model.

Stress Analysis of a Tire Under Vertical Load by a Finite Element Method

1977 ◽  
Vol 5 (2) ◽  
pp. 102-118 ◽  
Author(s):  
H. Kaga ◽  
K. Okamoto ◽  
Y. Tozawa
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Computer Program ◽  
Temperature Rise ◽  
Strain Energy ◽  
Internal Stresses ◽  
Vertical Load ◽  
The Finite Element Method ◽  
Internal Temperature ◽  
Element Method

Abstract An analysis by the finite element method and a related computer program is presented for an axisymmetric solid under asymmetric loads. Calculations are carried out on displacements and internal stresses and strains of a radial tire loaded on a road wheel of 600-mm diameter, a road wheel of 1707-mm diameter, and a flat plate. Agreement between calculated and experimental displacements and cord forces is quite satisfactory. The principal shear strain concentrates at the belt edge, and the strain energy increases with decreasing drum diameter. Tire temperature measurements show that the strain energy in the tire is closely related to the internal temperature rise.

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.

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