Mixed Finite Element Analysis of Elastomeric Butt-Joints

2005 ◽  
Vol 129 (1) ◽  
pp. 11-18 ◽  
Author(s):  
P. A. Kakavas ◽  
G. I. Giannopoulos ◽  
N. K. Anifantis
Keyword(s):  
Finite Element ◽  
Strain Energy ◽  
Poisson Ratio ◽  
Mixed Finite Element ◽  
Three Dimensional ◽  
Butt Joint ◽  
Element Formulation ◽  
Butt Joints ◽  
Element Analysis ◽  
Strain Energy Density Function

This paper presents a mixed finite element formulation approximating large deformations observed in the analysis of elastomeric butt-joints. The rubber has been considered as nearly incompressible continuum obeying the Mooney/Rivlin (M/R) strain energy density function. The parameters of the model were determined by fitting the available from the literature uniaxial tension experimental data with the constitutive equation derived from the M/R model. The optimum value of the Poisson ratio is adjusted by comparing the experimentally observed diametral contraction of the model with that numerically obtained using the finite element method. The solution of the problem has been obtained utilizing the mixed finite element procedure on the basis of displacement/pressure mixed interpolation and enhanced strain energy mixed formulation. For comparison purposes, an axisymmetric with two-parameter M/R model and a three-dimensional (3D) with nine-parameters M/R model of the butt-joint are formulated and numerical results are illustrated concerning axisymmetric or general loading. For small strains the stress and/or strain distribution in the 2D axisymmetric butt-joint problem was compared with derived analytical solutions. Stress distributions along critical paths are evaluated and discussed.

Development of A Three-Dimensional Membrane Element for the Finite Element Analysis of Tires

1991 ◽  
Vol 19 (1) ◽  
pp. 23-36 ◽  
Author(s):  
K. Ishihara
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Computing Time ◽  
Three Dimensional ◽  
Complex Nature ◽  
Element Formulation ◽  
Membrane Element ◽  
Element Analysis ◽  
The Finite Element Analysis ◽  
Modeling Strategy

Abstract A three-dimensional membrane element was developed for the finite element analysis of tires. In general, the three-dimensional finite element analysis of tires uses a lot of computing time because of the complex nature of the problem. Major sources of complexity are, for example, nonlinearities in kinematics, material properties, boundary conditions, and the multilayer structure which is inherent to the tire. One of the ways to overcome this situation can be in the modeling strategy. This paper describes an approach where the cord-rubber composite components of the tire are modeled by membrane elements. The number of nodes required in the tire model using this strategy is considerably reduced, without any loss of accuracy, compared with models in which only ordinary solid elements are used. The nonlinear finite element formulation, numerical examples, and a comparison of the results with those obtained from models using solid elements and experimental values are given in the paper.

The Cosserat Point Element as an Accurate and Robust Finite Element Formulation for Implicit Dynamic Simulations

2019 ◽  
Vol 17 (01) ◽  
pp. 1844006
Author(s):  
Mahmood Jabareen ◽  
Yehonatan Pestes
Keyword(s):  
Finite Element ◽  
Energy Function ◽  
Strain Energy ◽  
Three Dimensional ◽  
Nonlinear Dynamic Analysis ◽  
Strain Energy Function ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Dynamic Simulations ◽  
Cosserat Point

The reliability of numerical simulations manifested the need for an accurate and robust finite element formulation. Therefore, in the present study, an eight node brick Cosserat point element ( CPE ) for the nonlinear dynamic analysis of three-dimensional (3D) solids including both thick and thin structures is developed. Within the present finite element formulation, a strain energy function is proposed and additively decoupled into two parts. One part is characterized by any 3D strain energy function, while the other part controls the response to inhomogeneous deformations. Several example problems are presented, which demonstrate the accuracy and the robustness of the developed CPE in modeling the dynamic response of elastic structures.

A Lagrange Multiplier Mixed Finite Element Formulation for Three-Dimensional Contact of Biphasic Tissues

2006 ◽  
Vol 129 (3) ◽  
pp. 457-471 ◽  
Author(s):  
Taiseung Yang ◽  
Robert L. Spilker
Keyword(s):  
Finite Element ◽  
Soft Tissue ◽  
Lagrange Multiplier ◽  
Contact Surface ◽  
Lagrange Multipliers ◽  
Mixed Finite Element ◽  
Three Dimensional ◽  
Contact Analysis ◽  
Finite Element Formulation ◽  
Element Formulation

A three-dimensional (3D) contact finite element formulation has been developed for biological soft tissue-to-tissue contact analysis. The linear biphasic theory of Mow, Holmes, and Lai (1984, J. Biomech., 17(5), pp. 377–394) based on continuum mixture theory, is adopted to describe the hydrated soft tissue as a continuum of solid and fluid phases. Four contact continuity conditions derived for biphasic mixtures by Hou et al. (1989, ASME J. Biomech. Eng., 111(1), pp. 78–87) are introduced on the assumed contact surface, and a weighted residual method has been used to derive a mixed velocity-pressure finite element contact formulation. The Lagrange multiplier method is used to enforce two of the four contact continuity conditions, while the other two conditions are introduced directly into the weighted residual statement. Alternate formulations are possible, which differ in the choice of continuity conditions that are enforced with Lagrange multipliers. Primary attention is focused on a formulation that enforces the normal solid traction and relative fluid flow continuity conditions on the contact surface using Lagrange multipliers. An alternate approach, in which the multipliers enforce normal solid traction and pressure continuity conditions, is also discussed. The contact nonlinearity is treated with an iterative algorithm, where the assumed area is either extended or reduced based on the validity of the solution relative to contact conditions. The resulting first-order system of equations is solved in time using the generalized finite difference scheme. The formulation is validated by a series of increasingly complex canonical problems, including the confined and unconfined compression, the Hertz contact problem, and two biphasic indentation tests. As a clinical demonstration of the capability of the contact analysis, the gleno-humeral joint contact of human shoulders is analyzed using an idealized 3D geometry. In the joint, both glenoid and humeral head cartilage experience maximum tensile and compressive stresses are at the cartilage-bone interface, away from the center of the contact area.

Stiffness and design for strength of trapezoidal Belleville springs

2011 ◽  
Vol 46 (8) ◽  
pp. 825-836 ◽  
Author(s):  
N L Pedersen ◽  
P Pedersen
Keyword(s):  
Finite Element ◽  
Stress Distribution ◽  
Cross Sections ◽  
Poisson Ratio ◽  
Three Dimensional ◽  
Displacement Curve ◽  
Structural Behaviour ◽  
Design Standards ◽  
Element Analysis ◽  
Non Linear

Belleville springs or coned disc springs are commonly used in machine design. The geometric dimensions of the spring and the determination of non-linear force–displacement curve are regulated by different standards. However, the theory behind Belleville spring design standards is founded on a study published in 1936. Furthermore, the common spring design with cross-sections of uniform thickness poses problems in terms of non-uniformity of stress distribution. In view of this, non-linear three-dimensional finite element analyses of spring designs including uniform or variable thickness are carried out in this paper. Finite element results are compared with analytical predictions and critically analysed in terms of the effect of Poisson ratio, overall stiffness, and stress distribution in the spring. This is done in order to verify the range of validity of design standards. Finite element analysis emerges as a powerful and computationally cheap approach to assess the structural behaviour of Belleville springs regardless of their geometry and level of non-linearity.

scholarly journals Finite Element Formulation of Fractional Constitutive Laws Using the Reformulated Infinite State Representation

2021 ◽  
Vol 5 (3) ◽  
pp. 132
Author(s):  
Matthias Hinze ◽  
André Schmidt ◽  
Remco I. Leine
Keyword(s):  
Finite Element ◽  
Three Dimensional ◽  
Constitutive Law ◽  
Benchmark Problems ◽  
Element Formulation ◽  
Algebraic Equations ◽  
State Representation ◽  
Element Analysis ◽  
Closed Form Solutions ◽  
Infinite State

In this paper, we introduce a formulation of fractional constitutive equations for finite element analysis using the reformulated infinite state representation of fractional derivatives. Thereby, the fractional constitutive law is approximated by a high-dimensional set of ordinary differential and algebraic equations describing the relation of internal and external system states. The method is deduced for a three-dimensional linear viscoelastic continuum, for which the hydrostatic and deviatoric stress-strain relations are represented by a fractional Zener model. One- and two-dimensional finite elements are considered as benchmark problems with known closed form solutions in order to evaluate the performance of the scheme.

Acoustic Finite Element Analysis of Coupled Cavities Having Bulk-Reacting Absorbing Materials

1995 ◽  
Author(s):  
A. Qian ◽  
R. S. Ballinger
Keyword(s):  
Finite Element ◽  
Three Dimensional ◽  
Propagation Speed ◽  
Acoustic Medium ◽  
Element Formulation ◽  
Element Analysis ◽  
One Dimensional ◽  
Cavity Structure ◽  
Absorbing Material ◽  
Complex Propagation

Abstract This research presents the finite element formulation of a bulk-reacting sound absorbing material for use in interior cavity solutions. The bulk properties of the absorbing material are represented by complex density and complex propagation speed. Coupling between the vibrating cavity structure and the acoustic medium is considered. The continuity of sound pressure and the particle velocity at the interface between the acoustic domains having different properties is satisfied. Two case studies, a one-dimensional duct and a three-dimensional cavity, are considered. Analytical solutions and experimental results are compared to the finite element results. Excellent agreement has been achieved.

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