Nonlinear Load-Deflection Relations of Bonded Elastomeric Circular Disks and Strips

1992 ◽  
Vol 65 (5) ◽  
pp. 917-931 ◽  
Author(s):  
Yun Ling ◽  
Peter A. Engel ◽  
William L. Brodsky
Keyword(s):  
Finite Element ◽  
Empirical Formula ◽  
Ritz Method ◽  
Element Analysis ◽  
Energy Functions ◽  
Nonlinear Load ◽  
Shape Factors ◽  
Strain Energy Functions ◽  
Circular Disks ◽  
Large Shape

Abstract The nonlinear load-deflection relations of bonded circular disks and infinitely long strips are studied. Finite element analysis is used to evaluate the empirical formula proposed by Payne, which justifies the need for a better formula to predict the load-deflection relation for blocks with large shape factors under a relatively large deformation. General expressions for the load-deflection relations of blocks under axisymmetrical and plane-strain deformations are presented based on a variational approach, i.e. the Raleigh-Ritz method, in which no specific form of strain energy functions is required. Nonlinear load-deflection relations of circular discs and infinitely long strips made of a Mooney-Rivlin material are explicitly given in a power series form. It is found that these solutions agree well with the finite element results and are much more accurate than the empirical formula. It is shown that the solutions obtained by the Raleigh-Ritz method are not sensitive to deformations assumed.

Finite Bending and Straightening of Hyperelastic Materials: Analytical Solution and FEM

2019 ◽  
Vol 11 (09) ◽  
pp. 1950084 ◽  
Author(s):  
Sara Sheikhi ◽  
Mohammad Shojaeifard ◽  
Mostafa Baghani
Keyword(s):  
Finite Element ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Optimization Procedure ◽  
Element Analysis ◽  
Energy Functions ◽  
Hyperelastic Materials ◽  
Finite Bending ◽  
Strain Energy Functions ◽  
Analytical Approaches

In this research, an incompressible, isotropic, nonlinear elastic rectangular block and a circular cylindrical sector are studied under bending and straightening moments, respectively. Analytical approaches are presented on implementing of the left Cauchy–Green tensor and Cauchy stresses. In addition, finite element analysis of both problems is carried out using UHYPER user-defined subroutine in ABAQUS to verify the analytical methods. Four different invariant-based strain energy functions, including neo-Hookean, Mooney–Rivlin, Arruda–Boyce, and recently proposed polynomial Exp-Exp models, are examined, and the results are compared. Material parameters of silicon rubber for the strain energy functions are identified by applying an optimization procedure. Finite element method results confirmed the analytical approach with great compatibility. Results showed that the length of the unbent beam does not affect the stress. Likewise, the initial angle of curved structure does not affect the unbending moment and stresses. Moreover, the Exp-Exp model had a slightly different result rather than other strain energies, which means that this model is more conservative than its counterparts. Furthermore, the Exp-Exp strain energy function is calibrated for tissue-like phantom and is compared with experimental data.

Finite Element Analysis by Using Hyper-Elastic Properties for Rubber Component

2011 ◽  
Vol 488-489 ◽  
pp. 190-193
Author(s):  
Chang Su Woo ◽  
Hyun Sung Park ◽  
Wae Gi Shin
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Element Analysis ◽  
Energy Functions ◽  
Hyper Elastic ◽  
Rubber Component ◽  
Strain Energy Functions

The material modeling of hyper-elastic properties in rubber is generally characterized by the strain energy function. The strain energy functions have been represented either in term of the strain in variants that are functions of the stretch ratios, or directly in terms of the principal stretch. Successful modeling and design of rubber components relies on both the selection of an appropriate strain energy function and an accurate determination of material constants in the function. Material constants in the strain energy functions can be determined from the curve fitting of experimental stress-strain data. The uniaxial tension, equi-biaxial tension and pure shear test were performed to acquire the constants of the strain energy functions which were Mooney-Rivlin and Ogden model. Nonlinear finite element analysis was executed to evaluate the behavior of deformation and strain distribute by using the commercial finite element code. Also, the fatigue tests were carried out to obtain the fatigue failure. Fatigue failure was initiated at the critical location was observed during the fatigue test of rubber component, which was the same result predicted by the finite element analysis.

Evaluation and Repair of Cracks on Statically Loaded Beams Using Piezoelectric Actuation

2021 ◽  
Vol 11 (1) ◽  
pp. 34-49
Author(s):  
Goutam Roy ◽  
Brajesh Kumar Panigrahi ◽  
Goutam Pohit
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Ritz Method ◽  
Actuation Voltage ◽  
Piezoelectric Actuation ◽  
Cracked Beam ◽  
Element Analysis ◽  
Various Boundary Conditions ◽  
Piezoelectric Patch ◽  
Loading Patterns

In the present work, damage produced by a crack in a statically loaded beam is first evaluated. Subsequently, an attempt is made to repair the effect of the crack by attaching a piezoelectric patch to the beam as an actuator. Static analysis of PZT patched cracked beam along with rotational spring is performed using Ritz method. Subsequently, a finite element analysis is performed by using ABAQUS 6.12 to collate the analytical results. It is shown in the study that when PZT patch is subjected to external electric field, it yields a local reactive moment, which counters the crack effects. An equation is procured in order to compute the required actuation voltage for repairing of cracks. A parametric study is performed for various boundary conditions and loading patterns. It is distinctly noticed that the technique nullifies the discontinuity in slope curve which develops due to a crack.

Finite Element Analysis of Load-Deflection and Creep Characteristics of Compressed Rubber Components for Vibration Control Devices

1996 ◽  
Vol 118 (3) ◽  
pp. 328-336 ◽  
Author(s):  
B. S. Lee ◽  
E. I. Rivin
Keyword(s):  
Finite Element ◽  
High Performance ◽  
Power Transmission ◽  
Cylindrical Shape ◽  
Element Analysis ◽  
Nonlinear Load ◽  
Rubber Blends ◽  
Creep Characteristics ◽  
Control Devices ◽  
Nonlinear Components

Elastomeric (rubber-like) materials are extensively used in various machine design applications, particularly for flexible elements of vibration/shock/noise control devices and of power transmission couplings. In order to have high performance characteristics, such elements should accommodate large static and dynamic loads and/or large deflections in a limited size. In many applications high damping, low creep and substantial nonlinearity of the load-deflection characteristic are required. These contradictory requirements are often impossible to satisfy just by selecting special rubber blends. It was demonstrated in [9] that for unbonded rubber flexible elements of a cylindrical shape loaded in a radial direction, desirable nonlinear load-deflection characteristics can be naturally obtained, and creep rate can be significantly reduced as compared with conventional shapes of bonded rubber elements loaded in compression. This paper presents the second part of the study [9]. It applies the Finite Element Method to analyze large deformations of nonlinear components made of viscoelastic materials. Some convenient and efficient methods are proposed to determine material constants for the analytical study of static load-deflection characteristics and creep. These proposed methods result in good agreement between the numerical results and the experimental results in [9]

A Nested Finite Element Methodology (NFEM) for Stress Analysis of Electronic Products—Part I: Theory and Formulation

2000 ◽  
Vol 123 (2) ◽  
pp. 141-146 ◽  
Author(s):  
Krishna Darbha ◽  
Abhijit Dasgupta
Keyword(s):  
Finite Element ◽  
Stress Analysis ◽  
Ritz Method ◽  
Element Analysis ◽  
Thermomechanical Stress ◽  
Surface Mount ◽  
Field Displacement ◽  
Analysis Technique ◽  
P Type ◽  
Finite Element Methodology

In this paper, the authors present a stress analysis technique based on a novel nested finite element methodology (NFEM). The NFEM is similar in concept to an earlier proposed multi-domain Rayleigh-Ritz methodology (Ling, S., 1997, “A Multi-Domain Rayleigh-Ritz Method for Thermomechanical Stress Analysis of Surface Mount Interconnects in Electronic Assemblies,” Ph.D. dissertation, Univ., of Maryland), that is based on a nested multi-field displacement assumption. The nested multi-field displacement technique may be viewed as a localized cascading of the p-type refinement in conventional finite element analysis. The concept and formulation of NFEM are presented in this paper while the application of NFEM to analyze the viscoplastic stress-state in two popular surface mount electronic interconnect styles is presented in Part II of this series. To illustrate the concept of NFEM, the formulation and results are provided for a one-dimensional viscoplastic example.

scholarly journals Wrinkling of Tympanic Membrane Under Unbalanced Pressure

2017 ◽  
Vol 84 (4) ◽  
Author(s):  
Bo Wang ◽  
Pravarsha Ghanta ◽  
Sandra Vinnikova ◽  
Siyuan Bao ◽  
Junfeng Liang ◽  
...  
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Analytical Solution ◽  
Tympanic Membrane ◽  
Middle Ear ◽  
Approximate Analytical Solution ◽  
Ritz Method ◽  
Transmission Function ◽  
Acoustic Transmission ◽  
Element Analysis

Mechanics of tympanic membrane (TM) is crucial for investigating the acoustic transmission through the ear. In this study, we studied the wrinkling behavior of tympanic membrane when it is exposed to mismatched air pressure between the ambient and the middle ear. The Rayleigh–Ritz method is adopted to analyze the critical wrinkling pressure and the fundamental eigenmode. An approximate analytical solution is obtained and validated by finite element analysis (FEA). The model will be useful in future investigations on how the wrinkling deformation of the TM alters the acoustic transmission function of the ear.

Compressive Stress Relaxation and Nonlinear Finite Element Analysis of Ethylene/Acrylic Vamac® Terpolymer Elastomer (AEM)

2004 ◽  
Author(s):  
Rick D. Fong ◽  
Erol Sancaktar
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Stress Relaxation ◽  
Compressive Stress ◽  
Nonlinear Finite Element Analysis ◽  
Nonlinear Finite Element ◽  
Time Dependency ◽  
Element Analysis ◽  
Shape Factors

The main purpose of this paper is to investigate the time dependency of rubber viscoelastic characteristics at various shape factors (SF) and compression percentages (%), namely Compressive Stress Relaxation (CSR) and Retaining Sealing Force (RSF). Results from nonlinear Finite Element Analysis (FEA) were found corresponding with the static CSR data, which could be used for estimating long term CSR effects of particular products with similar SF and compression % and operation environments.

scholarly journals Design of 3D printable prosthetic foot to implement nonlinear stiffness behavior of human toe joint based on finite element analysis

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Hui-Jin Um ◽  
Heon-Su Kim ◽  
Woolim Hong ◽  
Hak-Sung Kim ◽  
Pilwon Hur
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Nonlinear Stiffness ◽  
Element Analysis ◽  
Shape Factors ◽  
Prosthetic Foot ◽  
Human Foot ◽  
Stiffness Characteristic ◽  
General Feeling ◽  
Foot Function

AbstractToe joint is known as one of the critical factors in designing a prosthetic foot due to its nonlinear stiffness characteristic. This stiffness characteristic provides a general feeling of springiness in the toe-off and it also affects the ankle kinetics. In this study, the toe part of the prosthetic foot was designed to improve walking performance. The toe joint was implemented as a single part suitable for 3D printing. The various shape factors such as curved shape, bending space, auxetic structure, and bending zone were applied to mimic human foot characteristics. The finite element analysis (FEA) was conducted to simulate terminal stance (from heel-off to toe-off) using the designed prosthetic foot. To find the structure with characteristics similar to the human foot, the optimization was performed based on the toe joint geometries. As a result, the optimized foot showed good agreement with human foot behavior in the toe torque-angle curve. Finally, the simulation conditions were validated by comparing with human walking data and it was confirmed that the designed prosthetic foot structure can implement the human foot function.

scholarly journals Design of 3D Printable Prosthetic Foot to Implement Nonlinear Stiffness Behavior of Human Toe Joint Based On Finite Element Analysis

2021 ◽  
Author(s):  
Hui-Jin Um ◽  
Heon-Su Kim ◽  
Woolim Hong ◽  
Hak-Sung Kim ◽  
Pilwon Hur
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Nonlinear Stiffness ◽  
Element Analysis ◽  
Shape Factors ◽  
Prosthetic Foot ◽  
Human Foot ◽  
Foot Structure ◽  
General Feeling ◽  
Foot Function

Abstract The toe joint is one of the critical factors in designing a prosthetic foot. This is because its nonlinear stiffness provides a general feeling of springiness in the toe-off and it also affects the ankle kinetics. In this study, the toe part of the prosthetic foot was designed to improve walking performance. The toe joint was implemented as a single part suitable for 3D printing. The various shape factors such as curved shape, bending space, auxetic structure, and bending zone were applied to mimic human foot characteristics. The finite element analysis (FEA) was conducted to simulate terminal stance (from heel-off to toe-off) using the designed prosthetic foot. To find the structure with characteristics similar to the human foot, the optimization was performed based on the toe joint geometries. As a result, the optimized foot showed good agreement with human foot behavior in the toe torque-angle curve. Finally, the simulation conditions were validated by comparing with human walking data and it was confirmed that the designed prosthetic foot structure can implement the human foot function.

scholarly journals Finite-Element Analysis on Compressive Performance of a Novel Glue-Laminated Cornstalk Scrimber

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Wei Tian ◽  
Yongmei Qian ◽  
Zunpeng Liu ◽  
Yiming Wang
Keyword(s):  
Finite Element ◽  
Axial Compression ◽  
Green Building ◽  
Building Industry ◽  
Transverse Displacement ◽  
Element Analysis ◽  
Nonlinear Load ◽  
Finite Element Software ◽  
Compressive Performance ◽  
Novel Material

Novel glue-laminated cornstalk scrimber is a new timber substitute produced by special techniques, without damaging the original fibers in cornstalks. This novel material outperforms ordinary timber in the resistance to water, damping, insect, and fire and provides a desirable green building material. However, glue-laminated cornstalk scrimber has not been widely implemented in the building industry, because the application of cornstalk products is limited to decoration panels. With the aid of the finite-element software Abaqus, this paper simulates the glue-laminated cornstalk scrimber specimens with different slenderness ratios under axial compression and analyzes the compressive performance of such specimens. The results show that the height of glue-laminated cornstalk scrimber is negatively correlated with the buckling load and nonlinear load under axial compression and positively correlated with the transverse displacement and axial displacements induced by axial compression. The research results provide a good reference for improving the design and application of glue-laminated cornstalk scrimber.

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