Torsional axisymmetric finite element model for problems in elasticity

1986 ◽  
Vol 13 (5) ◽  
pp. 583-587
Author(s):  
Ming G. Lau
Keyword(s):  
Finite Element ◽  
Element Model ◽  
Displacement Function ◽  
Infinite Medium ◽  
The State ◽  
Tangential Displacement ◽  
Shear Stresses ◽  
Pure Torsion ◽  
Typical Application ◽  
The Third

This note describes how the displacements and shear stresses of an axisymmetric elastic component, when loaded in torsion, can be computed by modelling the component with torsional axisymmetric finite elements. The model developed represents only minor modifications of the well-known plane stress or plane strain finite element technique.In the analysis, the model is split into a mesh of triangular annuli. Each node of each element has only one degree of freedom, the tangential displacement. The state of strain in each element is represented by a three-term displacement function, one representing a rigid body rotation, the second representing the state of torsion, and the third representing the state of strain in a hollow thin disc.The model has been applied satisfactorily to three torsional problems with known theoretical solutions. The first problem involves the computation of torsional shear stresses of a uniform shaft subjected to pure torsion. In the second problem, the solution is obtained for a conical shaft. In the third problem, known as the Reissner–Sagoci problem, an elastic semi-infinite medium is subjected to a torsional displacement on a small area of the surface.A typical application of the model to the problem of a shrink-fitted assembly subjected to torsion is discussed. Key words: torsion, finite element, elasticity, axisymmetry.

scholarly journals Finite Element Model for Linear Elastic Thick Shells Using Gradient Recovery Method

2017 ◽  
Vol 2017 ◽  
pp. 1-14
Author(s):  
Achille Germain Feumo ◽  
Robert Nzengwa ◽  
Joseph Nkongho Anyi
Keyword(s):  
Finite Element ◽  
Fundamental Form ◽  
Element Model ◽  
Shear Stresses ◽  
Gradient Recovery ◽  
Recovery Method ◽  
The Third ◽  
New Family ◽  
Convergence Results ◽  
Third Fundamental Form

This research purposed a new family of finite elements for spherical thick shell based on Nzengwa-Tagne’s model proposed in 1999. The model referred to hereafter as N-T model contains the classical Kirchhoff-Love (K-L) kinematic with additional terms related to the third fundamental form governing strain energy. Transverse shear stresses are computed and C0 finite element is proposed for numerical implementation. However, using straight line triangular elements does not guarantee a correct computation of stress across common edges of adjacent elements because of gradient jumps. The gradient recovery method known as Polynomial Preserving Recovery (PPR) is used for local interpolation and applied on a hemisphere under diametrically opposite charges. A good agreement of convergence results is observed; numerical results are compared to other results obtained with the classical K-L thin shell theory. Moreover, simulation on increasing values of the ratio of the shell shows impact of the N-T model especially on transverse stresses because of the significant energy contribution due to the third fundamental form tensor present in the kinematics of this model. The analysis of the thickness ratio shows difference between the classical K-L theory and N-T model when the ratio is greater than 0.099.

Finite Element Analysis of Tire/Rim Interface Forces Under Braking and Cornering Loads

1992 ◽  
Vol 20 (2) ◽  
pp. 83-105 ◽  
Author(s):  
J. P. Jeusette ◽  
M. Theves
Keyword(s):  
Finite Element ◽  
Shear Stress ◽  
Contact Pressure ◽  
Element Model ◽  
Shear Stresses ◽  
Detailed Knowledge ◽  
Stress Distributions ◽  
Element Analysis ◽  
Plane Shear ◽  
Normal Contact

Abstract During vehicle braking and cornering, the tire's footprint region may see high normal contact pressures and in-plane shear stresses. The corresponding resultant forces and moments are transferred to the wheel. The optimal design of the tire bead area and the wheel requires a detailed knowledge of the contact pressure and shear stress distributions at the tire/rim interface. In this study, the forces and moments obtained from the simulation of a vehicle in stationary braking/cornering conditions are applied to a quasi-static braking/cornering tire finite element model. Detailed contact pressure and shear stress distributions at the tire/rim interface are computed for heavy braking and cornering maneuvers.

Reduction of Free-Edge Stress Concentration

1985 ◽  
Vol 52 (4) ◽  
pp. 801-805 ◽  
Author(s):  
P. R. Heyliger ◽  
J. N. Reddy
Keyword(s):  
Finite Element ◽  
Stress Concentration ◽  
Finite Element Model ◽  
Three Dimensional ◽  
Element Model ◽  
Free Edge ◽  
Shear Stresses ◽  
Normal Stresses ◽  
Interlaminar Shear ◽  
Three Dimensional Elasticity

A quasi-three dimensional elasticity formulation and associated finite element model for the stress analysis of symmetric laminates with free-edge cap reinforcement are described. Numerical results are presented to show the effect of the reinforcement on the reduction of free-edge stresses. It is observed that the interlaminar normal stresses are reduced considerably more than the interlaminar shear stresses due to the free-edge reinforcement.

A SPECTRAL/hp NONLINEAR FINITE ELEMENT ANALYSIS OF HIGHER-ORDER BEAM THEORY WITH VISCOELASTICITY

2012 ◽  
Vol 04 (01) ◽  
pp. 1250010 ◽  
Author(s):  
V. P. VALLALA ◽  
G. S. PAYETTE ◽  
J. N. REDDY
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Virtual Work ◽  
Constitutive Relations ◽  
Beam Theory ◽  
Element Model ◽  
Higher Order ◽  
Time Step ◽  
Third Order ◽  
The Third

In this paper, a finite element model for efficient nonlinear analysis of the mechanical response of viscoelastic beams is presented. The principle of virtual work is utilized in conjunction with the third-order beam theory to develop displacement-based, weak-form Galerkin finite element model for both quasi-static and fully-transient analysis. The displacement field is assumed such that the third-order beam theory admits C0 Lagrange interpolation of all dependent variables and the constitutive equation can be that of an isotropic material. Also, higher-order interpolation functions of spectral/hp type are employed to efficiently eliminate numerical locking. The mechanical properties are considered to be linear viscoelastic while the beam may undergo von Kármán nonlinear geometric deformations. The constitutive equations are modeled using Prony exponential series with general n-parameter Kelvin chain as its mechanical analogy for quasi-static cases and a simple two-element Maxwell model for dynamic cases. The fully discretized finite element equations are obtained by approximating the convolution integrals from the viscous part of the constitutive relations using a trapezoidal rule. A two-point recurrence scheme is developed that uses the approximation of relaxation moduli with Prony series. This necessitates the data storage for only the last time step and not for the entire deformation history.

A Finite Element Model for Elastic and Slip Responses of Fusion Magnets

1980 ◽  
Vol 102 (2) ◽  
pp. 219-225
Author(s):  
T. Y. Chang ◽  
H. Suzuki ◽  
M. Reich
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Bonding Strength ◽  
Element Model ◽  
Type Model ◽  
Shear Stresses ◽  
Homogenization Procedure ◽  
Numerical Examples ◽  
Proposed Model ◽  
Interlayer Slip

A finite element model to simulate the elastic and slip responses of fusion magnets under operating loads is proposed. To represent the elastic actions, a material homogenization procedure based on the existing composite technology was applied to obtain the effective stress strain relations for the heterogeneous, laminated magnets. In addition, a friction-type model was utilized to simulate the interlayer slip of the magnets when the shear stresses reach the bonding strength of the adhesives. Numerical examples are given to demonstrate the applicability of the proposed model.

Inflight Deicing of Self-Actuating Aircraft Wing Structures With Piezoelectric Actuators

2002 ◽  
Author(s):  
Y. J. Lin ◽  
Suresh V. Venna
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Laminated Composite ◽  
Piezoelectric Actuators ◽  
Element Model ◽  
Harmonic Excitation ◽  
Dynamic Responses ◽  
Underlying Structure ◽  
Shear Stresses ◽  
Modeling And Analysis

Self-actuating aircraft wings for in-flight deicing with minimal power requirements are proposed. Lightweight piezoelectric actuators are utilized to excite the wing structure to its natural frequencies to induce shear stresses on the surface of the wing. The shears are generated in such a way that they are sufficient to break the weak bond between the ice layer and the wing surface. A laminated composite cantilever plate is used for the modeling and analysis. Analytical model is developed to predict the natural frequencies and shear stresses on the surface of the plate and finite element modal analysis is carried out to verify the results. In addition, finite element model involving the ice deposited on the underlying structure is built. The dynamic responses of the structure to harmonic excitation to its first five natural frequencies are investigated. It is observed that significant amount of ice de-bonding from the substrate occurs in the third mode, or the second symmetric mode. Moreover, the energy requirements of the piezoelectric actuators to actuate an adaptive composite structure with given weight are evaluated.

Groove Geometry and Mold Shrinkage Effects on Die Stress in Flip Chip Molded BGAs (FCMBGA)

2013 ◽  
Vol 2013 (DPC) ◽  
pp. 000455-000470
Author(s):  
Bora Baloglu ◽  
Miguel Jimarez ◽  
Ahmer Syed
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Flip Chip ◽  
Element Model ◽  
Shear Stresses ◽  
Back Side ◽  
Molding Process ◽  
Finite Elements Analysis ◽  
Design Guideline ◽  
Structural Support

Exposed die flip chip molded BGA (FCMBGA) packages are preferred for their improved thermal performance and reduced system cost. In this package type, mold compound replaces the traditional capillary underfill and also provides a better stiffening option for the package without the need for additional structural support such as lid and/or stiffening ring. In addition, it allows better utilization of the board real estate as the passive components can be placed closer to the die. Groove or an undercut is the shape of the mold around the exposed die that is formed during the molding process. To ensure a mold-free top surface of the die, a seal (soft insert) that has a larger surface area than the die is being used to cover the die top surface. This larger portion of the seal outlines the groove geometry when it is compressed on top of the die. Seal size can be designed to establish certain groove geometry. Thus, it is important to characterize/understand the effects of the groove geometry as it is a design parameter and can be adjusted to create more robust molded packages. In this study, specific groove width and depth values for various package configurations are investigated using finite elements analysis, FEA. Initially, a detailed finite element model is prepared and warpage simulation is performed. Model correlation to the actual Shadow Moiré is obtained. Then, using the correlated finite element model, die back side stress and shear stresses, where die faces mold compound, are obtained for a thermal cool down simulation from the molding temperature. Mold compound shrinkage is also considered by using an adjusted thermal expansion coefficient value. As a validation study, a test mold chase/tool for varying insert sizes has been designed and, molded packages with different groove geometries and different mold compounds were build. Using the correlation between the test data and the simulation results an order of importance (based on the groove geometry parameters and mold compound's material properties) will be presented which then, can be used as a design guideline to change the groove geometry to produce more robust molded packages.

The Method of Modal Parameters to Determine the Boundary Condition of Finite Element Model

1991 ◽  
Author(s):  
Chen Shiyu ◽  
Wang Fengquan
Keyword(s):  
Boundary Condition ◽  
Finite Element ◽  
Finite Element Model ◽  
Interpolation Method ◽  
Element Model ◽  
Accurate Method ◽  
Modal Parameters ◽  
Computation Method ◽  
Modal Parameter ◽  
The Third

Abstract In this paper, a method used to determine the boundary condition of Finite Element Model with structure modal parameters is presented. On deriving the method, the theory of Finite Element Model for dynamic calculating is used. Combined with the modal parameters got from experiment, a FEM-Modal Parameter equation to determine the boundary condition is put forward. For solving the equation, three methods are given. The first is the accurate method. The second is the full mode computation method by means of generlized inverse matrix. The third is the interpolation method of frequency. An applied example is given and the results of calculation fully verify the effectiveness of the method offered.

Finite Element Analysis of Six Transcortical Pin Parameters and Their Effect on Bone–Pin Interface Stresses in the Equine Third Metacarpal Bone

2019 ◽  
Vol 33 (02) ◽  
pp. 121-129
Author(s):  
Timothy B. Lescun ◽  
Stephen B. Adams ◽  
Russell P. Main ◽  
Eric A. Nauman ◽  
Gert J. Breur
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Axial Loading ◽  
Element Model ◽  
Metacarpal Bone ◽  
Distal Limb ◽  
Element Analysis ◽  
Minimal Impact ◽  
The Third ◽  
Tomography Scan

Abstract Objective The objectives of this study were to validate a finite element model of the equine distal limb transfixation cast and to determine the effect of six transcortical pin parameters on bone–pin interface (BPI) stresses in the third metacarpal bone. Study Design A transfixation cast finite element model was developed from a computed tomography scan of the third metacarpal bone and modelled pin elements. The model was validated by comparing strain measured around a 6.3-mm transfixation pin in the third metacarpal bone with the finite element model. The pin parameters of diameter, number, location, spacing, orientation and material were evaluated by comparing a variety of pin configurations within the model. Results Pin diameter and number had the greatest impact on BPI stress. Increasing the diameter and number of pins resulted in lower BPI stresses. Diaphyseal pin location and stainless-steel pins had lower BPI stresses than metaphyseal location and titanium alloy pins, respectively. Offset pin orientation and pin spacing had minimal impact on BPI stresses during axial loading. Conclusion The results provide evidence that diameter and number are the main pin parameters affecting BPI stress in an equine distal limb transfixation cast. Configurations of various pin size and number may be proposed to reduce BPI stresses and minimize the risk of pin related complications. Further refinement of these models will be required to optimize pin configurations to account for pin hole size and its impact on overall bone strength.

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