scholarly journals A Mixed Stress/Displacement Approach Model of Homogeneous Shells for Elastodynamic Problems

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Axel Fernando Domínguez Alvarado ◽  
Alberto Díaz Díaz
Keyword(s):  
Finite Element ◽  
Frequency Analysis ◽  
Constitutive Equations ◽  
Lagrange Equation ◽  
Shell Element ◽  
Harmonic Load ◽  
Plane Normal ◽  
Out Of Plane ◽  
Element Technique ◽  
Stress Boundary Conditions

This paper presents the development of a model of homogeneous, moderately thick shells for elastodynamic problems. The model is obtained by adapting and modifying SAM-H model (stress approach model of homogeneous shells) developed by Domínguez Alvarado and Díaz in (2018) for static problems. In the dynamic version of SAM-H presented herein, displacements and stresses are approximated by polynomials of the out-of-plane coordinate. The stress approximation coincides with the static version of SAM-H when dynamic effects are neglected. The generalized forces and displacements appearing in the approximations are the same as those involved in a classical, moderately thick shell model (CS model) but the stress approximation adopted herein is more complex: the 3D motion equations and the stress boundary conditions at the faces of the shell are verified. The generalized motion and constitutive equations of dynamic SAM-H model are obtained by applying a variant of Euler–Lagrange equation which includes pertinently Hellinger–Reissner functional. In the constitutive equations, Poisson’s effect of out-of-plane normal stresses on in-plane strains is not ignored; this is one important feature of SAM-H. To test the accuracy of dynamic SAM-H model, the following structures were considered: a hollow sphere and a catenoid. In each case, eigenfrequencies are first calculated and then a frequency analysis is performed applying a harmonic load. The results are compared to those of a CS model, MITC6 (mixed interpolation of tensorial components with 6 nodes per element) shell element calculations, and solid finite element computations. In the two problems, CS, MITC6, and dynamic SAM-H models yield accurate eigenfrequencies and eigenmodes. Nevertheless, the frequency analysis performed in each case showed that dynamic SAM-H provides much more accurate amplitudes of stresses and displacements than the CS model and the MITC6 shell finite element technique.

The Effect of Initial Forces on the Hydroelastic Vibration and Stability of Planar Curved Tubes

1974 ◽  
Vol 41 (2) ◽  
pp. 355-359 ◽  
Author(s):  
J. L. Hill ◽  
C. G. Davis
Keyword(s):  
Finite Element ◽  
Internal Pressure ◽  
Constant Curvature ◽  
Elastic Limit ◽  
Center Line ◽  
Finite Element Technique ◽  
Line Shapes ◽  
Circular Arcs ◽  
Out Of Plane ◽  
Element Technique

The effect of initial forces on the vibration and stability of curved, clamped, fluid conveying tubes is analyzed by the finite-element technique. The tubes are initially planar with general center-line shapes approximated by constant curvature arcs. The effect of internal pressure is included. Numerical results are presented with, and without, the effects of the initial in-plane forces, for circular arcs S, L, and spiral configurations. Neglecting initial forces results in out-of-plane buckling, while including these forces prevents buckling within the elastic limit, in all configurations studied.

An Efficient Finite Element Modeling of Composite Stiffened Shells

2014 ◽  
Vol 553 ◽  
pp. 673-678
Author(s):  
Hamid Sheikh ◽  
Liang Huang
Keyword(s):  
Finite Element ◽  
Finite Element Modeling ◽  
Degrees Of Freedom ◽  
Torsional Rigidity ◽  
Shell Element ◽  
Beam Element ◽  
Shell Elements ◽  
Element Modeling ◽  
Stiffened Shells ◽  
Element Technique

This paper presents an efficient finite element modeling technique for stiffened composite shells having different stiffening arrangements. The laminated shell skin is modeled with a triangular degenerated curved shell element having 3 corner nodes and 3 mid-side nodes. An efficient curved beam element compatible with the shell element is developed for the modeling of stiffeners which may have different lamination schemes. The formulation of the 3 nod degenerated beam element may be considered as one of the major contributions. The deformation of the beam element is completely defined in terms of the degrees of freedom of shell elements and it does not require any additional degrees of freedom. As the usual formulation of degenerated beam elements overestimates their torsional rigidity, a torsion correction factor is introduced for different lamination schemes. Numerical examples are solved by the proposed finite element technique to assess its performance.

Analysis for Tire Mold Design

1974 ◽  
Vol 2 (3) ◽  
pp. 195-210 ◽  
Author(s):  
R. A. Ridha
Keyword(s):  
Finite Element ◽  
Material Properties ◽  
Shell Element ◽  
Structural Behavior ◽  
Temperature History ◽  
Small Displacement ◽  
Toroidal Shell ◽  
Mold Design ◽  
Orthotropic Properties ◽  
Element Technique

Abstract An analysis is presented for determining tire deformation due to shrinkage. The analysis uses composite theory and the finite element technique in modeling the material properties and the structural behavior. The constant strain toroidal shell element developed by Wilson for small displacement and isotropic properties is modified for orthotropic properties which depend on the element location. Temperature history and the buildup of shrink forces during cure are determined experimentally. The shrink forces are represented by a set of equivalent loads applied at the nodes. Good correlation is obtained between calculated and experimental displacements. The analysis is applied in relating the mold shape to the final shape of the tire.

Refined Methods for Tire Computation

1989 ◽  
Vol 17 (4) ◽  
pp. 291-304 ◽  
Author(s):  
A. Domscheit ◽  
H. Rothert ◽  
T. Winkelmann
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Shell Element ◽  
Material Model ◽  
Nonlinear Material ◽  
Shell Elements ◽  
Is Implementation ◽  
Numerical Studies ◽  
Static Contact ◽  
Element Technique

Abstract Realistic computation of automobile tires is best achieved by modeling the whole tire with finite element methods. A numerical solution of the quasi-static contact problem for the whole tire requires a refined mesh of elements with redundant degrees of freedom when nonlinear material assumptions are considered. Both laminated shell elements and incompressible continuum elements are used here. The stiffness matrix of a shell element is determined by numerically integrating all layers within the thickness of each element. Numerical studies have been made by a finite element technique that includes shell elements and Swanson's material model, which covers large deformations. The major contribution of this paper is implementation of a composite theory that includes effects of large displacements on the stiffness into an existing element. Swanson's material law was also simplified and implemented.

scholarly journals A Stress Approach Model of Moderately Thick, Homogeneous Shells

2018 ◽  
Vol 2018 ◽  
pp. 1-16 ◽  
Author(s):  
Axel Fernando Domínguez Alvarado ◽  
Alberto Díaz Díaz
Keyword(s):  
Theoretical Development ◽  
Equilibrium Equations ◽  
Linear Elastic ◽  
Finite Element Software ◽  
Plane Normal ◽  
Stiffness Matrices ◽  
Out Of Plane ◽  
Model Equations ◽  
Stress Boundary Conditions ◽  
Stress Boundary

This paper presents the theoretical development of a new model of shells called SAM-H (Stress Approach Model of Homogeneous shells) and adapted for linear elastic shells, from thin to moderately thick ones. The model starts from an original stress polynomial approximation which involves the generalized forces and verifies the 3D equilibrium equations and the stress boundary conditions at the faces of the shell. Hellinger-Reissner functional and Reissner’s variational method are applied to determine the generalized fields and equations. The generalized forces and displacements are the same as those obtained in a classical, moderately thick shell model (CS model). The equilibrium and constitutive equations have some differences from those of a CS model, mainly in consideration of applied stress vectors at the upper and lower faces of the shell and the stiffness matrices. Another feature of the SAM-H model is the inclusion of the Poisson’s effect of out-of-plane normal stresses on in-plane strains. As a first application example to test the accuracy of the model, the case of a pressurized hollow sphere is considered. The analytical results of stresses and displacements of the SAM-H and CS models are compared to those of an exact 3D resolution. In this example, SAM-H model proves to be much more accurate than the CS model and its approximation of the normal out-of-plane stress is very precise. Finally, an implementation of the SAM-H model equations in a finite element software is performed and a case study is analyzed to show the advantages of using the SAM-H model.

Finite Element Analysis of Interface Cracks Using Multiple Point Constraints

2006 ◽  
Vol 41 (4) ◽  
pp. 311-321
Author(s):  
C H Liu ◽  
Jui-Hsiang Lin
Keyword(s):  
Finite Element ◽  
Crack Tip ◽  
Multiple Point ◽  
Element Analysis ◽  
Interface Cracks ◽  
Closed Mode ◽  
Nodal Displacements ◽  
Element Technique ◽  
Stress Boundary Conditions ◽  
Virtual Crack Extension Method

A finite element technique to analyse closed-mode interface cracks is proposed in this study. Stress boundary conditions for a closed-tip model are transformed into multiple point constraints (MPCs) for nodal displacements. These constraints are imposed upon the finite element solutions to simulate closed-tip stress fields in crack-tip elements. This technique can deal with small as well as large crack-tip contact zones, and no special elements other than the standard quarter-point elements are needed. Since stresses approach infinity at the crack tip in a quarter-point element, dominant terms are used in deriving MPCs for nodal displacements. Fracture parameters are obtained by using the virtual crack extension method, and numerical results are in good agreement with analytical results.

Dynamic Finite Element Analysis of a Piezoelectric Bimorph Beam Deflector With Consideration of Hysteresis Effect

2003 ◽  
Author(s):  
Paul C. P. Chao ◽  
C. W. Chiu ◽  
J. S. Huang ◽  
H. C. Tseng
Keyword(s):  
Finite Element ◽  
Constitutive Equations ◽  
Hysteresis Effect ◽  
Piezoelectric Bimorph ◽  
Governing Equations ◽  
Element Analysis ◽  
Dynamic Finite Element Analysis ◽  
Polarization Term ◽  
Bimorph Beam ◽  
Element Technique

This study is devoted to propose a method of finite element technique to account for the hysteresis effect of a piezoelectric bimorph beam deflector. To this end, the constitutive equations of a general piezoelectric material are first modified to include the hysteresis effect by adding a polarization term in one of constitutive equations. Based on these modified constitutive equations and employment of Preisach model for hysteresis, the governing equations of the bimorph beam are derived through the utilization of Hamilton’s principle and calculus of variation. In addition, according to the common physical rules, boundary, transition and continuous conditions are next formulated to complement the governing equations. Simulations are finally conducted to show the effectiveness of the proposed modeling technique and decipher the dynamic behavior of the piezoelectric beam with consideration of hysteresis effect.

Prediction of Tread Pattern Wear by an Explicit Finite Element Model3

2007 ◽  
Vol 35 (4) ◽  
pp. 276-299 ◽  
Author(s):  
J. C. Cho ◽  
B. C. Jung
Keyword(s):  
Finite Element ◽  
Wear Rate ◽  
Tangential Stress ◽  
Rate Equation ◽  
Constitutive Equations ◽  
Slip Velocity ◽  
Test Results ◽  
Explicit Finite Element ◽  
Driving Condition ◽  
Driving Conditions

Abstract Tread pattern wear is predicted by using an explicit finite element model (FEM) and compared with the indoor drum test results under a set of actual driving conditions. One pattern is used to determine the wear rate equation, which is composed of slip velocity and tangential stress under a single driving condition. Two other patterns with the same size (225/45ZR17) and profile are used to be simulated and compared with the indoor wear test results under the actual driving conditions. As a study on the rubber wear rate equation, trial wear rates are assumed by several constitutive equations and each trial wear rate is integrated along time to yield the total accumulated wear under a selected single cornering condition. The trial constitutive equations are defined by independently varying each exponent of slip velocity and tangential stress. The integrated results are compared with the indoor test results, and the best matching constitutive equation for wear is selected for the following wear simulation of two other patterns under actual driving conditions. Tens of thousands of driving conditions of a tire are categorized into a small number of simplified conditions by a suggested simplification procedure which considers the driving condition frequency and weighting function. Both of these simplified conditions and the original actual conditions are tested on the indoor drum test machines. The two results can be regarded to be in good agreement if the deviation that exists in the data is mainly due to the difference in the test velocity. Therefore, the simplification procedure is justified. By applying the selected wear rate equation and the simplified driving conditions to the explicit FEM simulation, the simulated wear results for the two patterns show good match with the actual indoor wear results.

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