Rayleigh-Ritz Analysis of Vibrating Plates Based on a Class of Eigenfunctions

2009 ◽  
Author(s):  
Giuseppe Catania ◽  
Silvio Sorrentino
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Boundary Conditions ◽  
Linear Combination ◽  
Equation Of Motion ◽  
Extensive Literature ◽  
Shape Functions ◽  
Element Analysis ◽  
Vibrating Plates ◽  
General Basis

In the Rayleigh-Ritz condensation method the solution of the equation of motion is approximated by a linear combination of shape-functions selected among appropriate sets. Extensive literature dealing with the choice of appropriate basis of shape functions exists, the selection depending on the particular boundary conditions of the structure considered. This paper is aimed at investigating the possibility of adopting a set of eigenfunctions evaluated from a simple stucture as a general basis for the analysis of arbitrary-shaped plates. The results are compared to those available in the literature and using standard finite element analysis.

Estimation of Residual Stresses in Steel Welded Joints Using Three Dimensional Finite Element Analysis

2018 ◽  
Author(s):  
Shivdayal Patel ◽  
B. P. Patel ◽  
Suhail Ahmad
Keyword(s):  
Residual Stress ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Residual Stresses ◽  
Boundary Conditions ◽  
Welding Speed ◽  
Welded Joints ◽  
Plate Thickness ◽  
Welding Process ◽  
Element Analysis

Welding is one of the most used joining methods in the ship industry. However, residual stresses are induced in the welded joints due to the rapid heating and cooling leading to inhomogenously distributed dimensional changes and non-uniform plastic and thermal strains. A number of factors, such as welding speed, boundary conditions, weld geometry, weld thickness, welding current/voltage, number of weld passes, pre-/post-heating etc, influence the residual stress distribution. The main aim of this work is to estimate the residual stresses in welded joints through finite element analysis and to investigate the effects of boundary conditions, welding speed and plate thickness on through the thickness/surface distributions of residual stresses. The welding process is simulated using 3D Finite element model in ABAQUS FE software in two steps: 1. Transient thermal analysis and 2. Quasi-static thermo-elasto-plastic analysis. The normal residual stresses along and across the weld in the weld tow region are found to be significant with nonlinear distribution. The residual stresses increase with the increase in the thickness of the plates being welded. The nature of the normal residual stress along the weld is found to be tensile-compressive-tensile and the nature of normal residual stress across the weld is found to be tensile along the thickness direction.

Dynamics Simulation and Analysis of Planetary Reducer

2013 ◽  
Vol 765-767 ◽  
pp. 422-426 ◽  
Author(s):  
Ling Ling ◽  
Yuan Yuan Yi
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Boundary Conditions ◽  
Electric Vehicle ◽  
Coupling Model ◽  
Dynamics Simulation ◽  
Element Analysis ◽  
Flexible Coupling ◽  
Object Of Study ◽  
Planet Carrier

Taking a planetary reducer in an electric vehicle as the object of study, a rigid-flexible coupling model was established to perform the dynamics simulation. The variational regularities of the meshing forces, output speed and acting forces of bearings were obtained, and then a finite element analysis of the planet carrier was carried out. This method can not only solve the problem of the boundary conditions of planet carrier which are difficult to define in finite element analysis, but also improve the accuracy of analysis results when the influence of carrier flexibility on the whole system is considered in dynamics simulation, which lays the foundation for further research on reducers.

Variational Formulations for the Finite Element Analysis of Noise Radiation from High-Speed Machinery

1981 ◽  
Vol 103 (4) ◽  
pp. 385-391 ◽  
Author(s):  
B. S. Thompson
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Boundary Conditions ◽  
High Speed ◽  
Acoustic Medium ◽  
Field Equations ◽  
Element Analysis ◽  
Vibrational Response ◽  
The Finite Element Analysis ◽  
Structural Interface

Variational theorems are presented for analyzing the vibrational response of flexible linkage mechanisms and the surrounding acoustic medium in which they are immersed. These theorems are established by generalizing Hamilton’s principle through using Lagrange multipliers to incorporate field equations and boundary conditions within the functional. The same philosophy is adopted to handle the conditions at the fluid-structural interface. When independent arbitrary variations of the system parameters are permitted, these acousto-elastodynamic theorems yield as characteristic equations the equation of motion for each member of the linkage, the acoustical wave equation, the compatibility conditions at the interface between the fluid and solid continua, and also the boundary conditions. These variational statements provide the foundations for several different classes of finite element analysis.

Finite element analysis of calibration factors for the modified incremental strain method

2003 ◽  
Vol 38 (1) ◽  
pp. 45-51 ◽  
Author(s):  
B-W Hwang ◽  
C-M Suh ◽  
S-H Kim
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Boundary Conditions ◽  
Reference Model ◽  
Strain Relaxation ◽  
Hole Drilling ◽  
Element Analysis ◽  
Bending Load ◽  
Incremental Strain ◽  
Strain Method

To modify the incremental strain method used to evaluate non-uniform residual stress, a finite element analysis (FEA) of the reference model used to describe a hole-drilling test was conducted. The calibration factors for the x and y directions were obtained from the analysis and then their differences were compared under various loading conditions. A hole-drilling test using a steel plate as the reference specimen was introduced, and under the pure bending load, strain relaxation was measured at each hole-drilling step to determine the calibration factors. Although the calibration factors in the x and y directions varied with the boundary conditions used in the FEA, their differences were reduced to zero for all depths when the prescribed loads as the boundary conditions in the x and y directions became the same. In addition, it was analytically and experimentally confirmed that the calibration factors did not vary with the direction. Accordingly, by making the calibration factors equal in the x and y directions in the modified equation for the incremental strain method, no singularity is produced in the stress calculations.

Need for CT-based bone density modelling in finite element analysis of a shoulder arthroplasty revealed through a novel method for result analysis

2014 ◽  
Vol 0 (0) ◽  
Author(s):  
Werner Pomwenger ◽  
Karl Entacher ◽  
Herbert Resch ◽  
Peter Schuller-Götzburg
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Bone Density ◽  
Boundary Conditions ◽  
Density Distribution ◽  
Shoulder Arthroplasty ◽  
Cumulative Distribution ◽  
Patient Specific ◽  
Element Analysis ◽  
Shoulder Complex

AbstractTreatment of common pathologies of the shoulder complex, such as rheumatoid arthritis and osteoporosis, is usually performed by total shoulder arthroplasty (TSA). Survival of the glenoid component is still a problem in TSA, whereas the humeral component is rarely subject to failure. To set up a finite element analysis (FEA) for simulation of a TSA in order to gain insight into the mechanical behaviour of a glenoid implant, the modelling procedure and the application of boundary conditions are of major importance because the computed result strongly depends upon the accuracy and sense of realism of the model. The goal of this study was to show the influence on glenoid stress distribution of a patient-specific bone density distribution compared with a homogenous bone density distribution for the purpose of generating a valid model in future FEA studies of the shoulder complex. Detailed information on the integration of bone density properties using existing numerical models as well as the applied boundary conditions is provided. A novel approach involving statistical analysis of values derived from an FEA is demonstrated using a cumulative distribution function. The results show well the mechanically superior behaviour of a realistic bone density distribution and therefore emphasise the necessity for patient-specific simulations in biomechanical and medical simulations.

A Penetration-Based Finite Element Method for Hyperelastic 3D Biphasic Tissues in Contact: Part 1-Derivation of Contact Boundary Conditions

2005 ◽  
Vol 128 (1) ◽  
pp. 124-130 ◽  
Author(s):  
Kerem Ün ◽  
Robert L. Spilker
Keyword(s):  
Finite Element Method ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Boundary Conditions ◽  
Solid Phase ◽  
Contact Boundary ◽  
Element Analysis ◽  
Efficient Manner ◽  
Biphasic Tissues ◽  
Element Method

In this study, we extend the penetration method, previously introduced to simulate contact of linear hydrated tissues in an efficient manner with the finite element method, to problems of nonlinear biphasic tissues in contact. This paper presents the derivation of contact boundary conditions for a biphasic tissue with hyperelastic solid phase using experimental kinematics data. Validation of the method for calculating these boundary conditions is demonstrated using a canonical biphasic contact problem. The method is then demonstrated on a shoulder joint model with contacting humerus and glenoid tissues. In both the canonical and shoulder examples, the resulting boundary conditions are found to satisfy the kinetic continuity requirements of biphasic contact. These boundary conditions represent input to a three-dimensional nonlinear biphasic finite element analysis; details of that finite element analysis will be presented in a manuscript to follow.

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