A General Form of Dirichlet Boundary Conditions Used in Finite Element Analysis

2009 ◽  
Author(s):  
L. Jendele ◽  
V. Cervenka
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Element Analysis

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.

Checking the Automated Construction of Finite Element Simulations From Dirichlet Boundary Conditions

2019 ◽  
Author(s):  
Kevin N. Chiu ◽  
Mark D. Fuge
Keyword(s):  
Finite Element ◽  
Topology Optimization ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Fem Simulation ◽  
Computational Design ◽  
Dirichlet Boundary Conditions ◽  
Governing Equations ◽  
Variational Form ◽  
Key Issues

Abstract From engineering analysis and topology optimization to generative design and machine learning, many modern computational design approaches require either large amounts of data or a method to generate that data. This paper addresses key issues with automatically generating such data through automating the construction of Finite Element Method (FEM) simulations from Dirichlet boundary conditions. Most past work on automating FEM assumes prior knowledge of the physics to be run or is limited to a small number of governing equations. In contrast, we propose three improvements to current methods of automating the FEM: (1) completeness labels that guarantee viability of a simulation under specific conditions, (2) type-based labels for solution fields that robustly generate and identify solution fields, and (3) type-based labels for variational forms of governing equations that map the three components of a simulation set — specifically, boundary conditions, solution fields, and a variational form — to each other to form a viable FEM simulation. We implement these improvements using the FEniCS library as an example case. We show that our improvements increase the percent of viable simulations that are run automatically from a given list of boundary conditions. This paper’s procedures ultimately allow for the automatic — i.e., fully computer-controlled — construction of FEM multi-physics simulations and data collection required to run data-driven models of physics phenomena or automate the exploration of topology optimization under many physics.

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.

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