scholarly journals Singularity Study of Sectorial Domain by Weak Formulation and Fractal Finite Element in Hamilton System

2019 ◽  
Vol 11 (1) ◽  
pp. 16-22
Author(s):  
Kewei Ding
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stress Singularity ◽  
Polar Coordinate System ◽  
Hamiltonian Mechanics ◽  
State Equations ◽  
Weak Formulation ◽  
Hamilton System ◽  
Polar Coordinate ◽  
Element Method

The weak formulation of mixed state equations including boundary conditions are presented in polar coordinate system, mixed variational formulation is established in sectorial domain. The fractal finite element method is used to analyse the sector domain problem. The present result is exactly analogous to the Hamiltonian mechanics for a dynamic system by simulating time variable t with coordinate variable r. The stress singularity at singular point is investigated by means of the fractal finite element method. The present study satisfies the continuity conditions of stresses and displacements at the interfaces. The principle and method suggested here have clear physical concepts. So this method would be easily popularized in dynamics analysis of elasticity.

A Coupled SBFEM-FEM Approach for Evaluating Stress Intensity Factors

2013 ◽  
Vol 353-356 ◽  
pp. 3369-3377 ◽  
Author(s):  
Ming Guang Shi ◽  
Chong Ming Song ◽  
Hong Zhong ◽  
Yan Jie Xu ◽  
Chu Han Zhang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Complex Geometry ◽  
Stress Singularity ◽  
Intensity Factors ◽  
Finite Element Software ◽  
Scaled Boundary Finite Element ◽  
Element Method

A coupled method between the Scaled Boundary Finite Element Method (SBFEM) and Finite Element Method (FEM) for evaluating the Stress Intensity Factors (SIFs) is presented and achieved on the platform of the commercial finite element software ABAQUS by using Python as the programming language. Automatic transformation of the finite elements around a singular point to a scaled boundary finite element subdomain is realized. This method combines the high accuracy of the SBFEM in computing the SIFs with the ability to handle material nonlinearity as well as powerful mesh generation and post processing ability of commercial FEM software. The validity and accuracy of the method is verified by analysis of several benchmark problems. The coupled algorithm shows a good converging performance, and with minimum additional treatment can be able to handle more problems that cannot be solved by either SBFEM or FEM itself. For fracture problems, it proposes an efficient way to represent stress singularity for problems with complex geometry, loading condition or certain nonlinearity.

Mesh Sensitivity and FEA for Multi-Layered Electronic Packaging

1999 ◽  
Vol 123 (3) ◽  
pp. 218-224 ◽  
Author(s):  
Cemal Basaran ◽  
Ying Zhao
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Damage Mechanics ◽  
Stress Singularity ◽  
Free Edge ◽  
Elastic Analysis ◽  
Linear Elastic ◽  
Inelastic Analysis ◽  
Mesh Sensitivity ◽  
Element Method

Multi-layered stacks are commonly used in microelectronic packaging. Traditionally, these systems are designed using linear-elastic analysis either with analytical solutions or finite element method. Linear-elastic analysis for layered structures yields very conservative results due to stress singularity at the free edge. In this paper, it is shown that a damage mechanics based nonlinear analysis not just leads to a more realistic analysis but also provides more accurate stress distribution. In this paper these two approaches are compared. Moreover, mesh sensitivity of the finite element analysis in stack problems is studied. It is shown that the closed form and elastic finite element analyses can only be used for preliminary studies and elastic finite element method is highly mesh sensitive for this problem. In elastic analysis the stress singularity at the free edge makes mesh selection very difficult. Even when asymptotic analysis is used at the free edge, the results are very conservative compared to an inelastic analysis. Rate sensitive inelastic analysis does not suffer from the stress singularity and mesh sensitivity problems encountered in elastic analysis.

Strong Formulation Finite Element Method Based on Differential Quadrature: A Survey

2015 ◽  
Vol 67 (2) ◽  
Author(s):  
Francesco Tornabene ◽  
Nicholas Fantuzzi ◽  
Francesco Ubertini ◽  
Erasmo Viola
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Mapping Technique ◽  
Computational Domain ◽  
Weak Formulation ◽  
Static Conditions ◽  
Strong Formulation ◽  
Element Method

A survey of several methods under the heading of strong formulation finite element method (SFEM) is presented. These approaches are distinguished from classical one, termed weak formulation finite element method (WFEM). The main advantage of the SFEM is that it uses differential quadrature method (DQM) for the discretization of the equations and the mapping technique for the coordinate transformation from the Cartesian to the computational domain. Moreover, the element connectivity is performed by using kinematic and static conditions, so that displacements and stresses are continuous across the element boundaries. Numerical investigations integrate this survey by giving details on the subject.

Research on Generalized Compatibility Equations of Quasi-Conforming Element Methods

2011 ◽  
Vol 94-96 ◽  
pp. 1651-1654
Author(s):  
Ke Wei Ding
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Continuity Condition ◽  
Weak Continuity ◽  
The Finite Element Method ◽  
Weak Formulation ◽  
Equilibrium Conditions ◽  
Stress Equilibrium ◽  
Generalized Compatibility ◽  
Element Method

Brief development process of the finite element method, foundation of quasi-conforming element has been analyzed from weak formulation generalized compatibility equations and its weak continuity condition in this paper. The quasi-conforming element methods are the exact solution of generalized compatibility equations and satisfy the weak continuity requirement naturally. The quasi-conforming element methods do not satisfy stress equilibrium conditions and concision calculating process of matrix’s athwart. The discrete precision can be predicted in prior. It also extends space of original finite element method and is landmark in computational mechanics.

scholarly journals A finite element method for extended KdV equations

2016 ◽  
Vol 26 (3) ◽  
pp. 555-567 ◽  
Author(s):  
Anna Karczewska ◽  
Piotr Rozmej ◽  
Maciej Szczeciński ◽  
Bartosz Boguniewicz
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Solutions ◽  
Subsequent Paper ◽  
Weak Formulation ◽  
Water Wave Problem ◽  
Wave Dynamics ◽  
Kdv Equations ◽  
Reasonable Description ◽  
Element Method

Abstract The finite element method (FEM) is applied to obtain numerical solutions to a recently derived nonlinear equation for the shallow water wave problem. A weak formulation and the Petrov–Galerkin method are used. It is shown that the FEM gives a reasonable description of the wave dynamics of soliton waves governed by extended KdV equations. Some new results for several cases of bottom shapes are presented. The numerical scheme presented here is suitable for taking into account stochastic effects, which will be discussed in a subsequent paper.

scholarly journals Numerical solution of Navier stokes equation using control volume and finite element method

2016 ◽  
Vol 5 (1) ◽  
pp. 63
Author(s):  
Musa Adam Aigo
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Solution ◽  
Stokes Equation ◽  
Control Volume ◽  
Navier Stokes ◽  
Weak Formulation ◽  
Navier Stokes Equation ◽  
Fast Solution ◽  
Element Method

<p>The aim of this paper is twofold first we will  provide a numerical solution of the Navier Stokes equation using the Projection technique and finite element method. The problem will be introduced in weak formulation and a Finite Element method will be developed, then solve in a fast way the sparse system derived. Second, the projection method with Control volume approach will be applied to get a fast solution, in iterations count.</p>

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