Special finite element shape functions for axisymmetric magnetic problems

1993 ◽  
Vol 29 (6) ◽  
pp. 2398-2400 ◽  
Author(s):  
S.R. Gratkowski
Keyword(s):  
Finite Element ◽  
Shape Functions ◽  
Element Shape

Finite Element Analysis Over Tangled Meshes

2012 ◽  
Author(s):  
Josh Danczyk ◽  
Krishnan Suresh
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Functional Space ◽  
Mesh Optimization ◽  
Element Formulation ◽  
Shape Functions ◽  
Element Analysis ◽  
Patch Tests ◽  
Galerkin Formulation ◽  
Element Shape

In finite element analysis (FEA), tasks such as mesh optimization and mesh morphing can lead to overlapping elements, i.e., to a tangled mesh. Such meshes are considered ‘unacceptable’ today, and are therefore untangled using specialized procedures. Here it is shown that FEA can be easily extended to handle tangled meshes. Specifically, by defining the nodal functional space as an oriented linear combination of the element shape functions, it is shown that the classic Galerkin formulation leads to a valid finite element formulation over such meshes. Patch tests and numerical examples illustrate the correctness of the proposed methodology.

Finite Element Incremental Approach and Exact Rigid Body Inertia

1996 ◽  
Vol 118 (2) ◽  
pp. 171-178 ◽  
Author(s):  
A. A. Shabana
Keyword(s):  
Finite Element ◽  
Rigid Body ◽  
Rigid Bodies ◽  
Simple Expression ◽  
Shape Functions ◽  
Large Rotation ◽  
Nodal Coordinates ◽  
Inertia Properties ◽  
Element Shape ◽  
Body Inertia

In the dynamics of multibody systems that consist of interconnected rigid and deformable bodies, it is desirable to have a formulation that preserves the exactness of the rigid body inertia. As demonstrated in this paper, the incremental finite element approach, which is often used to solve large rotation problems, does not lead to the exact inertia of simple structures when they rotate as rigid bodies. Nonetheless, the exact inertia properties, such as the mass moments of inertia and the moments of mass, of the rigid bodies can be obtained using the finite element shape functions that describe large rigid body translations by introducing an intermediate element coordinate system. The results of application of the parallel axis theorem can be obtained using the finite element shape functions by simply changing the element nodal coordinates. As demonstrated in this investigation, the exact rigid body inertia properties in case of rigid body rotations can be obtained using the shape function if the nodal coordinates are defined using trigonometric functions. The analysis presented in this paper also demonstrates that a simple expression for the kinetic energy can be obtained for flexible bodies that undergo large displacements without the need for interpolation of large rotation coordinates.

A New Solution for MKDV Equation Using Galerkin Finite Element Method

2017 ◽  
Vol 14 (1) ◽  
pp. 800-806 ◽  
Author(s):  
K. R Raslan ◽  
Z. F Abu Shaeer
Keyword(s):  
Finite Element ◽  
Mkdv Equation ◽  
Galerkin Finite Element Method ◽  
Shape Functions ◽  
Unconditionally Stable ◽  
Galerkin Finite Element ◽  
Numerical Tests ◽  
Set Up ◽  
Element Shape ◽  
Invariants Of Motion

A finite element solution of the modified Korteweg-de Vries (MKdV) equation, based on Galerkin’s method using cubic splines as element shape functions, is set up. A linear stability analysis shows the scheme is unconditionally stable. Numerical tests for single, two and three solitons are used to assess the performance of the proposed scheme. The four invariants of motion are evaluated to determine the conservation properties of the algorithm.

US-FE-LSPIM TRI3 Element for Free Vibration Analysis

2012 ◽  
Vol 246-247 ◽  
pp. 1278-1282 ◽  
Author(s):  
Hui Hui Chen ◽  
Cheng Jia
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Element Model ◽  
Benchmark Problems ◽  
Element Formulation ◽  
Shape Functions ◽  
The Individual ◽  
Element Shape

For the purpose of construction an effective element model, the US- FE-LSPIM TRI3 element formulation, which is based on the concept of unsymmetric finite element formulation, is established. Classical linear triangle shape functions and FE-LSPIM TRI3 element shape functions are used as test and trial functions respectively. Classical linear triangle shape functions fulfill the requirements of continuity in displacement field for test functions. The FE-LSPIM TRI3 element shape functions synthesize the individual strengths of meshfree and finite element methods so they are more proper for trial functions. The element is applied in free vibration analysis of two dimension solids. Typical benchmark problems are solved. The results show that this element is more accurate and capable of good performances under both regular and irregular meshes.

A NEW CONJUGATED MAPPED INFINITE ELEMENT

2004 ◽  
Vol 12 (04) ◽  
pp. 543-570
Author(s):  
L.-X. LI ◽  
S. KUNIMATSU ◽  
J.-S. SUN ◽  
H. SAKAMOTO
Keyword(s):  
Finite Element ◽  
Slight Modification ◽  
Weighting Factor ◽  
Shape Functions ◽  
Infinite Element ◽  
Infinite Elements ◽  
The One ◽  
Geometry Mapping ◽  
Element Shape ◽  
Decay Behavior

Taking the Astley element for example, the conventional mapped infinite element is theoretically dissected in this paper. The study brings to light the reason why the results from the mapped infinite elements vary with the location of the mid-side points used in the geometry mapping. To remedy this deficiency, a new conjugated mapped infinite element is proposed whose shape functions exactly satisfy the multi-pole expansion in the infinite direction. Within the framework of this infinite element, shape functions for any type of wave are composed of the one in the conventional finite element for the same order multiplied by a factor that contains the information of the geometry mapping and the decay behavior of wave. In addition to the slight modification to the phase factor and the weighting factor, the present element permits a free geometry mapping, and therefore greatly expands the applicability of the mapped infinite element methods. To display the performance of the proposed element, typical examples are finally given.

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