Node-based Element Research Articles

3-D FE Method Analysis of Static Fields for Non-Conforming Meshes With Second-Order Node-Based Elements

A novel approach of using node-based, second-order polynomial shape functions to substitute the degrees of freedom corresponding to slave nodes by a linear combination of those corresponding to master nodes is shown to be a powerful and accurate tool to couple non-conforming meshes. This method is investigated and proposed to be used to consider moving domains, especially rotating parts. The numerical behavior is illustrated by an exhaustive accuracy investigation.

節点ベース要素で拡張した弾塑性NMM-DDAの開発と検証

歴史的な石積の建造物には，その基礎地盤の変形・破壊に起因し崩壊に至るものが少なくなく，近年地盤工学に基づく崩壊メカニズムの解明と合理的な修復方法の検討が求められている。本論文では，地盤と石積の複合構造物の変形解析法の開発を目的として，不連続体解析手法NMM-DDA（マニフォールド法―不連続変形法連成解析）の高度化を試みた。具体的には，増分形の支配方程式に弾塑性構成則を導入した弾塑性NMM-DDAの定式化と，従来の定ひずみ三角形要素をベースとするNMM-DDAで課題となる体積ロッキング回避のための節点ベース均一ひずみ要素の応用について示した。開発手法は弾性梁の曲げ問題や，帯基礎の支持力問題といった基礎的な境界値問題に適用し，理論解との比較によりその精度を確認した。

A Node-Based Element for Analysis of Planar Piezoelectric Structures

A novel node-based smoothing element for triangular and quadrilateral meshes is presented for static analysis of planar piezoelectric structures. In contrast to the smoothed finite element formulation that was based on sub-cells within an original quadrilateral element, this new method transforms a general original finite element mesh into a mesh of new smoothing cells individually associated with a single node which is termed as node-based elements. The displacement fields of the element are approximated by the linear interpolation functions of the original mesh while the approximations of mechanical strains and electric potential fields are normalized using the stabilized conforming nodal integration technique over each node-based element. This technique allows field gradients to be directly computed from interpolating shape functions by using boundary integrations along each edge of the node-based element. Furthermore, the present elements do not require any additional degrees of freedom and are insensitive to bad element shapes in the original mesh. Several numerical examples and comparative studies with other numerical results as well as analytic solutions in the literature are carried out in order to demonstrate the simplicity, efficiency and reliability of the novel elements.

A/sub r/ formulation using edge elements, for the calculation of 3-D fields in superconducting magnets

The Large Hadron Collider (LHC) project is an accelerator for protons and heavy ions, to be installed at CERN. The field distribution in the superconducting LHC main dipoles is dominated by the coil configuration and is very sensitive to the conductor position. Therefore modelling errors on the coil geometry have to be avoided using a method which does not require the meshing of the coil. For the 2-D calculation of iron induced field effects, the reduced vector potential formulation with node-based elements was recently applied. This paper deals with the extension of the method to three dimensions.

A functional for dynamic finite-element solutions in electromagnetics

A new is introduced that satisfies Maxwell's equations, provides minimization, and eliminates spurious solutions. An analytical method is developed that provides a means of evaluating forms. The analytical method confirms the effective form as the fundamental cause underlying the difficulties with spurious solutions that are not completely eliminated under all circumstances. It is shown that the curl-curl functional form allows for the existence of an improper gradient behavior in a general field expansion. The new is shown to be self adjoint and positive definite, thus providing an error minimization. Numerical results are obtained that demonstrate the effectiveness of the new to prevent spurious solutions using node-based elements.

Comparing 3D finite element formulations modeling scattering from a conducting sphere

Six tetrahedral finite-element varieties are used to model the frequency-domain open-region scattering problem of a ka=2 conducting sphere. A wave-absorbing boundary condition is imposed at kr=3. Linear and quadratic node-based elements display vector parasites, which are less significant in the quadratic element case. Whitney edge elements improve with increasing mesh density, but accuracy is costly due to approximately linear h-convergence. Whitney elements also result in acceptably fast convergence of a biconjugate gradient iterative solver, alone among the elements examined. Novel weighted Whitney elements show some effectiveness and appear free of vector parasites, but are not as cost-effective as Whitney elements. Higher-order tangential elements appear cost-effective, in that accurate solutions may be obtained at low mesh density. >