3-D Integral Formulation for Thin Electromagnetic Shells Coupled with an External Circuit

The aim of this article is to present a hybrid integral formulation for modelling structures made by conductors and thin electromagnetic shell models. Based on the principle of shell elements, the proposed method provides a solution to various problems without meshing the air regions, and at the same time helps to take care of the skin effect. By integrating the system of circuit equations, the method presented in this paper can also model the conductor structures. In addition, the equations describing the interaction between the conductors and the thin shell are also developed. Finally, the formulation is validated via an axisymmetric finite element method and the obtained results are compared with those implemented from another shell formulation.

Download Full-text

Some new results and current challenges in the finite element analysis of shells

Acta Numerica ◽

10.1017/s0962492901000034 ◽

2001 ◽

Vol 10 ◽

pp. 215-250 ◽

Cited By ~ 7

Author(s):

Dominique Chapelle

Keyword(s):

Finite Element ◽

Shell Theory ◽

Shell Structures ◽

Engineering Practice ◽

Element Analysis ◽

Shell Elements ◽

Shell Models ◽

The Finite Element Analysis ◽

Shell Finite Element ◽

Mathematical Analyses

This article, a companion to the article by Philippe G. Ciarlet on the mathematical modelling of shells also in this issue of Acta Numerica, focuses on numerical issues raised by the analysis of shells.Finite element procedures are widely used in engineering practice to analyse the behaviour of shell structures. However, the concept of ‘shell finite element’ is still somewhat fuzzy, as it may correspond to very different ideas and techniques in various actual implementations. In particular, a significant distinction can be made between shell elements that are obtained via the discretization of shell models, and shell elements – such as the general shell elements – derived from 3D formulations using some kinematic assumptions, without the use of any shell theory. Our first objective in this paper is to give a unified perspective of these two families of shell elements. This is expected to be very useful as it paves the way for further thorough mathematical analyses of shell elements. A particularly important motivation for this is the understanding and treatment of the deficiencies associated with the analysis of thin shells (among which is the locking phenomenon). We then survey these deficiencies, in the framework of the asymptotic behaviour of shell models. We conclude the article by giving some detailed guidelines to numerically assess the performance of shell finite elements when faced with these pathological phenomena, which is essential for the design of improved procedures.

Download Full-text

A Perturbation Finite Element Approach for Correcting Inaccuracies on Thin Shell Models with the Magnetic Field Formulation

Advances in Science Technology and Engineering Systems Journal ◽

10.25046/aj050322 ◽

2020 ◽

Vol 5 (3) ◽

pp. 166-170 ◽

Cited By ~ 1

Author(s):

Vuong Dang Quoc ◽

Quang Nguyen Duc

Keyword(s):

Magnetic Field ◽

Finite Element ◽

Thin Shell ◽

Finite Element Approach ◽

Shell Models ◽

Element Approach ◽

The Magnetic Field

Download Full-text

Design and Structural Analysis of a Rack System for Using in Agriculture

Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis ◽

10.11118/actaun201866030641 ◽

2018 ◽

Vol 66 (3) ◽

pp. 641-646

Author(s):

Miroslav Blatnický ◽

Ján Dižo ◽

Dalibor Barta

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Structural Analysis ◽

Fe Model ◽

Steel Tubes ◽

Shell Elements ◽

Human Power ◽

Construction Design ◽

Pull Out ◽

Pressure Pipeline

The paper deals with a construction design and structural analysis of the rack system which will be used for storage of steel tubes of pressure pipeline for fodder mixtures transportation in agricultural company. Structure of the designed equipment is made by the welding of steel parts and consists of the main framework and four pull-out racks on both sides. Racks move by means of human power through a rotating crank. Every individual pull-out racks is able to carries pipes of various dimensions, both length and diameter with total weight up to 3 tons with respect to customer requests. Since it is a prototype’s structure, we have designed main dimensions of it, material and technology for production and performed also structural analyses as the integral part of every engineering design. Structural analyses were conducted by means of numeric procedure known as finite element method. With respect to the used steel profiles shell elements were used for FE model. Analyses were performed for maximal loading cases in order to identify the level of safety in the most exposed locations of the structure.

Download Full-text

Vibrational Characteristics of Composite Shafts

Volume 7A: 17th Biennial Conference on Mechanical Vibration and Noise ◽

10.1115/detc99/vib-8277 ◽

1999 ◽

Author(s):

A. S. Sekhar ◽

N. Ravi Kumar

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Deformation Theory ◽

Great Influence ◽

Shear Deformation Theory ◽

Stacking Sequence ◽

Shell Elements ◽

First Order ◽

Composite Shaft ◽

Vibrational Characteristics

Abstract The present study aims in performing eigenvalue analysis and unbalance response for a rotor system having a composite shaft, modelled based on first order shear deformation theory using finite element method with shell elements. Different materials such as boron epoxy, carbon epoxy and graphite epoxy have been tried for various stacking sequences. From the study it is clear that the stacking sequence and material have great influence on the vibrational characteristics of composite shafts.

Download Full-text

Two-way coupling of thin shell finite element magnetic models via an iterative subproblem method

COMPEL The International Journal for Computation and Mathematics in Electrical and Electronic Engineering ◽

10.1108/compel-01-2020-0035 ◽

2020 ◽

Vol 39 (5) ◽

pp. 1085-1097 ◽

Cited By ~ 2

Author(s):

Vuong Quoc Dang ◽

Christophe Geuzaine

Keyword(s):

Finite Element ◽

Field Distribution ◽

Thin Shell ◽

Iterative Procedure ◽

Design Methodology ◽

Content Type ◽

Shell Models ◽

Shell Finite Element ◽

Corner Effects ◽

Convergence Solution

Purpose The purpose of this paper is to deal with the correction of the inaccuracies near edges and corners arising from thin shell models by means of an iterative finite element subproblem method. Classical thin shell approximations of conducting and/or magnetic regions replace the thin regions with impedance-type transmission conditions across surfaces, which introduce errors in the computation of the field distribution and Joule losses near edges and corners. Design/methodology/approach In the proposed approach local corrections around edges and corners are coupled to the thin shell models in an iterative procedure (each subproblem being influenced by the others), allowing to combine the efficiency of the thin shell approach with the accuracy of the full modelling of edge and corner effects. Findings The method is based on a thin shell solution in a complete problem, where conductive thin regions have been extracted and replaced by surfaces but strongly neglect errors on computation of the field distribution and Joule losses near edges and corners. Research limitations/implications This model is only limited to thin shell models by means of an iterative finite element subproblem method. Originality/value The developed method is considered to couple subproblems in two-way coupling correction, where each solution is influenced by all the others. This means that an iterative procedure between the subproblems must be required to obtain an accurate (convergence) solution that defines as a series of corrections.

Download Full-text

3D-SHELL ELEMENTS AND THEIR UNDERLYING MATHEMATICAL MODEL

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s0218202504003179 ◽

2004 ◽

Vol 14 (01) ◽

pp. 105-142 ◽

Cited By ~ 21

Author(s):

D. CHAPELLE ◽

A. FERENT ◽

K. J. BATHE

Keyword(s):

Mathematical Model ◽

Finite Element ◽

Engineering Practice ◽

Finite Element Discretization ◽

Finite Element Scheme ◽

Element Discretization ◽

Shell Elements ◽

Shell Models ◽

The Family ◽

Model Features

We focus on a family of shell elements which are a direct generalization of the shell elements most commonly used in engineering practice. The elements in the family include the effects of the through-the-thickness normal stress and can be employed to couple directly with surrounding media on either surfaces of the shell. We establish the "underlying" mathematical model of the shell discretization scheme, and we show that this mathematical model features the same asymptotic behaviors — when the shell thickness becomes increasingly smaller — as classical shell models. The question of "locking" of the finite element discretization is also briefly addressed and we point out that, for an effective finite element scheme, the MITC approach of interpolation is available.

Download Full-text

Drawing Process Analysis for Electrodeposited Nickel Coating by Finite Element Method

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.291-294.606 ◽

2011 ◽

Vol 291-294 ◽

pp. 606-609

Author(s):

Li Qun Zhou ◽

Yu Ping Li ◽

Cai Ming Fu

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Nickel Coating ◽

Process Analysis ◽

Steel Substrate ◽

Effective Strain ◽

Drawing Process ◽

Interfacial Stresses ◽

Shell Elements ◽

Element Method

A finite element method is used to simulate the deep drawing processes of nickel coating with steel substrate into battery shells. The Belytschko-Wong-Chiang shell elements are used and the kinematical work hardening model is adopted, while the ties with failure contact criterion is given to the coating and substrate interface. The stress-strain field and interfacial stresses in the drawing processes are obtained. The nickel coating appeared to be yielded in the drawing processes, of which the maximum effective stress reached 241MPa, and the biggest effective strain reached 0.7524. The interfacial stresses in the coating and substrate varied during the drawing process, and their maximal values reached 40MPa in compressive state.

Download Full-text