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

Acta Numerica ◽  
2001 ◽  
Vol 10 ◽  
pp. 215-250 ◽  
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.

scholarly journals 3D-SHELL ELEMENTS AND THEIR UNDERLYING MATHEMATICAL MODEL

2004 ◽  
Vol 14 (01) ◽  
pp. 105-142 ◽  
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.

scholarly journals Solid Modeling and Finite Element Analysis of an Overhead Crane Bridge

10.14311/712 ◽  
2005 ◽  
Vol 45 (3) ◽  
Author(s):  
C. Alkin ◽  
C. E. Imrak ◽  
H. Kocabas
Keyword(s):  
Finite Element ◽  
Optimization Method ◽  
Overhead Crane ◽  
Element Analysis ◽  
Box Girder ◽  
Shell Elements ◽  
Shell Models ◽  
And Performance ◽  
Design Calculations

The design of an overhead crane bridge with a double box girder has been investigated and a case study of a crane with 35 ton capacity and 13 m span length has been conducted. In the initial phase of the case study, conventional design calculations proposed by F. E. M. Rules and DIN standards were performed to verify the stress and deflection levels. The crane design was modeled using both solids and surfaces. Finite element meshes with 4-node tetrahedral and 4-node quadrilateral shell elements were generated from the solid and shell models, respectively. After a comparison of the finite element analyses, the conventional calculations and performance of the existing crane, the analysis with quadratic shell elements was found to give the most realistic results. As a result of this study, a design optimization method for an overhead crane is proposed. 

scholarly journals Study on Bearing Mechanism of Split Grouting Pile Based on Finite Element Simulation

2021 ◽  
Vol 2101 (1) ◽  
pp. 012008
Author(s):  
Jinman Wang ◽  
Shaofei Li ◽  
Mingru Zhou ◽  
Lin Zhong ◽  
Yiming Chen
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Static Load ◽  
Load Test ◽  
Engineering Practice ◽  
Static Load Test ◽  
Element Analysis ◽  
Grouting Pressure ◽  
The Finite Element Analysis ◽  
Field Static

Abstract In order to realize the directional and controllable splitting of splitting grouting, the field grouting test was carried out. Using a new grouting pipe designed, the splitting direction and size of the branch vein are effectively controlled through the control of grouting pressure and grouting amount. In order to explore the bearing characteristics of split grouting pile and provide necessary parameters for the design of split grouting pile composite foundation in engineering practice, the field static load test and indoor geotechnical test of split grouting pile are designed, and the ultimate bearing capacity of single pile and necessary soil parameters are obtained. In order to make up for the limitations of field static load test, the three-dimensional finite element model of pile, soil and branch vein of split grouting pile is established by using the finite element analysis software ABAQUS. The finite element analysis results are compared with the measured values of field test, and the variation laws of pile shaft axial force, stress and displacement of branch vein at different depths, pile side friction, etc. are further explored, Through these changes, the interaction and load transfer mechanism between pile and soil are analyzed, which provides a reference for optimal design.

A Three-Dimensional Rolling Contact Model for a Reinforced Rubber Tire

1989 ◽  
Vol 17 (3) ◽  
pp. 217-233 ◽  
Author(s):  
L. O. Faria ◽  
J. M. Bass ◽  
J. T. Oden ◽  
E. B. Becker
Keyword(s):  
Finite Element ◽  
Three Dimensional ◽  
Rolling Contact ◽  
Element Analysis ◽  
Contact Constraint ◽  
The Finite Element Analysis ◽  
Friction Term ◽  
Fiber Reinforcements ◽  
Incompressibility Constraint ◽  
Shell Finite Element

Abstract A steady state formulation of the rolling contact problem with friction that allows the analysis of free rolling, cornering, acceleration, and braking is presented. This formulation is applied to the finite element analysis of tires. A layered shell finite element with shear deformation that allows for large deflection and rotation is developed. In each layer, orthotropic Hookean materials or Mooney-Rivlin type materials with fiber reinforcements can be used and the incompressibility constraint is enforced with Lagrange multipliers. The contact constraint is enforced with a penalty and the friction term, instead of the usual Coulomb friction, is regularized by a differentiable form that makes it more suitable for numerical analysis. A numerical example for a typical tire is also given.

scholarly journals Finite elements with continuous stress fields in calculation of folded prismatic thin-walled rods and shells

2018 ◽  
Vol 196 ◽  
pp. 01018
Author(s):  
Sergey Nazarenko ◽  
Nina Blokhina
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Degrees Of Freedom ◽  
High Efficiency ◽  
Stress Fields ◽  
Displacement Fields ◽  
Element Analysis ◽  
The Finite Element Analysis ◽  
Shell Finite Element ◽  
Rectangular Shell

The article deals with methods of creating a rectangular wall-beam finite element with eight degrees of freedom per node and continuous stress fields along the boundaries. This effect is achieved by specifying displacement fields in the plane of the element in forms similar to those in finite elements of Bogner, Fox, and Schmitt plate. The article provides algebraic expressions for displacement forms; methods of forming reaction and stress matrices are also considered. Test calculations carried out with the help of “Computational mechanics” FEM complex have proved high efficiency of the finite element analysis performed. A rectangular shell finite element with twelve degrees of freedom per node was developed as a combination of membrane finite element and Bogner, Fox and Schmitt plate element.

Shell Finite Elements for the Analysis of Multifield Problems in Multilayered Composite Structures

2016 ◽  
Vol 828 ◽  
pp. 215-236 ◽  
Author(s):  
Maria Cinefra ◽  
Erasmo Carrera
Keyword(s):  
Finite Element ◽  
Composite Structures ◽  
Single Layer ◽  
Shell Element ◽  
Element Analysis ◽  
The Finite Element Analysis ◽  
Multilayered Plates ◽  
Plates And Shells ◽  
Elasticity Solutions ◽  
Shell Finite Element

This paper deals with the analysis of layered structures under thermal and electro-mechanical loads. Constitutive equations for multifield are considered and the Principle of Virtual Displacements (PVD) is employed to derive the governing equations. The MITC9 shell finite element based on the Carrera's Unified Formulation (CUF) has been applied for the analysis. The models grouped in the CUF have variable through-the-thickness kinematic and they provide an accurate distribution of displacements and stresses along the thickness of the laminate. The shell element has nine nodes and the Mixed Interpolation of Tensorial Components (MITC) method is used to contrast the membrane and shear locking phenomenon. The finite element analysis of multilayered plates and shells has been addressed. Variable kinematics, as well as layer-wise and equivalent single layer descriptions, have been considered for the presented FEs, according to CUF. A few problems are analyzed to show the effectiveness of the proposed approach. Various laminations, thickness ratios and curvature ratios are considered. The results, obtained with different theories contained in the CUF, are compared with both the elasticity solutions given in literature and the analytical solutions obtained using the CUF and the Navier's method.

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