Element Analysis Of Shell Structures Research Articles

The 4th Industrial Revolution and Business Education Reform

Based on recent research works, important concepts on the finite element analysis of shell structures and the relations among them are presented in this paper. We review the basic shell mathematical model, which is the underlying mathematical model of the continuum mechanics based shell finite elements. The asymptotic theory of shell structures then is reviewed and we present how to evaluate the asymptotic behavior in finite element solutions. S-norm is introduced as an error measure of finite element solutions and we show "locking" in the convergence curves of shell finite element solutions. We discuss the concept of "uniform optimal convergence" in finite element analysis of shells. We finally summarize requirements on ideal shell finite elements and propose how to perform benchmark tests of shell finite elements.

Coupled multiscale finite element analysis of shell structures

AbstractIn this paper, a coupled two‐scale shell model is presented. A variational formulation and associated linearisation for the coupled global‐local boundary value problem is derived. The discretisation of the shell is performed with quadrilaterals, whereas the local boundary value problems at the integration points of the shell are discretised using 8‐noded or 27‐noded brick elements, or solid shell elements. The coupled boundary value problem is simultaneously solved within a Newton iteration scheme. Solutions for small strain problems are computed within the so‐called FE2 method. In an important test, the correct material matrix for the stress resultants assuming linear elasticity and a homogeneous continuum is verified. Examples show that the developed two‐scale model is able to analyse the global and local mechanical behaviour of heterogeneous shell structures. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Influence functions and goal‐oriented error estimation for finite element analysis of shell structures

AbstractIn this paper, we first present a consistent procedure to establish influence functions for the finite element analysis of shell structures, where the influence function can be for any linear quantity of engineering interest. We then design some goal‐oriented error measures that take into account the cancellation effect of errors over the domain to overcome the issue of over‐estimation. These error measures include the error due to the approximation in the geometry of the shell structure. In the calculation of the influence functions we also consider the asymptotic behaviour of shells as the thickness approaches zero. Although our procedures are general and can be applied to any shell formulation, we focus on MITC finite element shell discretizations. In our numerical results, influence functions are shown for some shell test problems, and the proposed goal‐oriented error estimation procedure shows good effectivity indices. Copyright © 2005 John Wiley & Sons, Ltd.

最近のFEMシェル要素の研究について(J02-3 シェル構造の研究展望,J02 シェル構造の計算力学と先端アプリケーション)

A survey was made to cover the recent development in the finite element analysis of shell structures. It was found that the considerable efforts have been made in the past five years to create new types of finite elements for analyzing various mechanical behaviors of shell structures, particularly of composite shell structures.

Stochastic finite element analysis of shells with combined random material and geometric properties

In this work, an extended stochastic formulation of the triangular composite facet shell element TRIC is presented for the case of combined uncertain material (Young’s modulus, Poisson’s ratio) and geometric (thickness) properties. These properties are assumed to be described by uncorrelated two-dimensional homogeneous stochastic fields. The stochastic finite element analysis of shell structures is performed using the spectral representation method for the description of the random fields in conjunction with Monte Carlo simulation (MCS) for the computation of the response variability. Useful conclusions regarding the influence of each one of the structural parameters on the response variability are derived from the numerical tests examined.

On applications of parallel solution techniques for highly nonlinear problems involving static and dynamic buckling

Within this contribution the efficient finite element analysis of shell structures with highly nonlinear behavior is presented. The coupled nonlinear system of equations resulting from the FE discretization is solved using Newton-like procedures, thus the solution of a linear system of equations is needed in each Newton iteration. For fine discretizations the resulting linear systems of equations become very large and their solution dominates the computational effort. Consequently, parallel computers offer major capabilities to reduce the CPU time needed. A geometrical approach for parallelization is used, standard methods for the graph partitioning are employed. It is well known that iterative methods for the solution of linear equation systems are much more suitable for parallelizing compared to direct methods. Therefore in a first step the use of such methods is investigated for the application to badly conditioned problems typical for shell problems in particular in failure situations with almost singular matrices. In the analysis of shell structures with tendencies to buckle a static and a dynamic approach are discussed considering both physical and computational aspects.

Fundamental considerations for the finite element analysis of shell structures

The objective in this paper is to present fundamental considerations regarding the finite element analysis of shell structures. First, we review some well-known results regarding the asymptotic behaviour of a shell mathematical model. When the thickness becomes small, the shell behaviour falls into one of two dramatically different categories; namely, the membrane-dominated and bending-dotninated cases. The shell geometry and boundary conditions decide into which category the shell structure falls, and a seemingly small change in these conditions can result into a change of category and hence into a dramatically different shell behaviour. An effective finite element scheme should be applicable to both categories of shell behaviour and the rate of convergence in either case should be optimal and independent of the shell thickness. Such a finite element scheme is difficult to achieve but it is important that existing procedures be analysed and measured with due regard to these considerations. To this end, we present theoretical considerations and we propose appropriate shell analysis test cases for numerical evaluations.

Finite element analysis of shell structures

A survey of effective finite element formulations for the analysis of shell structures is presented. First, the basic requirements for shell elements are discussed, in which it is emphasized that generality and reliability are most important items. A general displacement-based formulation is then briefly reviewed. This formulation is not effective, but it is used as a starting point for developing a general and effective approach using the mixed interpolation of the tensorial components. The formulation of various MITC elements (that is, elements based on Mixed Interpolation of Tensorial Components) are presented. Theoretical results (applicable to plate analysis) and various numerical results of analyses of plates and shells are summarized. These illustrate some current capabilities and the potential for further finite element developments.

Finite element analysis of smooth, folded and multi-shell structures

The paper is concerned with the nonlinear theory and finite element analysis of shell structures with an arbitrary geometry, loading and boundary conditions. A complete set of shell field equations and side conditions (boundary and jump conditions) is derived from the basic laws of continuum mechanics. The developed shell theory includes the so-called drilling couples as well as the drilling rotation. It is shown that this property is crucial in the analysis of irregular shell structures, such as those containing folds, branches, column supports, stiffeners, etc. The relevant variational principles with relaxed regularity requirements are also presented. These principles provide the mathematical basis for the formulation of various classes of shell finite elements. The developed finite elements include a displacement/rotation based Lagrange family, a stress resultant based mixed and a semi-mixed family as well as so-called assumed strain elements. All elements have six degrees of freedom at each node, three translational and three rotational ones, including the drilling rotation formulated on the foundation of an exact (in defined sense) shell theory. As such, they are equally applicable to smooth as well as to irregular shell structures. The general applicability of the developed elements is illustrated through an extensive numerical analysis of the representative test examples. In order to obtain a still deeper insight into the problem a Lagrange family of standard degenerated shell elements with five degrees of freedom per node and an element with six degrees of freedom per node based on the von Karman plate theory are considered as well. The presented numerical results include complex plate and doubly-curved shell structures. Linear and non-linear solutions with a pre- and post-buckling analysis are discussed.

A co-rotational, updated Lagrangian formulation for geometrically nonlinear finite element analysis of shell structures

A co-rotational, updated Lagrangian formulation for geometrically nonlinear analysis of shells is presented. In this finite element procedure, a standard updated Lagrangian formulation is employed to generate the tangent stiffness matrix, and a co-rotational theory is used for updating element strain, stress and internal force vectors during the Newton-Raphson iterations. Large rotation theory has been accommodated to take into account the nonvectorial characteristic of the rotational degrees-of-freedom. The present procedure is ideally suited for implementation in existing linear finite element programs and its effectiveness has been demonstrated by a number of numerical examples.

The application of a finite shell element for composites containing piezo-electric polymers in vibration control

Advanced composite structures with integrated sensors and actuators are becoming increasingly important due to the demand for very large, low-mass space structures. This paper focuses on the finite element analysis of shell structures with thin piezo-electric layers bonded to the surfaces. A finite element formulation taking the piezo-electric effect into account is given and a finite shell element is presented, allowing for the computation of these advanced composite structures. The dynamic matrix equation accounting for the piezo-electric material response is formulated and found to have the same form as the well-known equation of structural dynamics. By using the second or direct method of Lyapunov, a control law is derived, which is used in vibration control and ensures asymptotic stability. A numerical example is given to show the accuracy of the finite element, as well as the efficiency of the algorithm.