Plates vs Shells
Plates vs Shells
(OP)
What are the general differences between plates and shell elements? What is a good general handbook for FEA? I'd like something with an explanation of the different element formulations, solver theories, and potential pitfalls.





RE: Plates vs Shells
------------
See FAQ569-1083 for details on how to make best use of Eng-Tips.com
RE: Plates vs Shells
RE: Plates vs Shells
RE: Plates vs Shells
Finite element formulations can consider representing a shell of revolution, a curved shell element or faceted plate elements. The first is described by a conic form of revolution. The second is a portion of a shell element that has two radii of curvature. The third is a flat plate with infinite radii of curvature. Various tri- quad- penti- planforms of the plate can be postulated and differing degrees of freedom can be considered for each class of element. Finite element formulations have been proposed to represent the displacement field within the element. Compatability is assured and equilibrium can be violated, but minimized using energy considerations.
The shell of revolution element can be represented by a single line along the length of the shell. The displacement field can be accurately defined when the user considers a specific shell theory, accounting for the various degrees of freedom. Both axisymmetric and non-axisymmetric responses can be considered. To represent the same shell of revolution with faceted plate elements, the circumferential geometry is approximated. The number of elements required to produce an accurate solution is dependent upon the loading condition and the number of elements required to represent the bending that takes place. A transformation matrix must be suppiled for each element accounting for the placement of the element along the shell's circumferential surface and how it is transformed into a global system. If one were to consider a curved shell element that has a finite planform in each direction, the compatability of the normals at the adjacent edges are assured.
I have found that for shell of revolution analysis, going back to basics and representing the governing equations from stress-strain relations, equilibrium and stress-displacement permits a far more accurate representation (a two-point boundary value problem). Solving these equations numerically generally eleminates all of the questions that arise in finite element formulations.
RE: Plates vs Shells
I was taught that the major differece between a plate and a shell is that shells have curvature plates do not. Both can carry memberane, bending and shear stress resultants.
One has a choice as how to represent a shell. The shell can be considered as part of a conic that has two principle radii of curvature. The shell can be considered as a shell of revolution or as a shell segment.
Finite element methods formulate a stiffness based upon some displacement representation for the planform being considered. The shell of revolution is represent by a reference surface line following the axial curvature of a conic. The shell segment or the plate element has a two-dimensional planform. The geomtry of the assembled elements can be defined along the circumferential direction. The topography of this representation is dependent upon the shell being represented and the loading under investigation. Again displacement representations are developed that assure compatability but not equilibrium. The facated plate element requires an additional consideration or approximation by transforming the edges of adjacent elements to have compatable normals and then a proper global tranformation. Also, the approximation of curvature using flat elements can be a major problem.
With all of the above problems, I find it more convienent to start with the basic equations of equilibrium, strain-displacement and stress-strain relations and develop a two point boundary problem. Solve these equations numerically. Most of the issues between flat plates and curved elements go away.
Several references on this subject can be obtain at my website http://www.volcano.net/~d.citerley
RE: Plates vs Shells
RE: Plates vs Shells
I assumed that the definition of a PLATE was an element capable of supporting both in-plane and lateral loads. The PLATE definition also includes that the assumption of being flat. A SHELL is considered to be a PLATE with two dimensional curvature or as a complete shell of revolution that supports both in-plane and lateral loads. .
A discussion of plate finite elements, their formulation and corresponding kinematic and static displacements is presented in Table 3.1, Bathe, K. and E.L. Wilson, Numerical Methods in Finite Element Analysis, Prentice-Hall 1976. If one were to consider the use of these elements to emulate the response of a SHELL to any given set of loads, a plane stress and a plate bending finite element needs to be combined to represent a finite element PLATE. This requires 3 displacement variables at each node to be considered as degrees of freedom. The CQUAD or CTRIA series of isoparametric membrane-bending or plane strain quadrilateral or triangular plate elements used in MSC NASTRAN performs this task. ANSYS has similar elements. Neither set considers membrane-bending coupling.
Computer programs such as BOSOR4, BOSOR5 and STAGS, developed by Lockheed’s D. Bushnell and B. Almroth, et al, use specific shell theories to develop “finite elements” that incorporate the membrane-bending coupling. The first two use a conic description for defining a shell of revolution segment, while STAGS uses arbitrary shell segments to define the geometry. Similarly, ADINA uses a shell concept, but with a differing isoparametric field descriptions to arrive at a 2D SHELL element. Membrane-bending coupling is properly considered. For this class of element, six degrees of freedom at each node are often used.
A summary of computer codes , capable of performing the analysis requested by the OP, their references, capabilities and availability can be found in the paper: “Shell Analysis,” A Kalnins and L. Weingarten, Shock and Vibration Computer Programs—Reviews and Summaries, SVM-10, 1975 pp 507-525. By reading the references contained therein, one could develop an understanding of what is involved in performing a “proper” analysis and just how PLATE and SHELL elements are used.
I can not accept the use of plane stress elements alone to properly represent the response of a SHELL subject to arbitrary loadings.
RE: Plates vs Shells
RE: Plates vs Shells