New Thin Plate and Shell Triangles with Translational Degrees of Freedom Only

1999 ◽  
pp. 79-89
Author(s):  
E. Oñate ◽  
F. Zarate
Keyword(s):  
Thin Plate ◽  
Degrees Of Freedom ◽  
Plate And Shell

Analysis of Thin Plate Structures Using the Absolute Nodal Coordinate Formulation

2005 ◽  
Vol 219 (4) ◽  
pp. 345-355 ◽  
Author(s):  
K Dufva ◽  
A A Shabana
Keyword(s):  
Finite Element ◽  
Thin Plate ◽  
Absolute Nodal Coordinate Formulation ◽  
Mass Matrix ◽  
Plate Element ◽  
Shell Elements ◽  
Absolute Nodal Coordinate ◽  
Plate And Shell ◽  
Spatial Parameters ◽  
The Absolute

The absolute nodal coordinate formulation can be used in multibody system applications where the rotation and deformation within the finite element are large and where there is a need to account for geometrical non-linearities. In this formulation, the gradients of the global positions are used as nodal coordinates and no rotations are interpolated over the finite element. For thin plate and shell elements, the plane stress conditions can be applied and only gradients obtained by differentiation with respect to the element mid-surface spatial parameters need to be defined. This automatically reduces the number of element degrees of freedoms, eliminates the high frequencies due to the oscillations of some gradient components along the element thickness, and as a result makes the plate element computationally more efficient. In this paper, the performance of a thin plate element based on the absolute nodal coordinate formulation is investigated. The lower dimension plate element used in this investigation allows for an arbitrary rigid body displacement and large deformation within the element. The element leads to a constant mass matrix and zero Coriolis and centrifugal forces. The performance of the element is compared with other plate elements previously developed using the absolute nodal coordinate formulation. It is shown that the finite element used in this investigation is much more efficient when compared with previously proposed elements in the case of thin structures. Numerical examples are presented in order to demonstrate the use of the formulation developed in this paper and the computational advantages gained from using the thin plate element. The thin plate element examined in this study can be efficiently used in many applications including modelling of paper materials, belt drives, rotor dynamics, and tyres.

scholarly journals Application of Multigrid Method to Thin Plate and Shell

2006 ◽  
Vol 47 (546) ◽  
pp. 622-626
Author(s):  
Hiroshi FUKIHARU ◽  
Mizuki SAWADA ◽  
Yasuto YOKOUCHI
Keyword(s):  
Thin Plate ◽  
Multigrid Method ◽  
Plate And Shell

GEOMETRICALLY NONLINEAR STABILITY ANALYSIS OF SHELLS USING GENERALIZED CONFORMING SHALLOW SHELL ELEMENT

2001 ◽  
Vol 01 (03) ◽  
pp. 313-332 ◽  
Author(s):  
JIANHENG SUN ◽  
ZHIFEI LONG ◽  
YUQIU LONG ◽  
CHUNSHENG ZHANG
Keyword(s):  
Degrees Of Freedom ◽  
Shallow Shell ◽  
Shell Element ◽  
Linear Analysis ◽  
Continuity Condition ◽  
Body Motion ◽  
Geometrically Nonlinear ◽  
Nonlinear Stability Analysis ◽  
Plate And Shell ◽  
Element Theory

A generalized conforming finite element theory was presented to satisfy the C1 continuity condition for plate and shell element. The effectiveness of the theory in the linear analysis has been proved. This paper discusses the membrane locking phenomenon of shallow shell element based on the satisfaction of the requirement of rigid body motion, and a technique is developed to eliminate the membrane locking phenomenon. Accordingly a geometrically nonlinear generalized conforming rectangular shallow shell element with tangential degrees of freedom of midpoints of sides is formulated. Nonlinear numerical analysis of shell stability shows that the element exhibits high precision and fast convergence characteristics.

Nonlinear Computational Welding Mechanics for Large Structures

2016 ◽  
Author(s):  
Kazuki Ikushima ◽  
Masakazu Shibahara
Keyword(s):  
Thin Plate ◽  
Degrees Of Freedom ◽  
Large Scale ◽  
Computing Time ◽  
Ship Hull ◽  
Welding Deformation ◽  
Work Time ◽  
Plate Structures ◽  
Large Structures ◽  
Computational Welding Mechanics

Large-scale thin-plate structures including ships are constructed by welding, and distortion can occur after welding. Welding deformation can increase cost and work time, and so it is important to investigate welding deformation before construction. In this research, to predict welding deformation on the construction of a large thin-plate structure, Idealized Explicit FEM (IEFEM) was applied to the analysis of welding deformation on the construction of a ship hull block. In addition, to efficiently analyze deformation of the whole structure of a large-scale structure, an algebraic multigrid (AMG) method was introduced into the IEFEM. Then, this multigrid IEFEM (MGIEFEM) was applied to the analysis of welding deformation on the construction of a ship hull block. The ship hull block consisted of 10 million degrees of freedom and the MGIEFEM analysis was finished within the practical computing time of a week. Thus, it can be said that MGIEFEM is an effective tool for analyzing the welding deformation of real products.

HYBRID TREFFTZ FORMULATION FOR THIN PLATE ANALYSIS

2012 ◽  
Vol 09 (04) ◽  
pp. 1250053 ◽  
Author(s):  
MOHAMMAD REZAIEE-PAJAND ◽  
MAJID YAGHOOBI ◽  
MOHAMMAD KARKON
Keyword(s):  
Thin Plate ◽  
Degrees Of Freedom ◽  
Plate Boundary ◽  
Triangular Element ◽  
Bench Mark ◽  
Test Problems ◽  
Trefftz Method ◽  
Boundary Interpolation ◽  
Boundary Field ◽  
Interpolation Functions

In this paper, two efficient elements are proposed by utilizing hybrid Trefftz method for the analysis of thin plate bending. The triangular element, THT, and the quadrilateral element, QHT, which have 9 and 12 degrees of freedom, respectively. Two independent displacement fields are defined for internal and boundary of the elements. The internal field is selected in such a way that it satisfies the governing equation of the thin plate. Boundary field is dependent on the nodal degrees of freedom via boundary interpolation functions. For deriving boundary interpolation functions, element's edges are assumed to deform like a beam, and the related interpolation functions are used for the boundary fields. The solution accuracies of the famous and hard bench mark problems, such as circular and skew plates, prove the justification of suggested elements. Based on the various test problems, QHT in comparison to other four-sided elements, and THT in comparison to triangular ones, show better results and rapider convergence rate.

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