A local coordinate system for assumed strain shell element formulation

1995 ◽  
Vol 15 (5) ◽  
pp. 473-484 ◽  
Author(s):  
H. C. Park ◽  
S. W. Lee
2016 ◽  
Vol 16 (09) ◽  
pp. 1550053 ◽  
Author(s):  
Z. X. Li ◽  
T. Zheng ◽  
L. Vu-Quoc ◽  
B. A. Izzuddin

A 4-node co-rotational quadrilateral composite shell element is presented. The local coordinate system of the element is a co-rotational framework defined by the two bisectors of the diagonal vectors generated from the four corner nodes and their cross product. Thus, the element rigid-body rotations are excluded in calculating the local nodal variables from the global nodal variables. Compared with other existing co-rotational finite-element formulations, the present element has two features: (i) The two smallest components of the mid-surface normal vector at each node are defined as the rotational variables, leading to the desired additive property for all nodal variables in a nonlinear incremental solution procedure; (ii) both element tangent stiffness matrices in the local and global coordinate systems are symmetric owing to the commutativity of the nodal variables in calculating the second derivatives of strain energy with respect to the local nodal variables and, through chain differentiation with respect to the global nodal variables. In the modeling of composite structures, the first-order shear deformable laminated plate theory is adopted in the local element formulation, where both the thickness deformation and the normal stress in the direction of the shell thickness are ignored, and an assumed strain method is employed to alleviate the membrane and shear locking phenomena. Several examples involving composite plates and shells with large displacements and large rotations are presented to testify to the reliability and convergence of the present formulation.


1997 ◽  
Author(s):  
Chahngmin Cho ◽  
Brian Kemp ◽  
Sung Lee ◽  
Chahngmin Cho ◽  
Brian Kemp ◽  
...  

Author(s):  
Behrooz Fallahi ◽  
S. Lai ◽  
C. Venkat

Abstract The need for higher productivity has lead to the design of machines operating at higher speeds. At high speed the rigid body assumption is no longer valid and the links should be considered flexible. In this work a method which is based on Modified Lagrange Equation for modeling flexible mechanism is presented. The method posses a more computational efficiency for not requiring the transformation from the local coordinate system to the global coordinate system. Also an approach using the homogeneous coordinate for element matrices generation is presented. The approach leads to a formalism where the displacement vector is expressed as a product of two matrices and a vector. The first matrix is a function of rigid body motion. The second matrix is a function of rigid body configuration. The vector is a function of elastic displacement. This formal separation helps to facilitate the generation of element matrices using symbolic manipulations.


1995 ◽  
Vol 117 (3) ◽  
pp. 329-335 ◽  
Author(s):  
Behrooz Fallahi ◽  
S. Lai ◽  
C. Venkat

The need for higher manufacturing throughput has lead to the design of machines operating at higher speeds. At higher speeds, the rigid body assumption is no longer valid and the links should be considered flexible. In this work, a method based on the Modified Lagrange Equation for modeling a flexible slider-crank mechanism is presented. This method possesses the characteristic of not requiring the transformation from the local coordinate system to the global coordinate system. An approach using the homogeneous coordinate for element matrices generation is also presented. This approach leads to a formalism in which the displacement vector is expressed as a product of two matrices and a vector. The first matrix is a function of rigid body motion. The second matrix is a function of rigid body configuration. The vector is a function of the elastic displacement. This formal separation helps to facilitate the generation of element matrices using symbolic manipulators.


Author(s):  
Philippe Jetteur ◽  
Philippe Pasquet

A new 3D solid shell element is developed in SAMCEF™ code. The purpose of this element is to make the meshing easier starting from a 3D definition of the structure, it is not necessary to extract the mean surface of the shell. Here, we are not concerned by the meshing; we only are concerned by the element formulation. In order to improve the quality of the results, we add internal degrees of freedom as suggested by Simo and co-authors. We use the Enhanced Assumed Strain method. A special handling of the transverse shear is performed in order to pass successfully the plate patch test (constant bending) and to avoid shear locking. The formulation is based on the work of Bathe and Dvorkin for classical shell. The element has been developed in linear and non-linear analysis; it can be a mono or multilayer element.


2017 ◽  
Vol 929 (11) ◽  
pp. 2-10
Author(s):  
A.V. Vinogradov

Pretty before long there will be transition to the geodetic system of coordinates of GSK-2011. For the transition period it is necessary to develop a method of recalculating coordinates from one system to another. The existing methods of recalculating coordinates are designed for recalculating coordinate points of state geodetic networks (GGS) and geodetic local networks (GSS). For small areas (administrative districts, populated areas) simplified methods are more acceptable. You need to choose the resampling methods that can be applied in small businesses, performing surveying works. The article presents the the results of calculations of changes of coordinates of the same point in GSK-2011 and SC-95 in six-degree zones of Gauss projection. It was found that in each region values of the shifts changed to small ones. Therefore, it is possible to convert the coordinates of the points by the simplified formulae. For recalculation from the coordinates of GSK-2011 in SK-95 or local coordinate system (WCS) of the administrative district it is necessary to find the origin of coordinates, scale value and rotation of the coordinate axes. The error of the conversion shall not exceed 0,001 m. The coordinates of the initial point of the local coordinate system relative to the central meridian of the local coordinate system shall be added in the list of parameters of the transition from local coordinate system to the state one.


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