Mapping of C* Elements in Finite Element Method using Transformation Matrix
Mapping between local and global coordinates is an
important issue in finite element method, as all calculations are
performed in local coordinates. The concern arises when subparametric
are used, in which the shape functions of the field variable
and the geometry of the element are not the same. This is particularly
the case for C* elements in which the extra degrees of freedoms
added to the nodes make the elements sub-parametric. In the present
work, transformation matrix for C1* (an 8-noded hexahedron
element with 12 degrees of freedom at each node) is obtained using
equivalent C0 elements (with the same number of degrees of
freedom). The convergence rate of 8-noded C1* element is nearly
equal to its equivalent C0 element, while it consumes less CPU time
with respect to the C0 element. The existence of derivative degrees
of freedom at the nodes of C1* element along with excellent
convergence makes it superior compared with it equivalent C0
element.
[1] B. Bigdeli, An Investigation of *C Convergence in the Finite Element Method, Ph.D Thesis, New South Wales University, Australia, 1996. [2] F.L. Stassa, Applied Finite Element Method, CBS International Editions, 1985. [3] J.L. Tocher, Analysis of Plate Bending Using Triangular Elements, Ph.D Dissertation, University of California, Berkely, 1962. [4] R.W. Clough, Comparison of Three Dimensional Finite Elements, Proceeding of the symposium on Application of Finite Element Method in Civil Engineering, Vanderbilt University, Nashville, pp. 1-26, 1969. [5] S. Ahmad, B.M. Irons, and O.C. Zienkiewicz, Analysis of Thick and Thin Shell Structure by Curved Finite Element, International Journal for Numerical Methods in Engineering, 2 , 419-451, 1974. [6] D.J. Allman, A Compatible Triangular Element Including Vertex Rotation for Plain Elasticity Analysis, Computers and Structures, 19, pp. 1-8, 1984. [7] B. Sharifi Hamadani, The study of the convergence of *C elements in 3-D elasticity (in Persian), MSc Thesis, Mechnaical Engineering Department, Bu-Ali Sina University, Hammadan, Iran, 2001.
[1] B. Bigdeli, An Investigation of *C Convergence in the Finite Element Method, Ph.D Thesis, New South Wales University, Australia, 1996. [2] F.L. Stassa, Applied Finite Element Method, CBS International Editions, 1985. [3] J.L. Tocher, Analysis of Plate Bending Using Triangular Elements, Ph.D Dissertation, University of California, Berkely, 1962. [4] R.W. Clough, Comparison of Three Dimensional Finite Elements, Proceeding of the symposium on Application of Finite Element Method in Civil Engineering, Vanderbilt University, Nashville, pp. 1-26, 1969. [5] S. Ahmad, B.M. Irons, and O.C. Zienkiewicz, Analysis of Thick and Thin Shell Structure by Curved Finite Element, International Journal for Numerical Methods in Engineering, 2 , 419-451, 1974. [6] D.J. Allman, A Compatible Triangular Element Including Vertex Rotation for Plain Elasticity Analysis, Computers and Structures, 19, pp. 1-8, 1984. [7] B. Sharifi Hamadani, The study of the convergence of *C elements in 3-D elasticity (in Persian), MSc Thesis, Mechnaical Engineering Department, Bu-Ali Sina University, Hammadan, Iran, 2001.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:55541", author = "G. H. Majzoob and B. Sharifi Hamadani", title = "Mapping of C* Elements in Finite Element Method using Transformation Matrix", abstract = "Mapping between local and global coordinates is an
important issue in finite element method, as all calculations are
performed in local coordinates. The concern arises when subparametric
are used, in which the shape functions of the field variable
and the geometry of the element are not the same. This is particularly
the case for C* elements in which the extra degrees of freedoms
added to the nodes make the elements sub-parametric. In the present
work, transformation matrix for C1* (an 8-noded hexahedron
element with 12 degrees of freedom at each node) is obtained using
equivalent C0 elements (with the same number of degrees of
freedom). The convergence rate of 8-noded C1* element is nearly
equal to its equivalent C0 element, while it consumes less CPU time
with respect to the C0 element. The existence of derivative degrees
of freedom at the nodes of C1* element along with excellent
convergence makes it superior compared with it equivalent C0
element.", keywords = "Mapping, Finite element method, C* elements,Convergence, C0 elements.", volume = "1", number = "1", pages = "12-4", }