{"title":"Mapping of C* Elements in Finite Element Method using Transformation Matrix","authors":"G. H. Majzoob,B. Sharifi Hamadani","country":null,"institution":"","volume":1,"journal":"International Journal of Materials and Metallurgical Engineering","pagesStart":13,"pagesEnd":17,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/6459","abstract":"Mapping between local and global coordinates is an\r\nimportant issue in finite element method, as all calculations are\r\nperformed in local coordinates. The concern arises when subparametric\r\nare used, in which the shape functions of the field variable\r\nand the geometry of the element are not the same. This is particularly\r\nthe case for C* elements in which the extra degrees of freedoms\r\nadded to the nodes make the elements sub-parametric. In the present\r\nwork, transformation matrix for C1* (an 8-noded hexahedron\r\nelement with 12 degrees of freedom at each node) is obtained using\r\nequivalent C0 elements (with the same number of degrees of\r\nfreedom). The convergence rate of 8-noded C1* element is nearly\r\nequal to its equivalent C0 element, while it consumes less CPU time\r\nwith respect to the C0 element. The existence of derivative degrees\r\nof freedom at the nodes of C1* element along with excellent\r\nconvergence makes it superior compared with it equivalent C0\r\nelement.","references":null,"publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 1, 2007"}