C0- Continuity Isoparametric Formulation using Trigonometric Displacement Functions for One Dimensional Elements
This is an original research on the selection of the trigonometric shape functions in the finite element analysis of the one dimensional elements. A new family of C0- continuity elements is introduced using the trigonometric interpolation model. To relate the natural and global coordinate system for each element of specific structure (i.e. transformation mapping) in one dimensional element a new trigonometric function is used and the new determinant has been introduced instead of polynomial function and Jacobian determinant. The new introduced trigonometric determinant allows for the state of constant strain within the element satisfying the completeness requirement. However, this cannot be achieved using the Jacobian determinant to relate the coordinates while using the trigonometric functions. The finite element formulation presented in this paper gives comparable results with exact solution for all kinds of one dimensional analysis.
