Establishment And Application Of The Third Version Of Quadrilateral Area Coordinate

With the development of finite element method, more and more attention is paid to natural coordinate. Firstly, a new quadrilateral area coordinate (QACM-â…¢) with two coordinate components is proposed. Then related differential and integral formulae are given and the coordinate system that describes the mesh distortion is discussed. On the basis of the coordinate system, a four-node quadrilateral membrane element QACâ…¢-Q6 is constructed to test the performance of QAC-â…¢. The element can not only give the exact solution for pure bending problem by using distorted meshes, but also overcome trapezoidal locking for the MacNeal thin beam problem. The mixed application of three version quadrilateral area coordinates can be used to formulate a new 8-node quadrilateral membrane element. The formulation procedure and the expression of the shape function matrix of the element are very simple. The element possesses distinguished performance and is insensitive to mesh distortion. Secondly, two plate elements are constructed by the combination of area coordinate and analytical trial function and they have excellent performance through numerical examples. Finally, the shape function spectrum method is used to develop the new thin plate element. In other words, the new thin plate element and its shape functions (the higher order shape functions) are developed on the basis of the shape functional of the membrane element (the lower order shape functions). The derivation process of the element is much simplified and the expressions of the higher power shape functions are simple and clear.