Analysis of Plate Bending by Triangular Elements

A triangular element composed of three subelements is proposed with the use of a quadratic displacement function for each subelement. The function allows the rigid-body displacement of the element, satisfies the compatibility of displacements along the boundaries between subelements as well as adjacent elements, and leads to states of uniform stress or strain. Numerical examples are given to show the accuracy of the results obtained by the proposed method, its adaptability to the solution of plate bending problems which are difficult to treat by other procedures, and the monotonic convergence of the results toward available exact solutions as the mesh size becomes finer. The use of the proposed function in the derivation of the stiffness matrix for a polygonal element is also described.