Explicit Triangular Bending Element Matrix

In this method polynomials are assumed in terms of the dimensions of a general triangle to form an element stiffness matrix. To begin with, the number of coefficients in these functions is reduced by considering the geometric and static properties of a triangle. A particular plate solution is then used to evaluate the remaining coefficients in the element stiffness matrix. The resulting explicit matrix can be represented as two submatrices of numerical coefficients. A considerable amount of computer time (about 90%) is saved by using this explicit matrix, compared with the usual procedure. Results obtained from the analysis of simple plate problems were satisfactory. This method of deriving the stiffness matrix is quite general and can therefore be applied to any type of finite element.