Explicit Triangular Bending Element Matrix

by William S. Doyle, Sr. Lect.; Dept. of Civ. Engrg., Univ. of Cape Town, Cape Town, South Africa,
Robert L. Harrison, Res. Student; Dept. of Civ. Engrg., Univ. of Cape Town, Cape Town, South Africa,

Serial Information: Journal of the Structural Division, 1974, Vol. 100, Issue 7, Pg. 1459-1472

Document Type: Journal Paper


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.

Subject Headings: Matrix (mathematics) | Stiffening | Finite element method | Plates | Polynomials | Geometrics | Statics (mechanics) | Computing in civil engineering

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