STIFFNESS MATRIX OF THE 4-NODE QUADRILATERAL ELEMENT IN CLOSED-FORM

The stiffness matrix of a plane four-node quadrilateral finite element is given in closed form. when expressed as a FORTRAN subroutine and c ompared with the classical method of forming the stiffness matrix usin g Gaussian integration, the approach gives a CPU time speed-up of the order of 2-3 on a vector machine and of the order of 4-5 on a scalar m achine. The technique used to generate the terms of the stiffness matr ix made use of a computer algebra system which could clearly be extend ed to generate the matrices for other elements types.