Dv. Griffiths, STIFFNESS MATRIX OF THE 4-NODE QUADRILATERAL ELEMENT IN CLOSED-FORM, International journal for numerical methods in engineering, 37(6), 1994, pp. 1027-1038
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.