摘要：The explicit (semi-analytical) integration of an 8-noded
plane-finite-element stiffness matrix is presented in this work. The element
is superparametric having straight sides. Before to carry out the
integration, the integral expressions are grouped into several groups, thus
avoiding duplication of calculations. Symbolic manipulation and integration
is used to obtain the basic formulae to evaluate the stiffness matrix. Then,
the resulting expressions are manipulated, optimized and simplified in order
to reduce the computation time. Maple symbolic-manipulation software was used
to generate the closed expressions and to write down the corresponding
Fortran code. Comparisons between analytical integration and numerical
integration were made. Regarding the CPU time, it was shown that the
semi-analytical integration required less CPU time than numerical integration
to obtain stiffness matrices. Regarding the accuracy, several tests were
conducted on extremely distorted finite elements. Results shown that the
analytical expressions behave very well even in these cases.
