I. Kaljevic et al., DEVELOPMENT OF FINITE-ELEMENTS FOR 2-DIMENSIONAL STRUCTURAL-ANALYSIS USING THE INTEGRATED FORCE METHOD, Computers & structures, 59(4), 1996, pp. 691-706
The integrated force method has been developed in recent years for the
analysis of structural mechanics problems. In the intgrated force met
hod all independent forces are treated as unknown variables, which are
calculated by simultaneously imposing equations of equilibrium and co
mpatibility conditions. The development of a finite element library fo
r the analysis of two-dimensional problems using the integrated force
method is presented in this paper. Elements of triangular and quadrila
teral shapes, capable of modeling arbitrary domain configurations are
developed. The element equilibrium and flexibility matrices are derive
d by discretizing expressions for corresponding potential and compleme
ntary energies, respectively. Independent approximations of displaceme
nt and stress fields within finite elements are performed. Interpolati
on of the displacement field is done similarly as in the standard disp
lacement method. The stress field is approximated using full polynomia
ls of correct orders. A procedure for deriving the stress interpolatio
n polynomials that utilizes the definitions of stress components in te
rms of Airy's stress function is developed. Such derived stress fields
identically satisfy equations of equilibrium, and the resulting eleme
nt matrices are insensitive to the orientation of local coordinate sys
tems. A method to calculate the number of rigid body modes is devised,
and it is shown that the present elements do not possess spurious zer
o energy modes. A number of example problems are solved using the pres
ent library and the results are compared with corresponding analytical
solutions and those obtained from the standard displacement finite el
ement method. A good agreement of the results, and better performance
of the integrated force method, compared to the displacement method, i
n stress calculations, is observed.