DEVELOPMENT OF FINITE-ELEMENTS FOR 2-DIMENSIONAL STRUCTURAL-ANALYSIS USING THE INTEGRATED FORCE METHOD

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.