A hypercircle method of frame analysis. I: Theory. II: Practice (Q1098361)

The hypercircle method of \textit{J. L. Synge} and \textit{W. Prager} [Q. Appl. Math. 5, 241-269 (1947; Zbl 0029.23505)] is applied to the structural analysis of rigid-jointed planar frames. In Part I theoretical foundations of the method are developed and bounding formulae derived. These provide upper and lower bounds, as narrow as desired, on strain energy, local deformation and internal stress. A new procedure for reducing the number of statical and kinematical degrees of freedom is introduced. In Part II the hypercircle method of structural analysis, is shown to have certain advantages, in terms of computer time required, over conventional methods of analysis for very large rigid-jointed planar frames. This efficiency is achieved by the systematic use of ``superelements'' based on the four-node rectangular finite element.