Quasicomparison Functions and Substructure Synthesis for Framed Structures Stability Analysis

Abstract

The Rayleigh-Ritz-Meirovitch substructure synthesis method (RRMSSM) is extended to buckling analysis in framed structures. The objective is a computational procedure capable of yielding very accurate critical loads through solution of very-low-order eigenvalue problems. In this regard, numerical examples demonstrate that the convergence characteristics of the proposed RRMSSM for stability analysis are superior to those associated with the finite element method.

Additional results on integrals of beam eigenfunctions

“…As a matter of fact, work has been carried out also on integrals of beam-column eigenfunctions, where the term ‘beam-column’ implies that the concentration is on structural stability rather than vibrations, 22 and the result of the use of beam-column eigenfunctions and their simplest-expression integrals in the RRMSSM has been also very successful, in buckling analysis of frames. 23 Furthermore, clamped-free beam eigenfunctions have been used also in the modelling of aircraft substructures (fuselage, wings and stabilizers) in a new and efficient theory of dynamics and control of aircraft; computationally efficient because the computer power assumed is one of a personal computer as some aircraft – autopiloted unmanned aerial vehicles – may not carry multiprocessor supercomputers; 9 therefore, in this aircraft-dynamics case, avoidance of numerical integration may be important or economical.…”