Exact Buckling and Frequency Calculations Surveyed

Abstract

The usefulness and simplicity of an existing stiffness matrix method is emphasized by presenting it without its relatively complex proofs, and with simple examples. The method ensures that no natural frequencies are missed in undamped free vibration problems, and that no critical load factors are missed in buckling problems. This is maintained even when using the ‘exact’ member equations obtained by solving the appropriate differential equations. The method applies to all structures for which ‘exact’ member equations exist. The published applications are surveyed. They include rigidly jointed plane frames, space frames, and prismatic assemblies of flat or curved plates which are isotropic or anisotropic, and subjected to in‐plane normal or shear stresses. They also cover efficient multi‐level substructuring, design instead of analysis, damping, forced vibrations, elastic‐plastic collapse and programs for large computers, small computers, and programmable pocket calculators.