The determination of mode shapes for dynamically loaded rigid-plastic structures

Abstract

Mode solutions in rigid-plastic structures subjected to fixed external loads are dynamic solutions which are products of separate functions of space and time. If the small displacement assumptions are adopted, there will exist at least one mode shape for any structure subjected to given fixed external load, and possibly a multiplicity of modes. The time function is a simple linear function, and is easily determined once the mode shape is known. The paper puts forward, a simple in physical terms, algorithm for the determination of mode shapes. An iterative procedure is established in which each iteration is equivalent to the solution of a static limit analysis problem. Convergence is proved.