Stiffness identification of shear structure based on inverse formulation of Rayleigh's principle: Inverse formulation of variational principles of mechanics and structural optimization part 1

The shape, boundary conditions of the loads and displacements, and distributions of mass and stiffness of a continuum are given in classical variational principies, whereas an inverse variational principie deals with a type of problems where boundary shape is unknown. Another type of inverse formulation of variational principie proposed in this paper is applicable to sizing optimization or a stiffness identification probiem. This paper discusses an inverse formulation of Rayfeigh's principle that is useful to identify unknown stiffness for a given eigenvalue and eigenmode. An analytical exampfe is empioyed to illustrate that the inverse minimum principle of potential energy proposed in this paper is useful in identifying discretized stiffness distribution of a shear structure having designated eigenvalue and eigenmode.