Variational theory of thin shells and panels

Analytical formulation for local buckling and post-buckling analysis of stiffened laminated panels

“…A single variational principle, that comprehends both equilibrium and compatibility equations, is derived. An application of that formulation can be found in [11], where the post-buckling field of an isotropic truncated hemisphere under axial tensile load is studied applying Ritz method to solve the variational problem.…”

A semi-analytical framework for nonlinear vibration analysis of variable stiffness plates

“…By application of the techniques of variational analysis, it is straightforward to demonstrate that the Euler-Lagrange equations of Eq. ( 6) are indeed the dynamic out-of-plane equilibrium and the compatibility equations [42]. The weak-form formulation of the problem as per Eq.…”

Simplified Approach to Nonlinear Vibration Analysis of Variable Stiffness Plates

“…This result can be viewed as a generalization of the variational approaches of [25,28,31,32,35] for thin plates to incorporate transverse shear deformability in the framework of third-order plate theory. Note that the application proposed in this work regards the nonlinear vibrations, but the same variational principle can be used for other nonlinear problems, such as the post-buckling one.…”

“…The approach developed here relies upon a weak-form formulation of the problem, which proved to be effective in the application of direct solution methods [25,28,31,32]. The underlying variational principle is an extension of the early work due to Giavotto [33], originally developed for thin-plates, and extended here to the case of third-order theory. An application of the strong-form formulation of an analogous mixed strategy is found in [34] for the postbuckling analysis of transversally isotropic plates.…”

“…where the unknowns are given by the amplitudes of the sine and cosine parts of the solution postulated in Equation (35). The two equations above can be merged into one single scalar…”