Multiwall shear deformable orthotropic plates: moderate large deflections nonlinear analysis: through approximate methods and tests
This lecture presents the behavior of rectangular plates for an equally distributed load acting perpendicular to the surface. When the resulting deflections are relatively small, this problem has known analytical solutions. On the other hand, when the load and deflection are large, compressive and tensile in-plane forces are created in the plate that cause the plate to stiffen, the behavior is non-linear, and the solutions are only approximated.
Two types of plates were studied: a thin plate made of an isotropic material and a relatively thick hollow plate with an internal structure of different shapes. The hollow plate is homogenized into a thick orthotropic plate subject to shear deformations in its cross-section.
The results of the research were summarized in 5 articles, three of which have already been published and two are under peer review.
The behavior of the plates is described by the von Kármán equations set, which does not have a closed analytical solution for a rectangular plate. Therefore, a number of Finite Element Analyses were performed that allow to present the defections and stresses that are developed in the plate. The resulting membrane stress image shows the dangerous points on the plate and suggests ways to reduce the risk.
Calculating the partial derivatives of the deflection and the stress numerically makes it possible to place them within the equations and to demonstrate the correctness of the equations in certain areas of the plate. In addition to this, the use of statistical methods results in empirical expressions that represent the deflections and stresses in plates of different sizes and materials.
Analytical methods for calculating the equivalent elastic constants of hollow plates with a simple internal structure, and methods for measuring the constants in plates with a complex structure are presented. Also, surprising results will be presented in the analysis of thin rectangular plates with a large aspect ratio.