M.Sc Thesis
M.Sc Student Soffer Gil Tensile Buckling of Rectangular and Full Annular and Sectorial Plates with Elastic Foundation and Tensile Post-Buckling of Annular Plates Department of Civil and Environmental Engineering Professor Emeritus Yeoshua Frostig

Abstract

This research deals with the tensile buckling of rectangular and annular plates that may rest on an elastic foundation and the non-linear response of tensiled annular plates. It focuses on evaluating the critical tensile force and the corresponding buckling modes, while defining an approximated solution model for each case. In addition, one of its goals is to propose a simplified mathematical model that determines the critical tensile load and the number of waves simultaneously. Finally, the tensile post-buckling behavior of annular plates is investigated and a mathematical model is proposed to solve the problem without assuming the number of waves in the circumferential direction.

For the tensile buckling of a rectangular plate, a mathematical model was proposed to calculate the in-plane deformation field using the Method of Lines (MOL) technique for the pre-buckling stage. A transverse out-of-plane deformation was proposed that consists of a trigonometric function multiplied by a decay function, which is similar to the deformation shapes observed in various experiments. This approach allows a simplified, quick and reliable alternative to the finite element analysis.

For the tensile buckling of an annular plate, two models were proposed. The first one uses the perturbation approach and the second model uses the kinematic one. Both models are based on a trigonometric function in the circumferential direction for the out-of-plane deformation. The significant difference between the two models is that in the perturbations approach, the critical tensile load is minimized with respect to the number of waves, while in the kinematic one, the number of waves is defined along with the critical tensile load where the natural eigen frequency approaches zero.

The post-buckling behavior of an annular plate is developed, based on 5 shape-functions in the radial direction. Here, the out-of-plane deformation in the circumferential direction is solved without assuming the number of waves. Thereby, allowing both the number of waves and the shape of the waves to be determined simultaneously. In addition, when such an analysis is performed using finite elements, at certain load levels in the analysis, the out-of-plane deformation shape changes abruptly as the number of the circumferential waves changes. The proposed model here overcome such behaviors theoretically. Also here the governing equations consists of a system of fourth-order nonlinear ODEs. At key points along the analysis, the shape-functions are enhanced using Multi-term Extended Kantorovich Method, which improves the convergence of the numerical solution.

Finally, the use of analytical tools enables quick and precise solutions on one hand and enhances the physical insight of buckling due to tensile loads.