The mathematical modeling of fluid structure interactions with structural buckling - Nair, Anju V. (2018)
Circular plates are one of the main engineering structural members used in aerospace and construction industries. The circular plates are usually divided into different types such as orthotropic and isotropic owing to their type of material property. The buckling problem of these circular plates due to the temperature changes and its interaction with fluid are one of the great research interests. The thesis aims to present the mathematical formulations and numerical solutions to study the realistic response of orthotropic circular plates subjected to thermal loads as well as the vibration analysis of isotropic and orthotropic circular plates which comes in contact with fluid. The present research work discusses a new approach of mathematical formulations to tackle the postbuckling issues as well as fluid structure interaction problems of these structural members. It consists of four research problems, as two deals with postbuckling response of circular plates with orthotropic material properties and the other two dealing with the fluid structure interaction problems of orthotropic and isotropic circular plates. The first research problem analyses the effect of various approximate functions for the lateral displacement, as well as to evaluate the radial tensile load. The linear buckling load is evaluated using von Kármán approximations and hence by applying the values of linear buckling load and radial edge load, the thermal postbuckling strength of orthotropic circular plates are calculated for both simply supported and clamped boundary conditions. The mathematical formulation of the first problem assumes that the radial displacement is zero. This initial research problem is further reinvestigated as the second research problem to improve the accuracy of results in predicting the thermal postbuckling behavior of orthotropic circular plates. The results from these investigations are within the engineering accuracy (4.02 % for simply supported and 3.67 % for clamped boundary conditions) compared with the finite element method. The reinvestigation determines the radial displacement by selecting an admissible lateral displacement function. Therefore, the second problem determines the thermal postbuckling load of orthotropic circular plate by adding the integrated average. The error percentage is reduced to 1.13 % and 1.77 % for simply supported and clamped conditions, respectively. The third and fourth research problems determine vibration behavior of isotropic and orthotropic circular plates in contact with fluid, respectively. The natural frequencies and corresponding mode shape of the plates in air are evaluated by using Galerkin approximation. The numerical estimation of nondimensionalized added virtual mass incremental (NAVMI) factor is evaluated in uniform and nonuniform thickness cases using MAPLE software. It is found that the NAVMI factor decreases, with an increase in the order of mode number (n = 1, 2 and 3). Moreover, the NAVMI factor for a higher mode (n = 3) is smaller than for a lower mode (n = 1). Based on Rayleigh quotient, the natural frequencies of the plate in contact with fluid are evaluated by calculating the added virtual mass incremental (AVMI) factor for simply supported and clamped boundary conditions. The formulation determines that the natural frequencies of both the circular plates in contact with fluid increases with an increase in number of modes. The numerical results obtained from the present formulation will help the engineers to design safer and more economical structural members in contact with fluid.