Studies on Moderately Thick Composite Sector Plates - Sharma, Ashish (My University, 2006)
Rapid advancements made in materials science and manufacturing technologies has lead to the application of composite materials in various areas of engineering applica-tions like aerospace industries, marine structures, automobiles, power plant systems etc. The composite materials are often subjected to severe operating conditions with respect to kinds of loadings, temperature variations, vibration, shocks etc. The struc-tural configurations could be in various shapes, the most common being in the form of plates and shells. The plates can be of rectangular, circular, sectoral or of any other shape. There are different kinds of important and complicated phenomena like bend-ing, buckling, vibration etc. associated with these structural elements. Therefore, it is necessary to study adequately these aspects for accurate design estimates. The models studied could be linear for small deformation analysis in linearly elas-tic range. For large deformation analysis or for non-linear constitutive relationships, the model is non-linear. The stringent operating conditions often lead to deforma-tions comparable to plate thickness. This necessitates the application of geometrically non-linear formulations. The computational effort is reduced by reducing the general three dimensional problem to planar problem with the use of different kinds of plate theories. The formulation analyzed in this thesis applies the FSDT and takes in to account von-K´arm´an type of non-linearities. The differential equations governing the behavior of sector plates are more compli-cated as compared to other geometrical configurations. The present thesis attempts to study the behavior of laminated plates in sectoral domain using fast converging Chebyshev polynomials. The linear eigenvalue problems of buckling and free vibration of isotropic and lam-inated composite plates are studied. The non-linear algebraic equations generated from the static large deformation analysis are solved using an incremental iterative scheme based on Newton-Raphson technique. For the study of transient large de-formation response, the temporal discretization is done with the help of Houbolt implicit time marching method and the non-linearity is handled with the help of quadratic extrapolation along with fixed point iteration. Spatial and temporal con-vergence studies have been carried out. Results are validated for sector plates and square plates. The variations of response with a wide range of boundary conditions are studied. The effects of various geometrical parameters like sector angle, thickness ratio and annularity (ratio of inside to outside radii), and of material parameters like orthotropy and lamination schemes have been studied. Piezolaminated sector plates subjected to piezothermomechanical loadings are also studied.
Keywords: mechanical engineering; applied mechanics; mindlin sector plate; chebyshev polynomials; buckling; free vibration; cylindrical orthotropy; large deformation; non-linear transient response; poezothermomechanical respose