چكيده لاتين
Since the mathematical representation of most physical phenomena is usually in the form of algebraic, differential, or integral equations, solving these equations is essential for predicting their behavior. Although analytical and exact solutions are preferred, unfortunately, only a small fraction of simple problems can be solved exactly. Most practical and research problems are complex and inevitably require numerical solution methods to obtain approximate solutions. As a numerical method, isogeometric analysis (IGA) has been introduced as an efficient approach for solving differential equations due to its capability of accurately modeling geometry. In this method, B-splines and NURBS are utilized as basis functions to simultaneously approximate the geometry and the dependent variables of the governing equation.
In this dissertation, due to the complexity of the subject, beam and plate analyses are first examined, and in the final step, the analysis of functionally graded cylindrical shells is investigated using the isogeometric approach. In the beam analysis section, the concepts and formulation of the isogeometric method for analyzing straight and curved beams are presented. Then, isogeometric static and dynamic analyses are conducted on examples with different geometries. Additionally, suitable geometries for isogeometric analysis are generated using B-spline functions.
In the plate analysis section, after linear macro and micro-scale plate analysis, a geometrically nonlinear model for functionally graded microplates is developed based on the modified strain gradient theory, third-order shear deformation theory, and von Kármán nonlinear strain-displacement relations. In the modified strain gradient theory, three material length scale parameters are considered, which enable the prediction of size effects on the mechanical behavior of microplates. Moreover, if two out of these three length scale parameters are set to zero, the formulation reduces to the modified couple stress theory. It is also noteworthy that increasing the thickness-to-length scale parameter ratio results in greater deformation and a reduction in critical buckling load and vibration frequencies.
Finally, the buckling analysis of functionally graded cylindrical shells is investigated. For this purpose, a portion of the cylindrical shell geometry is constructed using B-spline functions in the curvilinear coordinate system. Then, based on the higher-order shear deformation model, the displacement field is formulated. After deriving the governing equations, they are discretized using NURBS basis functions according to the assumed displacement field. Ultimately, by imposing the essential boundary conditions, the buckling problem of circular cylindrical shells is solved. Furthermore, in the next phase, the post-buckling behavior of cylindrical shells is examined.
