Isogeometric Method Of Mechanical Behavior Analysis For Beam And Plate Structures

During the last decades, the Finite Element Method (FEM) has been developed to become the most popular method of structural analysis, and been intensively applied to practical engineering. In recent years, the emerging Isogeometric analysis presents great potential and bright prosperity to bridge the gap between Computer Aided Design (CAD) and the Finite Element Method (FEM). The IGA method features that the same exact geometry description is maintained throughout the analysis process including refinement. It invokes the isoparametric concept, and the basis functions of NURBS, the most widely used modeling tool in CAD, are used as shape functions for analysis. This implies that the independent refinement techniques of IGA elements can be utilized without a link to the CAD (Computer Aided Design) database, in contrast with the finite element methods. Furthermore, the NURBS-based isogeometric analysis is high-order continuous and robust.Curved beam and thin plats are widely used in civil engineering, hydraulic engineering, mechanical engineering, shipping engineering, aeronautic and airspace engineering. Their mechanical behaviors are quite complicated, and isogeometric method can be utilized to analyze them just due to the above-mentioned advantages. Therefore, this thesis aims to investigate the formulation and numerical implementation of isogeometric method for the static and dynamic behavior analysis of curved beams and thin plates. The detailed works are shown as follows.Firstly, the isogeometric formulas for static and free vibration analysis of curved beam are established by using the virtual displacement principle, and the corresponding numerical solutions are conducted. Formulas in the framework of Isogeometric method for static bending and free vibration analysis of curved beams are derived based on the Timoshenko theory, which takes account of transverse shear deformation. The curved beam models can be represented exactly by NURBS curves, and due to the direct relation of geometry and analysis, there is no any accuracy loss of geometry for curved beam models. Circular arch beam with constant curvature and parabolic as well as elliptical curved beams are involved in the numerical examples, and the effects of slenderness and opening angle on the natural frequency of curved beam are scrutinized. Comparison between the IGA and the reference solutions demonstrates the efficiency and accuracy of proposed method.Subsequently, formulation for static and free vibration analysis of plates is developed based on the principle of virtual displacement and Kirchhoff plate theory, and NUBRS is utilized for description of geometry and approximation of the unknown field variables. Several benchmark numerical examples are presented containing rectangular plate, circular plate, skew plate and L-shape plate structures with various boundary conditions. The numerical results show that there is higher accuracy for both of element subdivision and order elevation. Moreover, the solutions obtained by isogeometric approach are compared with FEM, mesh-free solution and other numerical methods, and the merit of computational efficiency and accuracy of isogeometric analysis is demonstrated.