Construction Method Of Isogeometrical Model Based On Hybrid Basis Functions And Its Application

Isogeometric analysis (IGA) is a method aimed at avoiding the meshing procedure of the traditional finite element analysis and a range of issues such as geometric information missing and geometric discretization errors that come with it by using the same basis for analysis as is used to describe the geometry,thus thus integrating CAE into a general CAD modeling system. The high-order geometric basis functions ensure the higher continuity within and between isogeometric elements at the cost of denser stiffness matrices,and the non-interpolatory nature makes the informations of coupling of patches, imposition of loads and boundary conditions not easy to embed into the control points. Basing on analysis and overview of the literature of research status of isogeometric, the selection strategy of analysis-suitable basis function,coupling method of patches,imposition of loads,accelerating computational methods of IGA and the sensitity analysis method based on IGA are deeply studied. According to the research achievenments, the software system for performance analysis based on IGA is developed and applied successfully to the shape error analysis of antenna functional surface.The dissertation is organized as follows:(1) Take full account of the limitations of geometric description ability of Bspline and NURBBS and the geometric complexity,an Euler-Bernoulli IGA beam element based on NURBS and a Kirchhoff-Love shell element based on unstructured T-splines are developed. Writing the basis functions as a linear combination of bemstein polynomials. Comparing with the traditional finite element analysis and the benchmark problem that have analytical solution, the great advantages in solution accuracy and convergence speed are verifed.(2) The construction and evaluation methods of IGA analysis model based on hybrid basis functions are proposed to deal with the geometrical complex products. The coupling between Euler-Bernoulli IGA beam elements based on NURBS, between the beam element and Kirchhoff-Love shell element based on unstructured T-splines is discussed. Stiffness matrix of the analysis model based on hybrid basis functions can then be assembled by integrating the coupling terms. Furthermore, the key technologies of the imposition method of loads which include the classification of elements within the loading domain and the handling of the numerical integration of the domain are presented. A numerical example is presented to demonstrate the accuracy of the imposition method, the combination of the imposition method and isogeometric analysis method based on hybrid basis function are applied to evaluating the surface errors of reflector antenna under multiple load cases.(3) To overcome the reduction of computational efficiency caused by the denser matrices of IGA element, a method to reduce the dimension of the sparse matrices of IGA based on the condensation of degree of freedom of substructures is proposed. First,two coupling cases,'curve-curve' and 'curve-surface',are discussed in the framework of variationally consistent weak coupling method. The assemblies are then divided into several reasonably smaller parts, namely substructures, and the technique of matrix reduction is used to reduce the size of substructures matrices by condensing the interior control points. By adopting the coupling methods, the condensed substructures can be coupled into a system with significantly reduced size. Due to the independence of the calculation and condensation of the substructures matrices,the multi-core parallel computing technology, which is very effective to reduce the computer time, can be easily integrated into the method. Two examples are presented to illustrate the good performance of the proposed method.(4) To avoid the repetitive meshing work, a sensitivity analysis method based on the uniform sampling in the framework of IGA is proposed. The novel sensitivity analysis method uses the optimal latin hypercube sampling instead of the random one and gains a more accurate and stabilized result by fitting the target of maximizing the minimum distance and minimizing the maximum distance between the trajectories. Since the geometry models are also numerical analysis models in IGA, the novel numerical analysis method is utilized to get the performance objectives at each design point, and then the influence of design factors on objectives can be estimated. The proposed sensitivity analysis method is veried to be more stable and accurate than that of current mathods by a test function. Finally, an application of the method in the surface errors design of antenna is presented.(5) The software system for performance analysis based on IGA is developed. The architecture and function modules of the software are described. The efficiency of evaluating the surface errors of the reflector antenna can be improved effectively by the software system, which shows the validity and feasibility of the new theories and methods proposed in this dissertation.