Research On Isogeomtric Analysis And Scaled Boundary Isogeometric Analysis And Their Applications In Engineering

Based on the Isogeometric Analysis (IGA) and Scaled Boundary Finite Element Method (SBFEM), a new numerical method termed as the Scaled Boundary Isogeometric Analysis Method (SBIGA) is proposed. SBIGA features high precision and high efficiency. Based on in-depth investigation into various related aspects, this method has been applied to the dynamic analysis of dam-reservoir-foundation system, structure mechanics, electromagnetic analysis and bending and vibration analysis of thin plate.IGA is a numerical method aiming to seamlessly integral CAD and CAE systems. Spline function employed in CAD geometry is inherited as function of computational analysis, which greatly improves accuracy of the gradient field of variables. And spline function can be very convenient for geometry refinement. SBFEM is a semi-analytical method for solving partial differential equations, in which the problem is reduced by one with only boundary discredited and the fundamental solution is unnecessary. It is superior to solve infinite domain and stress singularity problems containing crack tip.The newly proposed method SBIGA combines the advantages of IGA and SBFEM, which further improve the accuracy and efficiency beyond IGA and SBFEM. Thus, it is suitable to be applied to the practical engineering structure, where the accuracy and efficiency will be greatly improved. SBIGA can be seamlessly connected with IGA. Thus, an efficient simulation method is established for dam-reservoir-foundation system by coupling IGA and SBIGA, in which both structure-soil interaction and fluid-structure interaction are taken into consideration. IGA, SBFEM and SBIGA are extended to solve problems in new areas, including structure mechanics, electromagnetism, and elastic thin plate problems.In the process of research, the innovative achievements are as follows:(1) SBIGA was proposed by combining advantages of IGA and SBFEM. The discretized equation and solution procedure were derived for both elastic and dynamic problem for mechanics and electromagnetism, respectively. Both h-refinement and p-refinement can be easy implemented only one boundary and more flexible continuity can be reach in the circumferential direction while analytical property was hold in the radial direction. Faster ratio of convergence can be reached by SBIGA rather than other methods. The applying strategies for various types of boundary conditions in SBIGA were studied in detail. (2) An efficient simulation method was established for dam-reservoir-foundation system by coupling IGA and SBIGA, in which both structure-soil interaction and fluid-structure interaction are taken into consideration. In fluid-structure interaction, water compressibility, wave reflection at bottom of reservoir and radiation damping effect of infinite reservoir were efficiently portrayed, and pressure-force transformation matrix was constructed to leave out redundant operations. In soil-structure interaction, a new discretization strategy for acceleration unit-impulse response function was established, and the adaptive strategy was proposed to determine the series of acceleration unit-impulse response function. The coupled method was applied to seismic response analysis of high arch dam aiming to provide an important reference for seismic safety evaluation of dam.(3) Effective schemes were put forward for several issues encountered in the application of IGA, SBFEM and SBIGA in new areas. New search scheme of intersection point and local reconstruction for trimmed surface was proposed in IGA. Instead of element-based search scheme, the new scheme was oriented to trimmed curve and the interaction point was determined step by step along the tangent direction of the trimmed curve. Lagrange multiplier schemes were proposed for repeated control points and nonhomogeneous boundary value problems. IGA was expanded in electromagnetic field analysis, including problem of electrostatic field and waveguide eigenvalue. It significantly improved the computational efficiency and accuracy, which was important for design of electronic components, such as capacitors and waveguide. IGA was applied in the analysis of bending and vibration of thin plates by employing Nitsche functional. Degrees of freedom significantly were reduced due to eliminating the rotational degree of freedom, while C1continuity was also satisfied. The optimum stability parameters were discussed for bending and vibration, respectively. The concept of moving scaling center was proposed for eccentric domain, which further extended the scope of the method.It’s observed from the research work that IGA and SBIGA have good prospect and potential in engineering applications, and more extensive and in-depth study should be done.