Isogeometric Method For Static And Dynamic Analysis Of Shell Structure

Isogeometric analysis is a new Computer Aided Engineering which uses NURBS spline function as modeling function and interpolation function to realize the same expression of geometric model and analysis model.It has the advantages of avoiding meshing and realizing direct interaction between design and analysis.In this paper,considering the necessity of mechanical research for shell structures and the dominant position of Reissner-Mindlin shell theory in finite element analysis,following the development trend of computer-aided simulation methods,a Reissner-Mindlin shell element based on isogeometric is developed,and its static and dynamic analysis are studied.Theories derivation,algorithms writing and examples verification of linear elastic analysis,geometric nonlinear analysis and free vibration analysis are completed.The theory of isogeometric analysis is studied.The properties of B-spline basis function and NURBS basis function are illustrated,and the method of constructing curves and surfaces is discussed.The concepts and relations of four kinds spaces are studied and explained.The prefinement and h-refinement strategies and their application methods are described.Linear elastic analysis of Reissner-Mindlin shell based on isogeometric analysis is established.The four-coordinate system involved in Reissner-Mindlin shell is studied.The geometric model and displacement field are reconstructed by means of two-dimensional midsurface and normal vector based on the idea of degenerate shell.The strain description is derived from the linear strain tensor,the equilibrium equation is derived from the virtual work principle,and the tangent stiffness matrix is obtained.A complete algorithm is established and the square plate,cylindrical shell supported by rigid membrane and spherical shell with a hole are simulated.Geometric nonlinear analysis of Reissner-Mindlin shell based on isogeometric analysis is established.In order to solve the geometrical nonlinear problem,the stress and strain measurement of the nonlinear problem is firstly clarified.The Total-Lagrange description method is used to construct the physical equation combining the Green strain and the second Piola-Kirchhoff stress,and the geometric nonlinear equilibrium equation of Reissner-Mindlin shell is derived.The nonlinear equations are solved by Newton-Raphson method.The incremental step is calculated automatically for the algorithm,and the simulation is carried out for some classical examples.Free vibration for Reissner-Mindlin shell based on isogeometric analysis is established.The NURBS basis function is used to interpolate the displacement field only in the space domain,and the velocity vector and acceleration vector are solved in the time domain.According to the Bubnov-Galerkin method,the differential equation of dynamics for free vibration is derived in Sobolev space,and the final characteristic equation is obtained according to the properties for linear differential equation with constant coefficients of the second order.The Eigen module is used to solve the generalized eigenvalues,and the classical examples are simulated and verified.