Structural Vibration Modeling And Characteristic Analysis Based On Isogeometric Method

As an effective way to solve engineering analysis and calculation problems,finite element method has received extensive attention in engineering design and analysis.However,the cumbersome meshing and geometric errors caused by the discretization process limit the application of finite element in complex structural problems.The isogeometric method adopts the high-order continuous splines functions that accurately constructed geometry for engineering modeling and analysis,which avoids the complicated mesh generation and the geometric errors caused by discrete mode of traditional finite element method,especially has the advantage of realizing the seamless combination of Computer-aided design(CAD)and Computer-aided engineering(CAE).Since the isogeometric method was proposed relatively late,the modeling theory for complex structure vibration needs to be further improved.In the structural vibration characteristics study,there are still some key issues,such as the difficulty in simulating the complex boundary conditions of actual engineering,incomplete structural elements,and the multi-field coupling analysis model of composite three-dimensional structures that has not been established yet,etc.For this reason,this dissertation adopted the isogeometric method based on the non-uniform rational B-splines(NURBS)to conduct the vibration modeling and characteristic analysis of beams,plates and shells in engineering structures.The element types and application of isogeometric analysis were further developed and perfected.The research work carried out as follows:Based on the isogeometric method and plane elasticity theory,the modeling method and analysis model for the in-plane vibration of arbitrary quadrilateral plate under complex boundary conditions were established.Two-dimensional NURBS basis functions were used to describe the geometry and displacement domains of arbitrary quadrilateral plate structure,and the in-plane vibration analysis model of the plate structure with complex opening was established with the multi-pathes coupling technology.Two penalty factors were introduced at the boundary,the boundary constraints can be converted into a potential energy form for calculation by using the penalty function method and the boundary coordinate transformation relationship.Then the stiffness and mass matrix of the structure can be obtained by using the iso-parametric element idea to discretize the in-plane vibration equation.In the numerical results,the accuracy and effectiveness of this method were verified through numerical results and comparisons,and the effect of the material parameters,structural parameters and boundary constraints on the in-plane vibration characteristics of orthtropic quadrilateral plates and plates with complex opening were systematically analyzed.Aiming at the vibration problem of multi-directional functionally graded material curved shells,a modeling method of gradient isogeometric curved shells was proposed.First,based on the two-dimensional NURBS basis functions and first-order shear deformation shell theory,the geometry and displacement domains of multi-directional functionally graded curved shells were described.Then,the geometric position under the curvilinear coordinate system was determined by the relationship between the physical domain,and the gradient curved shell element was established from the material property parameters of the material composition along the curved shell surface with the power law or exponential distribution.Five sets of penalty factors were introduced at the boundary of the curved shell to realize the arbitrary boundary constraints of the functionally graded curved shell.This method avoided the geometric errors caused by commercial software based on the finite element method to discretize the curved shell structure,overcame the problem that commercial software based on the finite element method is difficult to effectively simulate and calculate multi-directional functionally graded structures,and it was not limited by geometric shapes and the geometric model and analysis model of the curved shell can be changed only by changing the control points and the weight.On this basis,the advantages of fast convergence speed and high accuracy of this method were verified through numerical examples,and the influence mechanism of material distribution and gradient index on the structural vibration of functionally graded cylindrical shells,hyperbolic shells and saddle-shaped shells was revealed.Based on three-dimensional elastic theory and isogeometric method,a vibration modeling method of the three-dimensional composite structure was established.This method not only considered two distribution types of functionally graded materials and three distribution types of porous materials,but also can accurately describe the geometric model and analysis model of the three-dimensional structure with linear and curved changes variable thicknesses.Since there were no simplified assumptions about the distribution of stress and strain,the method was suitable for solving the vibration problem of beam and plate structures with arbitrary thickness.In addition,on the basis of the functionally graded three-dimensional structural vibration analysis model,the characteristics of temperature-changing materials and the initial stress potential energy caused by temperature rise were considered,and the thermoelastic coupling vibration control equation of the functionally graded rectangular plates and ellipses plates under uniform temperature rise and thermodynamic first and second boundary conditions were derived.Numerical examples showed that the model has good convergence and accuracy,and its calculation results can be used as a calibration benchmark for simplified theory.Finally,the isogeometric method was applied to solve the structural vibration problem of gas turbine blades in engineering practice,with considering the factors of pre-twisted angle,installation angle and variable cross-section,an isogeometric analysis model of functionally graded three-dimensional blade vibration under rotating conditions was established to verify the superiority vibration modeling ability of the isogeometric method in complex structures.This model considered the effects of Coriolis force,centrifugal softening and centrifugal rigidity,and used three-dimensional NURBS basis functions to establish the displacement fields of the pre-twisted blade in the Cartesian Cartesian coordinate system to avoid the conversion process between multiple coordinate systems.Then,by using Hamilton's variational principle,the dynamic equation of the rotating blade was derived.Finally,a standard eigenvalue equations was obtained through discretizing equations and expanding dimensions.Numerical examples showed that this model has good convergence and accuracy,and explored the influence of installation angle,pre-twisted angle,variable cross-section,material properties and rotation speed on the vibration characteristics of the functionally graded three-dimensional blade structure under rotating conditions.