Research On Calculation Method Of Eigen-sensitivity Of Laminated Plates

Laminated plate is a basic structure commonly used in composite materials.It is important to study the influence of structural design parameters on the dynamic characteristics of laminated plates.With the application of laminates in engineering more and more widely,how to quickly and accurately design laminates with required characteristics has become a hot spot in engineering.This requires fast and accurate eigen-sensitivity calculation methods.At present,in the calculation method of eigen-sensitivity,the calculation methods of eigenvector sensitivity mainly include finite difference method,modal superposition method,Nelson class method and iteration method.In recent years,iterative method has been widely used on account of its advantages of symmetry and sparsity of coefficient matrix and its convenience in calculating the sensitivity of multiple eigenvectors.The eigen-sensitivity calculation of laminated model is more complicated due to many design parameters.Based on this background,the main research contents are as follows:（1）The current research status of eigen-sensitivity calculation of laminates is summarized at home and abroad.The constitutive relationship of monolayer composite,the classical laminate theory and the first-order shear deformation theory are introduced,and the necessity of using first-order shear deformation theory to solve the vibration problems of laminated plates is pointed out.The lay-up rules,the method of lay-up representation and the structure design of laminated plates are introduced.（2）A set of RSG plug-in for laminate modeling is developed with the help of Abaqus software.The plug-in can realize multiple calls by the user and improve the speed of pre-processing.The effectiveness of the plug-in is verified by the calculation of the natural frequency of the two laminate structures.Based on the results of modal analysis and the design sensitivity analysis module DSA of Abaqus software,the sensitivity calculation of the natural frequency of laminates to design parameters are studied.The default DSA solution of Abaqus is compared with the finite difference method,and the importance of the appropriate step-size to calculate the sensitivity of eigenvalues is pointed out.Applying Abaqus-Python secondary development technology,a method to calculate the optimal step-size is realized by programming.The optimal step-size is used to approximately calculate the partial derivatives of the relative stiffness matrix and mass matrix,and to calculate the eigenvalue sensitivity.Numerical examples verify the effectiveness of the proposed optimal step-size in solving eigenvalue sensitivity.（3）An adaptive iterative calculation method is proposed to solve the eigenvector sensitivity in a given frequency band.First,the mid-modes to be calculated are determined adaptively.Then,an iterative algorithm is constructed and used to adaptively approximate the unknown low-order modal and high-order modal contributions.This method only needs to carry out a few iterative calculations to obtain high-precision eigenvector sensitivity.Numerical examples demonstrate the effectiveness of the proposed method.