A rectangular finite element for laminated plate with bonded and/or embedded piezoelectric sensors and actuators is developed based on the variational principle and the first order shear deformation theory. The elemen...A rectangular finite element for laminated plate with bonded and/or embedded piezoelectric sensors and actuators is developed based on the variational principle and the first order shear deformation theory. The element has four-node, 20-degrees-of-freedom with one potential degree of freedom for each piezoelectric layer to represent the piezoelectric behavior. The higher order derivation of deflection is obtained by using the normal rotation expressions to take the effects of transverse shear deformation into considerations. The finite element can accurately simulate the deformation of both thin and moderately thick plates. A Fortran program is written and a number of benchmark tests are exercised to verify its effectiveness. Results are compared well with the existing data. The unbalanced composite with piezoelectric layers is then analyzed by using the model. Results show that the changes of the ratio between the thickness of positive angle layers and the negative angle layers have an effect on the deformation of the structure under the same electric loading.展开更多
A meshless local radial point interpolation method （LRPIM） for solving elastic dy-namic problems of moderately thick plates is presented in this paper. The discretized system equation of the plate is obtained using ...A meshless local radial point interpolation method （LRPIM） for solving elastic dy-namic problems of moderately thick plates is presented in this paper. The discretized system equation of the plate is obtained using a locally weighted residual method. It uses a radial basis function （RBF） coupled with a polynomial basis function as a trial function,and uses the quartic spline function as a test function of the weighted residual method. The shape function has the properties of the Kronecker delta function,and no additional treatment is done to impose essen-tial boundary conditions. The Newmark method for solving the dynamic problem is adopted in computation. Effects of sizes of the quadrature sub-domain and influence domain on the dynamic properties are investigated. The numerical results show that the presented method can give quite accurate results for the elastic dynamic problem of the moderately thick plate.展开更多
The method of lines based on Hu Hai-chang 's theory for the vibration and stability of moderate thick plates is developed. The standard nonlinear ordinary differential equation (ODE) system for natural frequencies...The method of lines based on Hu Hai-chang 's theory for the vibration and stability of moderate thick plates is developed. The standard nonlinear ordinary differential equation (ODE) system for natural frequencies and critical load is given by use of ODE techniques, and then any indicated eigenvalue could be obtained directly from ODE solver by employing the so-called initial eigenfunction technique instead of the mode orthogonality condition. Numerical examples show that the present method is very effective and reliable.展开更多
Bergan-Wang approach has one governing equation in one variable only, namely the transverse deflection of a moderately thick plate. This approach faces no numerical difficulties as the thickness becomes very small. Th...Bergan-Wang approach has one governing equation in one variable only, namely the transverse deflection of a moderately thick plate. This approach faces no numerical difficulties as the thickness becomes very small. The solution of a fully clamped rectangular plate is presented using two different series solutions. The results of a square plate are compared with the results of the classical plate theory, Reissner- Mindlin theory and the three dimensional theory of elasticity for different aspect ratios. Two types of clamped boundary conditions are investigated. The obtained results show that Bergan-Wang approach gives good agreement for both very thin and moderately thick plates.展开更多
文摘A rectangular finite element for laminated plate with bonded and/or embedded piezoelectric sensors and actuators is developed based on the variational principle and the first order shear deformation theory. The element has four-node, 20-degrees-of-freedom with one potential degree of freedom for each piezoelectric layer to represent the piezoelectric behavior. The higher order derivation of deflection is obtained by using the normal rotation expressions to take the effects of transverse shear deformation into considerations. The finite element can accurately simulate the deformation of both thin and moderately thick plates. A Fortran program is written and a number of benchmark tests are exercised to verify its effectiveness. Results are compared well with the existing data. The unbalanced composite with piezoelectric layers is then analyzed by using the model. Results show that the changes of the ratio between the thickness of positive angle layers and the negative angle layers have an effect on the deformation of the structure under the same electric loading.
基金supported by the National 973 Scientific and Technological Innovation Project (No. 2004CB719402)National Natural Science Foundation of China (No. 10672055)+3 种基金Key Project of NSFC (No. 60635020)Natural Science Foundation for Out standing Youth of China (No. 50625519)Hunan Provincial Natural Science Foundation of China (No. 07JJ6002)Scientific Research Fund of Hunan Provincial Education Department of China (No. 08C230)
文摘A meshless local radial point interpolation method （LRPIM） for solving elastic dy-namic problems of moderately thick plates is presented in this paper. The discretized system equation of the plate is obtained using a locally weighted residual method. It uses a radial basis function （RBF） coupled with a polynomial basis function as a trial function,and uses the quartic spline function as a test function of the weighted residual method. The shape function has the properties of the Kronecker delta function,and no additional treatment is done to impose essen-tial boundary conditions. The Newmark method for solving the dynamic problem is adopted in computation. Effects of sizes of the quadrature sub-domain and influence domain on the dynamic properties are investigated. The numerical results show that the presented method can give quite accurate results for the elastic dynamic problem of the moderately thick plate.
基金The project supported by the Pioneer Fundation of Tongji University
文摘The method of lines based on Hu Hai-chang 's theory for the vibration and stability of moderate thick plates is developed. The standard nonlinear ordinary differential equation (ODE) system for natural frequencies and critical load is given by use of ODE techniques, and then any indicated eigenvalue could be obtained directly from ODE solver by employing the so-called initial eigenfunction technique instead of the mode orthogonality condition. Numerical examples show that the present method is very effective and reliable.
文摘Bergan-Wang approach has one governing equation in one variable only, namely the transverse deflection of a moderately thick plate. This approach faces no numerical difficulties as the thickness becomes very small. The solution of a fully clamped rectangular plate is presented using two different series solutions. The results of a square plate are compared with the results of the classical plate theory, Reissner- Mindlin theory and the three dimensional theory of elasticity for different aspect ratios. Two types of clamped boundary conditions are investigated. The obtained results show that Bergan-Wang approach gives good agreement for both very thin and moderately thick plates.
