压电层合梁静动力学分析的高精度梁单元

给出了一个对复合材料压电层合梁进行数值分析的高精度压电层合梁单元。基于Shi三阶剪切变形板理论的位移场和Layer-wise理论的电势场,用力-电耦合的变分原理及Hamilton原理推导了压电层合梁单元列式。采用拟协调元方法推导了一个可显式给出单元刚度矩阵的两节点压电层合梁单元,并应用于压电层合梁的力-电耦合弯曲和自由振动分析。计算结果表明,该梁单元给出的梁挠度和固有频率与解析解吻合良好,并优于其它梁单元的计算结果,说明了本文所给压电层合梁单元的可靠性和准确性。研究结果可为力-电耦合作用下压电层合梁的力学分析提供一个简单、精确且高效的压电层合梁单元。

A high accuracy beam element for static and dynamic analysis of laminated piezoelectric beams

An accurate and efficient laminated piezoelectric beam element is presented for the finite element analysis of composite piezoelectric beams.A refined Shi third-order shear deformable plate theory is used for the kinematics of laminated composite beams.And a Layer-wise theory,which contains the electric parameter at each layer interfaces,is adopted to model the electrical field of the beams.The element formulation is deduced from the mechanical-electro coupled variational principle and Hamiltonian principle.By using the quasi-conforming element technique,a two-noded laminated piezoelectric beam element is derived,in which element stiffness matrix is given explicitly.The accuracy of this beam element is validated by the numerical examples of the bending and free vibration of the laminated piezoelectric beams.The numerical results clearly demonstrate that the deflections and natural frequencies of the laminated piezoelectric beams given by the present beam element are in good agreement with the analytical results,and they are more accurate than other numerical results given by the beam element with the same number of elements.Therefore,the present laminated piezoelectric beam element is reliable and accurate.The laminated piezoelectric beam element presented in the paper provides a simple,accurate and efficient numerical model for the analysis of laminated piezoelectric beams with coupled mechanical and electrical properties used in various engineering applications.