Hamilton体系下复合材料层合板特征值灵敏度分析研究

STUDIES ON THE SENSITIVITY ANALYSIS OF EIGENVALUES FOR COMPOSITE LAMINATED PLATES IN HAMILTONIAN SYSTEMS

在结构优化过程中,精确的结构参数灵敏度分析是最主要的困难之一。该文在Hamilton体系下推导了复合材料层合板特征值响应灵敏度系数的控制方程,基于BSWI(B-spline wavelet on the interval)样条小波有限元方法,利用二分法求得了四边固支复合材料层合板前四阶特征值对材料密度的灵敏度系数,并与有限差分法所得结果相比较,证明了该文所提出方法的可靠性。另外,该方法能够方便地拓展到复杂层合板壳结构以及智能材料层合板特征值灵敏度系数的求解问题中去。

In the structural shape optimization（SSO） procedures,one of the main difficulties is to perform an accurate sensitivity analysis for structural responses with respect to some parameters such as structural shape sizes and material properties and so on.Based on BSWI（B-spline wavelet on the interval） wavelets element method,the governing equation of sensitivity coefficients of the eigenvalue response for composite laminated plates is derived in Hamiltonian Systems.The sensitivity coefficients of the first 4 order eigenvalues are obtained by bisection method with respect to the density of composite laminated plates whose sides are clamped.And the numerical results of bisection method are compared with that of the finite difference ones.The reliability of this eigenvalue sensitivity analysis method which based on the wavelets and Hamiltonian Systems is proved by the comparison.On additions,the eigenvalue sensitivity analysis method proposed can be expediently extended to the eigenvalue sensitivity analysis of complex laminate shell structures and intelligent composite laminated structures.