基于布谷鸟搜索算法的弹性力学边界条件识别

Identification of elasticity boundary conditions based on cuckoo search algorithm

二维弹性力学Cauchy边界条件反问题的可进入测量部分边界上的全部面力和位移边界条件均已知,难进入测量部分边界上的所有边界条件需要求解。基于边界元方法,采用多项式函数近似未知的面力边界条件,将该反演问题转化为多项式系数识别问题。目标函数定义为已知边界上面力的计算值和给定值之间的最小二乘误差,利用布谷鸟算法最小化目标函数,实现对待求边界上面力边界条件的数值反演。未知位移由反演得到的面力结合其他已知边界条件代入正问题中求解得到。比较了未采用多项式和采用多项式近似的计算结果,并分别讨论了鸟巢数量、多项式阶数及测量误差对数值反演的影响。数值算例验证了布谷鸟算法联合多项式近似可准确有效地求解弹性力学Cauchy边界条件反问题。

For Cauchy boundary condition inverse problems in 2-D elasticity,all the boundary conditions on accessible part of the boundary are known,and the boundary conditions on the rest inaccessible part of the boundary need to be solved.In this paper,based on the boundary element method,and with a polynomial function to approximate the unknown traction boundary conditions,the inverse problem was transformed into a problem with the identification of unknown coefficients of the polynomial.The objective function was defined as the least square error between the calculated values and the given values of the tractions on the measurable part of the boundary.The unknown tractions on the immeasurable boundary were recognized by minimizing the objective function through the cuckoo search(CS)algorithm.Then,the unknown boundary displacements were obtained by solving the direct problem with the inversed tractions and the other known conditions.The calculation results with and without using polynomial approximation were compared,and the influences of nest number,polynomial order and measurement noise on the numerical inversion were also discussed.Numerical examples verify that the CS algorithm combined with polynomial approximation can accurately and effectively solve the Cauchy problem in elasticity.