基于MLNNI法的正交各向异性复合材料参数识别的逆算法

An Inverse Approach to Identify Material Properties of an Orthotropic Medium by the MLNNI Method

为有效确定二维各向异性材料的材料参数,提出一种基于无网格局部自然邻近插值法(MLNNI)的识别方法.该方法只需在目标域上构建节点数组.而其逆问题即求解以模拟数值和实测数据之间偏差为目标函数的最小值,并采用复变函数微分法(CVDM)计算用于获取新的参数的灵敏度系数.区别于有限差分法,复变函数微分法对步长大小不敏感,而且若步长足够小,灵敏度系数的精度可以非常精确.数值算例表明所提出的方法有效.

To determine material parameters of two-dimensional orthotropic materials, a new identification approach is proposed in this work based on the meshless local natural neighbor interpolation （MLNNI） method.It is only necessary to construct an array of nodes in the targeted domain.The identification inverse problem is formulated as the minimization of an objective function representing the difference between numerical simulation displacements and measured data.Sensitivity coefficients used to obtain parameter updates are calculated by the complex variable differentiation method （CVDM）.Unlike the finite difference method, CVDM has the advantage of step size insensitivity and sufficiently small steps.The accuracy of the sensitivity coefficients can approach the computer precision.Based on the investigation of numerical example, high accuracy results have been obtained, which demonstrates the potential of our proposed approach.