曲面拟合在拉格朗日反分析方法中应用的探讨

STUDIES ON THE APPLICATION OF CURVED SURFACE- FITTING METHOD TO LAGRANGIAN INVERSE ANALYSIS

把一组不同位置的速度(应变)波形构筑的x-t域离散成8节点或9节点单元,每个单元的插值函数为10或12参数多项式,利用拉格朗日反分析可以得到相应的应力(速度)波形。正如路径线法,曲面拟合反分析的某一单元函数值计算需要利用前一单元与该单元交界点的计算值,因而误差生成和发展有时很难预测、控制。文中对不同位置、不同数量量计线情况下,拉格朗日反分析中的曲面拟合法及路径线法误差生成、发展进行了分析,分析结果对材料实验中布置速度(应变)传感器的数量及其间距是有一定帮助的。

Space and time domain constructed by a series of velocity waveforms at different positions are discretized into eight or nine nodal elements,within each element,interpolating function is taken as polynomial which involves ten or twelve parameters. The corresponding stress histories can be obtained by using Lagrangian inverse analysis. As shown by path-line method for inverse analysis,the calculation of one element must make use of the calculated values of intersection points between the element and its preceeding adjacent one in the curved surface-fitting method for inverse analysis. So production and spread of error are sometimes difficult to predict and control. In this paper, production and spread in error are analysed from the curved surface-fitting and path-line method of inverse analysis for gage lines with different numbers and distances, the analytical results are helpful for arranging the number and positions of velocity transducers.