基于Kriging代理模型的拉压不同模量平面问题的近似求解

该文建议采用Kriging代理模型数值求解拉压不同模量平面问题。通过本构方程光滑化、有限元法及拉丁超立方采样技术,对拉压不同模量桁架与二维平面问题,给出了基于Kriging模型的近似数值解,以代理基于有限元的数值解,并探讨了样本点数目和问题规模对所建Kriging近似模型求解精度/效率的影响。数值算例表明：所提方法可为求解拉压不同模量平面问题提供精度合理的近似数值解。当问题规模较大且正问题需要多次求解时,该方法有望显著减少计算时间,这对于降低拉压不同模量反问题与优化问题的计算开销十分重要。

AN APPROXIMATE SOLUTION FOR THE BIMODULAR PLANE PROBLEM BASED ON KRIGING SURROGATE MODEL

Kriging surrogate model is suggested to approximate the solutions of bimodular plane elastic problems. By utilizing a smoothed constitutive equation, finite element method, and the Latin hypercube sampling skill, a Kriging model based approximate numerical solution is presented to surrogate the FEM based solution of bimodular trusses and 2D plane problems. The impacts of sample numbers and problem scales on the computing accuracy/efficiency of the surrogate model are investigated. Numerical tests indicate that the proposed approach is capable of providing an approximate numerical solution with a reasonable computing accuracy for the bimodular plane problem, and considerable amount of computing time can be saved particularly when the solutions of direct bimodular problems are continually required and the problem scale is relatively large. The work presented in this paper is significantly valuable for saving computing time in solving the inverse bimodular problem and bimodular optimization problem.