无网格基底函数对梁固有特性计算精度的影响

无网格法是基于移动最小二乘理论构造场函数,构造场函数中权函数和基底函数对无网格法的计算精度有很大影响.为了比较基底函数对无网格法计算精度的影响,本文利用Schmidt正交化方法构造出正交多项式基底函数.运用该正交多项式基和幂函数多项式基,选取了样条型权函数分别构造位移场函数,对弹性结构动力学基本方程进行无网格化离散,得到梁结构无网格动力学方程.采用罚函数方法满足本征边界条件,求解并得到了梁结构固有频率和模态的两种无网格解,与解析解进行了比较和精度分析,并结合均匀悬臂梁结构验证了得出的结论.

Meshless basis function effects on computation of inherency characteristic

Meshless method interpolation function is set up based on moving least-square method(MLSM),Base function and weight function have great effect on the computational precision of meshless method.In order to compare the influence of base function on computational precision,orthogonal polynomial serials are constructed by Schmidt orthogonalizing technique in this paper.Orthogonal polynomial and power function are separately chosen as basis functions,the quartic spline function is chosen as the weight function and Two kinds of field functions are constructed.Basic dynamic equations of structure are dispersed and meshless dynamic equations are gained.Enforced essential boundary conditions are implemented by penalty function.The two different results of natural frequency and modal are solved and compared with analytical result respectively,the computational precision is analysed.Conclusion are validated by example.