摘要
插值型重构核粒子法的形函数结合了包含Kronecker delta特性的简单函数和由基函数向量采用重构条件构造的增强函数,并且具有点插值特性和不低于核函数的高阶光滑性.该方法可直接施加本质边界条件,同时也保证了较高的计算精度.基于插值型重构核粒子法,文章提出了一种求解平面黏弹性力学问题的新方法.采用弹性-黏弹性对应原理和Laplace变换,将黏弹性问题转化为Laplace域内的准弹性问题,并采用插值型重构核粒子法进行求解,然后借助Laplace数值逆变换求得黏弹性问题的解.数值算例验证了本文所提方法的有效性.
The shape function of the interpolating reproducing kernel particle method combines a simple function including Kronecker delta property and an enhancement function constructed by the basis function vector using reconstruction conditions,and therefore has a point interpolation property and no less than the high-order smoothness of kernel function. This method can not only impose the essential boundary conditions directly but also assure the computational accuracy. A new method for the solution of two-dimensional viscoelastic problems was proposed based on the interpolating reproducing kernel particle method. By virtue of the elastic-viscoelastic correspondence principle and the Laplace transform technique,the viscoelastic problem was converted into a quasi-elastic problem in the Laplace domain,which was solved by the interpolating reproducing kernel particle method. Then the numerical inversion of Laplace transform was applied to obtain the viscoelastic solution.Numerical examples demonstrated the effectiveness of the proposed method.
作者
李情
陈莘莘
LI Qing;CHEN Shenshen(School of Civil Engineering and Architecture,East China Jiaotong University,Nanchang 330013,China)
出处
《湖南科技大学学报（自然科学版）》
CAS
北大核心
2021年第1期52-56,共5页
Journal of Hunan University of Science And Technology：Natural Science Edition
基金
国家自然科学基金资助项目(11772129)。
关键词
插值型重构核粒子法
LAPLACE变换
黏弹性
对应原理
interpolating reproducing kernel particle method
Laplace transformation
viscoelasticity
correspondence principle
