摘要
在保证级数的一致收敛的前提下,可以利用Laplace变换对有限一维空间弹性动力学边值问题给出公理化的严格求解过程,此过程能够作为Lavrentieff与Hilbert等著名学者的工作的补充。这一解答能够应用于岩土工程中的自由场计算问题,并且能够从原则上避免截断误差。在针对特定问题的计算中,该方法的效率明显高于有限元,并且在一定程度上弥补了现有的自由场专用计算软件不能计算纯弹性体的缺点。同时,作为解析解算法,该方法对于数值算法的精度分析有一定意义。
The axiomatic solution process for a one dimensional finite space elastic dynamic boundary value problem can be given by using Laplace transform under the premise of uniform convergence of series, and this process can be a supplement of the work of famous scholars such as Lavrentieff and Hilbert. This solution can be used for the free field analysis in geotechnical engineering, and it can also avoid truncation error in principle. The method in this paper has significantly higher efficiency than that of the finite element method in the calculation for a specific problem, and it can make up for the disadvantage of the existing free field dedicated calculation software which cannot calculate pure elastic bodies to a certain extent. Also, as an analytical algorithm, the method has some significance for the precision analysis of numerical algorithm.
出处
《工程力学》
EI
CSCD
北大核心
2015年第4期47-53,共7页
Engineering Mechanics
基金
清华大学自主科研计划课题项目(2012THZ02-2)
国家自然科学基金重点项目(51038007)
关键词
LAPLACE变换
有限一维空间
边值问题
公理化
一致收敛
波动方程
自由场
Laplace transform
finite one-dimensional space
boundary value problem
axiomatic
uniform convergence
wave equation
free field
