Possibilities of finite calculus in computational mechanics
Possibilities of finite calculus in computational mechanics
复制标题
有限微积分在计算力学中的可能性
DOI：
10.1002/nme.961
复制
发表时间：
2004
影响因子：
2.9
通讯作者：
E. Oñate
中科院分区：
文献类型：
--
作者：
E. Oñate
“有限微积分”一词指的是在有限大小的时空域中，通过引用通量、力等的平衡来推导力学中的控制微分方程。由这种方法得到的控制方程不同于无限小微积分理论的控制方程，它们包含了依赖于平衡域维度的新项。新的控制方程允许使用任何离散化程序推导自然稳定的数值格式。本文讨论了有限演算法在急梯度对流扩散问题、不可压缩流体流动和不可压缩固体力学问题及应变局部化情况下有限元解的可能性。版权所有©2004 John Wiley & Sons， Ltd
The expression ‘finite calculus’ refers to the derivation of the governing differential equations in mechanics by invoking balance of fluxes, forces, etc. in a space–time domain of finite size. The governing equations resulting from this approach are different from those of infinitesimal calculus theory and they incorporate new terms which depend on the dimensions of the balance domain. The new governing equations allow the derivation of naturally stabilized numerical schemes using any discretization procedure. The paper discusses the possibilities of the finite calculus method for the finite element solution of convection–diffusion problems with sharp gradients, incompressible fluid flow and incompressible solid mechanics problems and strain localization situations. Copyright © 2004 John Wiley & Sons, Ltd.