A SURVEY OF PARAMETRIZED VARIATIONAL-PRINCIPLES AND APPLICATIONS TO COMPUTATIONAL MECHANICS
A SURVEY OF PARAMETRIZED VARIATIONAL-PRINCIPLES AND APPLICATIONS TO COMPUTATIONAL MECHANICS
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DOI：
10.1016/0045-7825(94)90214-3
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发表时间：
1994-03-01
影响因子：
7.2
通讯作者：
FELIPPA, CA
中科院分区：
文献类型：
--
作者：
FELIPPA, CA
本综述介绍了参数化变分原理 (PVP) 领域的最新发展以及有限元计算力学的选定应用。 PVP 是包含对欧拉-拉格朗日方程没有影响的自由参数的变分原理。 基于规范函数（也称为零拉格朗日函数）的单场 PVP 理论是变分微积分逆问题的一个子集，其价值有限。 另一方面，从理论和实践的角度来看，多领域 PVP 更有趣。 在教程介绍之后，本文描述了弹性和电磁学多个领域中多场 PVP 的最新构造。 然后讨论有限元计算力学的三个应用：高性能有限元的推导、单元级误差指标的开发以及有限元模板的构建。 本文最后概述了开放研究领域。
This survey paper describes recent developments in the area of parametrized variational principles (PVPs) and selected applications to finite-element computational mechanics. A PVP is a variational principle containing free parameters that have no effect on the Euler-Lagrange equations. The theory of single-field PVPs, based on gauge functions (also known as null Lagrangians) is a subset of the Inverse Problem of Variational Calculus that has limited value. On the other hand, multifield PVPs are more interesting from theoretical and practical standpoints. Following a tutorial introduction, the paper describes the recent construction of multifield PVPs in several areas of elasticity and electromagnetics. It then discusses three applications to finite-element computational mechanics: the derivation of high-performance finite elements, the development of element-level error indicators, and the construction of finite element templates. The paper concludes with an overview of open research areas.