论文标题
一维变分问题的必要条件，适用于弹性
Necessary and sufficient conditions for one-dimensional variational problems with applications to elasticity
论文作者
论文摘要
本文涉及功能的弱且强大的最小化$φ（u）= \ int_a^b f（x，x，u（x），u'（x））\，dx $的必要条件，其中$ u \ in c^1（[a，b]，{\ mathbb r}^n）$。我们首先得出比已知条件更简单的条件，然后将其应用于几个特定问题，包括弹性理论中的稳定性问题。特别是，我们解决了[A. Majumdar，A。Raisch：三维中的扭曲杆，螺旋和屈曲溶液的稳定性，非线性27（2014），2841---2867]，通过找到最佳条件，以实现在各种端点约束下自然笔直的基尔chhoff杆的稳定性。
This paper deals with necessary and sufficient conditions for weak and strong minimizers of functionals $Φ(u)=\int_a^b f(x,u(x),u'(x))\,dx$, where $u\in C^1([a,b],{\mathbb R}^N)$. We first derive conditions which are simpler than the known ones, and then apply them to several particular problems, including stability problems in the elasticity theory. In particular, we solve some open problems in [A. Majumdar, A. Raisch: Stability of twisted rods, helices and buckling solutions in three dimensions, Nonlinearity 27 (2014), 2841--2867] by finding optimal conditions for the stability of a naturally straight Kirchhoff rod under various types of endpoint constraints.
