• 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>International Journal of Mechanical Engineering Education >On the energy theorems of elasticpin-jointed frames
【24h】

On the energy theorems of elasticpin-jointed frames

机译：关于弹性销钉连接框架的能量定理

获取原文
获取原文并翻译 | 示例
           
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

This paper shows, using only elementary mathematics, that, for a pin-jointed structure with non-linear elastic members, the classical minimum principles can be derived from one fundamental inequality. This is constructed from: (1) Young's inequality, which is applied to the force-extension law, which has been expanded to include terms for thermal expansion or lack of fit; (2) the principle of virtual work, which is first demonstrated using a compact version of an existing proof. The method clearly shows why the theorems of minimum total potential energy and minimum complementary energy are extremum principles and not just stationary ones. The energy theorems of Castigliano and Engesser are also derived from the same inequality. The case of Hookean behaviour is particularly simple, as Young's inequality reduces to the sum of the squares of the error in satisfying the force-extension law. The stiffness method for linear elastic pin-jointed frames is established without the need to use rotation matrices to generate the set of equations for the full frame. Matlab code for the analysis of a three-dimensional pin-jointed frame is included in an appendix.
机译：本文仅使用基础数学就表明，对于具有非线性弹性构件的销连接结构，经典的最小原理可以从一个基本不等式中得出。这是从以下方面构造的：（1）杨氏不等式，适用于力-延伸定律，该定律已扩展为包括热膨胀或缺乏拟合的术语； （2）虚拟工作原理，首先使用现有证明的精简版进行演示。该方法清楚地说明了为什么最小总势能和最小互补能定理是极值原理，而不仅仅是平稳原理。 Castigliano和Engesser的能量定理也源自相同的不等式。 Hookean行为的情况特别简单，因为Young的不等式减少为满足力延伸定律的误差平方和。建立了线性弹性销钉连接框架的刚度方法，而无需使用旋转矩阵来生成整个框架的方程组。附录中包含用于分析三维销钉连接框架的Matlab代码。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号