Beam Constraint Model: A Non-Linear Strain Energy Formulation for Generalized Two-Dimensional Beam Flexures
Beam Constraint Model: A Non-Linear Strain Energy Formulation for Generalized Two-Dimensional Beam Flexures
复制标题
DOI：
10.1115/detc2010-28184
复制
发表时间：
2010
期刊：
影响因子：
--
通讯作者：
S. Awtar;S. Sen
中科院分区：
文献类型：
--
作者：
S. Awtar;S. Sen
在过去，我们已经介绍了梁约束模型（BCM），它捕获了相关的非线性，以预测广义梁挠曲在其刚度和误差运动方面的约束特性。本文提出了一种符合BCM中横向荷载-位移和轴向几何约束关系的梁挠曲非线性应变能公式。导出了一种以梁端位移表示的明确应变能表达式，该表达式适用于广义加载条件、边界条件、初始曲率和梁形状。利用虚功原理，该广义梁的应变能表达式用于确定由多梁组成的挠曲机构的载荷-位移关系，从而确定约束特性。这种方法的好处在于它的数学效率和简洁性，这是使用能量方法所期望的。所有的分析结果都通过非线性有限元分析得到了高精度的验证。此外，提出的能量公式导致了对BCM性质的新见解。ASME版权所有©2010
In the past, we have introduced the Beam Constraint Model (BCM), which captures pertinent non-linearities to predict the constraint characteristics of a generalized beam flexure in terms of its stiffness and error motions. In this paper, a non-linear strain energy formulation for the beam flexure, consistent with the transverse-direction load-displacement and axial-direction geometric constraint relations in the BCM, is presented. An explicit strain energy expression, in terms of beam end-displacements, that accommodates generalized loading conditions, boundary conditions, initial curvature, and beam shape is derived. Using the Principle of Virtual Work, this strain energy expression for a generalized beam is employed in determining the load-displacement relations, and therefore constraint characteristics, for flexure mechanisms comprising multiple beams. The benefit of this approach is evident in its mathematical efficiency and succinctness, which is to be expected with the use of energy methods. All analytical results are validated to a high degree of accuracy via non-linear Finite Element Analysis. Furthermore, the proposed energy formulation leads to new insights into the nature of the BCM.Copyright © 2010 by ASME