Continuum Mechanics and Thermodynamics ( IF 2.6 ) Pub Date : 2022-07-02 , DOI: 10.1007/s00161-022-01119-2 Sorin Vlase, Marin Marin, Andreas Öchsner, Maria Luminita Scutaru
A planar mechanism represents a mechanism that is frequently used in engineering, and very often, the elasticity of some elements of the mechanism cannot be neglected. Consideration of all rigid elements does not allow the analysis of vibrations or situations of loss of stability of some elements. Gibbs–Appell’s generalized equations are used in this paper to obtain the governing equations for a two-dimensional finite element, which is in plane motion. Using Lagrange’s equations is the most widely used way for researchers to address such a problem. This is mainly due to the familiarity of researchers with this robust calculation method. There are two major advantages of applying this formalism: a smaller number of differentiation operations is needed to be performed and, by eliminating Lagrange multipliers, the number of unknowns decreases significantly. The method is applied for the plane multibody systems with elastic elements. We hope that this method, due to its simplicity, will be interesting for mechanical designers.
中文翻译:
用于柔性多体分析的广义 Gibbs-Appell 方程和二维有限元模型
平面机构代表了工程中经常使用的一种机构,而且很多时候,该机构的某些元件的弹性是不可忽视的。考虑所有刚性单元不允许分析振动或某些单元失去稳定性的情况。本文使用 Gibbs-Appell 的广义方程来获得平面运动的二维有限元的控制方程。使用拉格朗日方程是研究人员解决此类问题最广泛使用的方法。这主要是由于研究人员熟悉这种稳健的计算方法。应用这种形式有两个主要优点:需要执行较少数量的微分运算,并且通过消除拉格朗日乘子,未知数显着减少。该方法适用于具有弹性元件的平面多体系统。我们希望这种方法由于其简单性,对机械设计师来说会很有趣。