In this paper, equilibrium and stability of the von Mises truss subjected to a vertical load are analyzed from theoretical, numerical and experimental points of view. The bars of the truss are composed of a rubber material, so that large deformations can be observed. The analytical model of the truss is developed in the fully nonlinear context of finite elasticity and the constitutive behavior of the rubber is modeled using the Mooney–Rivlin law. The constitutive parameters are identified by means of a genetic algorithm that fits experimental data from uniaxial tests on rubber specimens. The numerical analysis is performed through a finite element (FE) model. Differently from the analytical and FE simulations that can be found in the literature, the models presented in this work are entirely developed in three-dimensional finite elasticity. Experiments are conducted with a device that allows the rubber specimens to undergo large axial deformations. For the first time, snap-through is observed experimentally on rubber materials, showing good agreement with both theoretical and numerical results. Further insights on Eulerian buckling of the rubber specimens and its interaction with the snap-through are given. A simple formulation to determine the critical load of the truss is presented and its accuracy is validated through experimental observation. Comparisons with a linear elasticity based approach demonstrate that an accurate prediction of snap-through and Eulerian buckling requires nonlinear formulations, such as the ones proposed in this work.

本文从理论，数值和实验的角度分析了垂直荷载下的von Mises桁架的平衡和稳定性。桁架的杆由橡胶材料组成，因此可以观察到较大的变形。桁架的分析模型是在有限弹性的完全非线性环境中开发的，并使用门尼-里夫林定律对橡胶的本构行为进行建模。本构参数通过遗传算法确定，该算法适合于橡胶样品单轴测试的实验数据。数值分析是通过有限元（FE）模型进行的。与文献中的分析和有限元模拟不同，本文中介绍的模型完全基于三维有限弹性来开发。使用允许橡胶样品经受较大轴向变形的装置进行实验。首次在橡胶材料上通过实验观察到了突跳现象，与理论和数值结果均显示出良好的一致性。进一步了解了橡胶样品的欧拉屈曲及其与卡扣的相互作用。介绍了一种确定桁架临界载荷的简单公式，并通过实验观察验证了其准确性。与基于线性弹性的方法进行的比较表明，对快速捕捉和欧拉屈曲的准确预测需要非线性公式，例如本工作中提出的公式。在橡胶材料上通过实验观察到了突跳现象，与理论和数值结果均显示出良好的一致性。进一步了解了橡胶样品的欧拉屈曲及其与卡扣的相互作用。介绍了一种确定桁架临界载荷的简单公式，并通过实验观察验证了其准确性。与基于线性弹性的方法进行的比较表明，对快速捕捉和欧拉屈曲的准确预测需要非线性公式，例如本工作中提出的公式。在橡胶材料上通过实验观察到了突跳现象，与理论和数值结果均显示出良好的一致性。进一步了解了橡胶样品的欧拉屈曲及其与卡扣的相互作用。介绍了一种确定桁架临界载荷的简单公式，并通过实验观察验证了其准确性。与基于线性弹性的方法进行的比较表明，对快速捕捉和欧拉屈曲的准确预测需要非线性公式，例如本工作中提出的公式。介绍了一种确定桁架临界载荷的简单公式，并通过实验观察验证了其准确性。与基于线性弹性的方法进行的比较表明，要准确预测击穿和欧拉屈曲，需要采用非线性公式，例如本工作中提出的公式。介绍了一种确定桁架临界载荷的简单公式，并通过实验观察验证了其准确性。与基于线性弹性的方法进行的比较表明，对快速捕捉和欧拉屈曲的准确预测需要非线性公式，例如本工作中提出的公式。