The nonlinear behaviour of a simply supported granular column loaded by an axial force is studied in this paper. The granular column is composed of rigid grains (discs) elastically connected by some shear and rotational springs. The in-plane buckling and post-buckling analysis in a geometrically exact framework is numerically investigated from a nonlinear difference eigenvalue problem. The granular column asymptotically behaves as an Engesser–Timoshenko column for a sufficiently large number of grains. An exact analytical solution of the buckling load of this discrete shear granular system is obtained from the linearization of the granular elastica problem. An asymptotic expansion is applied to the difference eigenvalue problem, to efficiently approximate the equation of the primary post-bifurcation branch of the discrete problem. Exact analytical solutions of the post-buckling branches are also available for the granular problem with few numbers of grains. Bifurcation diagrams of the granular elastica problem composed of few grains are numerically obtained with the simplex algorithm (for an exhaustive capture of all post-bifurcation branches). It is shown that the post-buckling of this granular column reveals complex behaviour similarly to the post-buckling of a generalized shear Hencky column (also called discrete Engesser elastica). Complex higher-order branches are exhibited, a phenomenon very similar to the discrete elastica problem. These branches reveal the specific nature of the discrete granular problem, as opposed to its continuum limit valid for an infinite number of grains

本文研究了受轴向力加载的简支颗粒柱的非线性行为。颗粒柱由刚性颗粒（圆盘）组成，通过一些剪切和旋转弹簧弹性连接。从非线性差分特征值问题对几何精确框架中的平面内屈曲和后屈曲分析进行了数值研究。对于足够多的颗粒，颗粒柱渐近地表现为 Engesser-Timoshenko 柱。该离散剪切颗粒系统的屈曲载荷的精确解析解是从颗粒弹性问题的线性化中获得的。渐近扩展应用于差分特征值问题，以有效地逼近离散问题的主要后分岔分支的方程。后屈曲分支的精确解析解也可用于具有少量晶粒的颗粒问题。由少数颗粒组成的颗粒弹性问题的分岔图是通过单纯形算法（用于详尽捕获所有分岔后的分支）在数值上获得的。结果表明，这种粒状柱的后屈曲表现出类似于广义剪切 Hencky 柱（也称为离散 Engesser elastica）的后屈曲的复杂行为。展示了复杂的高阶分支，这种现象与离散弹性问题非常相似。这些分支揭示了离散颗粒问题的特定性质，而不是它对无限数量的颗粒有效的连续统限制 由少数颗粒组成的颗粒弹性问题的分岔图是通过单纯形算法（用于详尽捕获所有分岔后的分支）在数值上获得的。结果表明，这种粒状柱的后屈曲表现出类似于广义剪切 Hencky 柱（也称为离散 Engesser elastica）的后屈曲的复杂行为。展示了复杂的高阶分支，这种现象与离散弹性问题非常相似。这些分支揭示了离散颗粒问题的特定性质，而不是它对无限数量的颗粒有效的连续统限制 由少数颗粒组成的颗粒弹性问题的分岔图是通过单纯形算法（用于详尽捕获所有分岔后的分支）在数值上获得的。结果表明，这种粒状柱的后屈曲表现出类似于广义剪切 Hencky 柱（也称为离散 Engesser elastica）的后屈曲的复杂行为。展示了复杂的高阶分支，这种现象与离散弹性问题非常相似。这些分支揭示了离散颗粒问题的特定性质，而不是它对无限数量的颗粒有效的连续统限制 结果表明，这种粒状柱的后屈曲表现出类似于广义剪切 Hencky 柱（也称为离散 Engesser elastica）的后屈曲的复杂行为。展示了复杂的高阶分支，这种现象与离散弹性问题非常相似。这些分支揭示了离散颗粒问题的特定性质，而不是它对无限数量的颗粒有效的连续统限制 结果表明，这种粒状柱的后屈曲表现出类似于广义剪切 Hencky 柱（也称为离散 Engesser elastica）的后屈曲的复杂行为。展示了复杂的高阶分支，这种现象与离散弹性问题非常相似。这些分支揭示了离散颗粒问题的特定性质，而不是它对无限数量的颗粒有效的连续统限制