Among the most studied models in mathematical physics, Timoshenko beam is outstanding for its importance in technological applications. Therefore it has been extensively studied and many discretizations have been proposed to allow its use in the most disparate contexts. However, it seems to us that available discretization schemes present some drawbacks when considering large deformation regimes. We believe these drawbacks to be mainly related to the fact that they are formulated without keeping in mind the mechanical phenomena for describing which Timoshenko continuum model has been proposed. Therefore, aiming to analyze the deformation of complex plane frames and arches in elastic large displacements and deformation regimes, a novel intrinsically discrete Lagrangian model is here introduced whose phenomenological application range is similar to that for which Timoshenko beam has been conceived. While being largely inspired by the ideas outlined by Hencky in his renowned doctoral dissertation, the presented approach overcomes some specific limitations concerning the stretch and shear deformation effects. The proposed model is applied to get the solutions for some relevant benchmark tests, both in the case of arch and frame structures. It is proved that, also when shear deformation effects are of relevance, the enriched, yet simple, model and numerical computation scheme herein proposed can be profitably used for efficient structural analyses of non-linear mechanical systems in rather nonstandard situations.

在数学物理学中研究最多的模型中，季莫申科束以其在技术应用中的重要性而著称。因此，已经对其进行了广泛的研究，并提出了许多离散化方法，以允许在最不同的情况下使用它。但是，在我们看来，当考虑大变形方案时，可用的离散化方案存在一些缺点。我们认为，这些缺陷主要与以下事实有关：它们在制定时就没有考虑到描述已提出的Timoshenko连续体模型的机械现象。因此，旨在分析弹性大位移和变形状态下复杂平面框架和拱的变形，这里介绍了一个新颖的内在离散的拉格朗日模型，其现象学的应用范围与蒂莫申科束的设想相似。尽管很大程度上受到了Hencky在其著名的博士学位论文中概述的思想的启发，但提出的方法克服了有关拉伸和剪切变形效应的一些特定限制。在拱和框架结构的情况下，所提出的模型被用于获得一些相关基准测试的解决方案。事实证明，当剪切变形效应具有相关性时，本文提出的丰富而又简单的模型和数值计算方案也可有益地用于在相当非标准的情况下对非线性机械系统进行有效的结构分析。尽管很大程度上受到了Hencky在其著名的博士学位论文中概述的思想的启发，但提出的方法克服了有关拉伸和剪切变形效应的一些特定限制。在拱和框架结构的情况下，所提出的模型被用于获得一些相关基准测试的解决方案。事实证明，当剪切变形效应具有相关性时，本文提出的丰富而又简单的模型和数值计算方案也可有益地用于在相当非标准的情况下对非线性机械系统进行有效的结构分析。尽管很大程度上受到了Hencky在其著名的博士学位论文中概述的思想的启发，但提出的方法克服了有关拉伸和剪切变形效应的一些特定限制。在拱和框架结构的情况下，所提出的模型被用于获得一些相关基准测试的解决方案。事实证明，当剪切变形效应具有相关性时，本文提出的丰富而又简单的模型和数值计算方案也可有益地用于在相当非标准的情况下对非线性机械系统进行有效的结构分析。在拱和框架结构的情况下，所提出的模型被用于获得一些相关基准测试的解决方案。事实证明，当剪切变形效应具有相关性时，本文提出的丰富而又简单的模型和数值计算方案也可有益地用于在相当非标准的情况下对非线性机械系统进行有效的结构分析。在拱和框架结构的情况下，所提出的模型被用于获得一些相关基准测试的解决方案。事实证明，当剪切变形效应具有相关性时，本文提出的丰富而又简单的模型和数值计算方案也可有益地用于在相当非标准的情况下对非线性机械系统进行有效的结构分析。