In this paper, an implicit gradient force‐based beam element is developed for analysis of reinforced concrete structures. The element is settled on the framework of Timoshenko beam theory, and adopts force interpolations to construct the element formulation. The sectional constitutive relation is described by the well‐known fiber model, where the multi‐axial softened damage‐plasticity model is used for concrete fibers and the uniaxial Menegotto‐Pinto model is used for steel fibers, thus the axial‐flexure‐shear interaction can be reflected naturally at material level. Furthermore, to overcome the localization issues arisen from strain‐softening responses, the implicit gradient theory is introduced to the element. The weak form of the gradient enhancement is derived and an efficient subscale numerical solution is developed. The implementation of the proposed element is discussed in detail. Finally, a series of illustrative numerical examples are utilized to demonstrate the performance of the proposed element, and the results indicate that the element is able to reproduce accurate and objective responses of reinforced concrete structures under monotonic and cyclic loadings.

中文翻译：

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基于隐式梯度增强力的Timoshenko纤维单元配方，用于钢筋混凝土结构

本文开发了一种基于隐式梯度力的梁单元，用于分析钢筋混凝土结构。单元在Timoshenko梁理论的框架内解决，并采用力插值法构造单元公式。截面本构关系由著名的纤维模型描述，其中多轴软化损伤-可塑性模型用于混凝土纤维，单轴Menegotto-Pinto模型用于钢纤维，因此轴向-弯曲-剪切相互作用可以在物质层面上自然体现出来。此外，为克服应变软化响应引起的局部化问题，将隐式梯度理论引入到单元中。推导了梯度增强的弱形式，并开发了有效的子尺度数值解。建议元素的实现将详细讨论。最后，利用一系列说明性的数值示例来证明所提出的构件的性能，结果表明该构件能够在单调和循环荷载下再现钢筋混凝土结构的准确和客观的响应。