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首页> 外文期刊>International Journal of Solids and Structures >Computational analysis of multi-stepped beams and beams with linearly-varying heights implementing closed-form finite element formulation for multi-cracked beam elements
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Computational analysis of multi-stepped beams and beams with linearly-varying heights implementing closed-form finite element formulation for multi-cracked beam elements

机译：对多裂纹梁单元采用闭合形式有限元公式的多步梁和线性变化梁的计算分析

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摘要

The model where the cracks are represented by means of internal hinges endowed with rotational springs has been shown to enable simple and effective representation of transversely-cracked slender Euler-Bernoulli beams subjected to small deflections. It, namely, provides reliable results when compared to detailed 2D and 3D models even if the basic linear moment-rotation constitutive law is adopted. This paper extends the utilisation of this model as it presents the derivation of a closed-form stiffness matrix and a load vector for slender multi-stepped beams and beams with linearly-varying heights. The principle of virtual work allows for the simple inclusion of an arbitrary number of transverse cracks. The derived at matrix and vector define an 'exact' finite element for the utilised simplified computational model. The presented element can be implemented for analysing multi-cracked beams by using just one finite element per structural beam member. The presented expressions for a stepped-beam are not exclusively limited to this kind of height variation, as by proper discretisation an arbitrary variation of a cross-section's height can be adequately modelled. The accurate displacement functions presented for both types of considered beams complete the derivations. All the presented expressions can be easily utilised for achieving computationally-efficient and truthful analyses.
机译：已经显示了通过带有旋转弹簧的内部铰链来表示裂缝的模型，该模型可以简单有效地表示受到小挠曲的横向开裂细长的Euler-Bernoulli梁。即，即使采用基本的线性矩-旋转本构关系，与详细的2D和3D模型相比，它也提供了可靠的结果。本文扩展了该模型的使用范围，因为它提供了细长多步梁和高度线性变化的梁的闭合形式刚度矩阵和载荷矢量的推导。虚拟工作原理允许简单地包含任意数量的横向裂纹。导出的at矩阵和vector为所使用的简化计算模型定义了“精确”有限元。可以通过每个结构梁构件仅使用一个有限元来实现所提出的元素来分析多裂梁。所呈现的阶梯梁的表达式不仅仅限于这种高度变化，因为通过适当的离散化，可以适当地模拟横截面高度的任意变化。为两种考虑的梁提供的精确位移函数完成了推导。所有呈现的表达式都可以轻松用于实现计算效率高和真实的分析。

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