Asymptotic formulation of the role of shear loads on multi-layered thin shells and classification of their deformation modes

IF 5.7 1区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY
Xiwei Pan , Yichao Zhu
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Abstract

Shell structures are generally modeled based on kinematic hypotheses, where some of the parameters are preferentially evaluated in a phenomenological manner. In this article, asymptotic analysis against the underlying three-dimensional equation system is considered so as to provide a rational framework for modeling and interpreting the deformation behavior of multi-layered thin shells (MTSs). Capable of accurately predicting both overall stiffness and detailed stress distribution, the proposed shell theory shows its distinguishing features at least in the following aspects. Firstly, it naturally introduces a rule for classifying the deformation modes of MTSs based on the magnitude of the maximum dimensionless principal curvature. Secondly, for each class, the hierarchy in the order of the involved field quantities is examined, and it is shown that when the product of the maximum principal curvature and the characteristic shell size reaches the magnitude of unity or larger, the resulting shell theory cannot be treated by natural extension of plate theories. Lastly, it is demonstrated that, for moderate shear forces and comparable material properties, a leading-order multi-layered shell theory derived from asymptotic analysis should suffice to output satisfactory predictions over the shell stiffness, as well as its internal stress distribution. Numerical examples of the deformation and strength analysis for MTSs are also presented to show the reliability of the leading-order model.
剪切荷载作用于多层薄壳的渐近公式及其变形模式的分类
壳结构通常基于运动学假设建模,其中一些参数优先以现象学的方式进行评估。本文考虑了对底层三维方程组的渐近分析,从而为多层薄壳(mts)的变形行为建模和解释提供了一个合理的框架。所提出的壳体理论能够准确地预测整体刚度和详细应力分布,至少在以下几个方面显示出其独特的特点。首先,引入了一种基于最大无量纲主曲率大小的mts变形模式分类规则。其次,对每一类所涉及的场量进行了层次分析,结果表明,当最大主曲率与特征壳尺寸的乘积达到或大于1量级时,得到的壳理论不能用板理论的自然推广来处理。最后,研究表明,对于中等剪切力和类似的材料性能,由渐近分析得出的首阶多层壳理论应该足以输出令人满意的壳刚度及其内应力分布预测。最后给出了mts变形和强度分析的数值算例,验证了该模型的可靠性。
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来源期刊
International Journal of Engineering Science
International Journal of Engineering Science 工程技术-工程:综合
CiteScore
11.80
自引率
16.70%
发文量
86
审稿时长
45 days
期刊介绍: The International Journal of Engineering Science is not limited to a specific aspect of science and engineering but is instead devoted to a wide range of subfields in the engineering sciences. While it encourages a broad spectrum of contribution in the engineering sciences, its core interest lies in issues concerning material modeling and response. Articles of interdisciplinary nature are particularly welcome. The primary goal of the new editors is to maintain high quality of publications. There will be a commitment to expediting the time taken for the publication of the papers. The articles that are sent for reviews will have names of the authors deleted with a view towards enhancing the objectivity and fairness of the review process. Articles that are devoted to the purely mathematical aspects without a discussion of the physical implications of the results or the consideration of specific examples are discouraged. Articles concerning material science should not be limited merely to a description and recording of observations but should contain theoretical or quantitative discussion of the results.
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