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基于弹性基础的含微观结构功能梯度薄板的屈曲理论分析

Theoretical Analysis of Buckling for Functionally Graded Thin Plates with Microstructure Resting on an Elastic Foundation.

作者信息

Jędrysiak Jarosław, Kaźmierczak-Sobińska Magda

机构信息

Department of Structural Mechanics, Łódź University of Technology, al. Politechniki 6, 90-924 Łódź, Poland.

出版信息

Materials (Basel). 2020 Sep 11;13(18):4031. doi: 10.3390/ma13184031.

DOI:10.3390/ma13184031
PMID:32932893
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC7557806/
Abstract

In this paper, the problem of the stability of functionally graded thin plates with a microstructure is presented. To analyse this problem and take into consideration the effect of microstructure, tolerance modelling is used. The tolerance averaging technique allows us to replace the equation with non-continuous, tolerance-periodic, highly oscillating coefficients of the system of differential equations with slowly-varying coefficients, which describes also the effect of the microstructure. As an example, the buckling of a microstructured functionally graded plate band on a foundation is investigated. To obtain results, the tolerance model and the asymptotic model combined together with the Ritz method are used. It is shown that the tolerance model allows us to take into account the effect of microstructure on critical forces.

摘要

本文提出了具有微观结构的功能梯度薄板的稳定性问题。为了分析这个问题并考虑微观结构的影响，采用了公差建模。公差平均技术使我们能够用具有缓慢变化系数的微分方程组来代替具有非连续、公差周期性、高度振荡系数的方程，该方程组也描述了微观结构的影响。作为一个例子，研究了基础上微结构功能梯度板带的屈曲。为了获得结果，将公差模型和渐近模型与里兹方法结合使用。结果表明，公差模型使我们能够考虑微观结构对临界力的影响。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8e92/7557806/02ba258112ad/materials-13-04031-g010.jpg
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https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8e92/7557806/d8c197c14a88/materials-13-04031-g006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8e92/7557806/2abc3e71ed24/materials-13-04031-g007.jpg
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https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8e92/7557806/02ba258112ad/materials-13-04031-g010.jpg

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