Yerel olmayan elastisite teorisi kullanılarak basit mesnetli Timoshenko nanokirişlerinin çökmeleri üzerinde kesit etkisi

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DOI : 10.29228/JCHAR.61956
Year-Number: 2022-2
Yayımlanma Tarihi: 2022-07-06 12:47:01.0
Language : İngilizce
Konu : Kompozit
Number of pages: 134-146
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Abstract

Tek doğrultulu ve farklı kesit şekilli nanomalzemelerin nano-elektro-mekanik sistemler (NEMS) teknolojisindeki geniş kullanımı nedeniyle bu tip malzemelerin mekanik davranışlarının bilinmesi önemli hale gelmiştir. Tek doğrultulu nanomalzemeler kiriş gibi uzunlamasına mekanik elemanlarla modellenebilir. Ayrıca, klasik kiriş modellerinin nanoyapıların mekaniğinde gerçekçi olmayan sonuçlar vermesi nedeniyle boyut etkisine dayanan formülasyonların kullanıldığı belirtilmelidir. Bu motivasyonla, bu çalışma nanoölçekli kirişlerin boyut etkili statik çökme davranışına kesit türünün etkisini ele almaktadır. Boyut etkisi olarak yerel olmayan elastisite teorisi kullanılmıştır. Nanokirişin mekanik davranışını daha gerçekçi araştırabilmek adına, kayma etkilerini gözetmesi nedeniyle Timoshenko kiriş teorisi kullanılmıştır. Buna göre, statik analizin diferansiyel denklemi, düzgün yayılı ve tekil gibi farklı yük tipleri altındaki her iki ucu basit mesnetli nanokirişler için çözülmüştür. Ardından, kare, daire, kutu ve halka kesitli nanokirişler için çökme değerleri ve çökme oranları sunulmuş ve sayısal sonuçlar detaylıca tartışılmıştır.

Keywords

Abstract

To know the mechanical behavior of such materials has been become important due to the wide use of one-dimensional and different cross-sectional nanomaterials in nano-electro-mechanical systems (NEMS) technology. One-dimensional nanomaterials can be modelled with longitudinal mechanical elements like beams. Also, in the mechanics of nanostructures, it should be specified that formulations based on size effect are used since classical beam models do not give realistic results. With this motivation, this study examines the effect of section type on the size dependent static deflection behavior of nano scaled beams. The nonlocal elasticity theory is employed as the size effect. In order to study the mechanical behavior of nanobeam more realistically, Timoshenko beam theory is formulated because it includes the shear effect. According to this, the differential equation of static analysis is solved for simply supported nanobeams under different load types such as uniform distributed and concentrated. Then, deflection values and deflection ratios ​​for nanobeams with square, circular, box, and hoop section are presented. Finally, a detailed discussions for numerical results are given.

Keywords

Kaynakça

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