Static Analysis of Porous Functionally Graded Cantilever Nano-Beams Via Modified Couple Stress Theory

Abstract

Porosity formation is a common phenomenon in functionally graded beams due to various problems during the manufacturing process. This study uses the finite element method within the modified couple stress theory framework to investigate vertical displacements of porous functionally graded cantilever nano-beams under static loads. Power law theory is used for the material distribution of the functionally graded beams, and two models are used for the porosity distribution, namely even and uneven distribution. Within the scope of the study, the effect of porosity distribution models, porosity parameter, material length scale parameter from modified couple stress theory and power law parameter on the vertical displacements of non-porous and porous functionally graded cantilever nano-beams are presented in tables and figures. It is concluded that the material length scale parameter has an increasing effect on the stiffness of the nano-beam and that nano-beams with uneven porosity distribution behave more rigidly than those with even porosity distribution.

Keywords

• Functionally graded material
• Porosity
• Nano-beam
• Modified couple stress theory
• Finite element method

DEĞİŞTİRİLMİŞ GERİLME ÇİFTİ TEORİSİ İLE GÖZENEKLİ FONKSİYONEL DERECELENDİRİLMİŞ KONSOL NANO-KİRİŞLERİN STATİK ANALİZİ

Abstract

Üretim aşamasında çeşitli sorunlar sebebiyle gözenek oluşumu fonksiyonel derecelendirilmiş kirişlerde sıklıkla gözlemlenmektedir. Bu çalışmada gözenekli fonksiyonel derecelendirilmiş konsol nanokirişlerin değiştirilmiş gerilme çifti teorisi çerçevesinde sonlu elemanlar yöntemi kullanılarak statik yükler altında düşey yer değiştirmeleri incelenmiştir. Fonksiyonel derecelendirilmiş kirişlerin malzeme dağılımlarında kuvvet yasası teorisi, gözenek dağılımı içinse düzenli ve düzensiz dağılım olmak üzere iki model kullanılmıştır. Çalışma kapsamında gözeneksiz ve gözenekli fonksiyonel derecelendirilmiş konsol nano-kirişlerin düşey yer değiştirmelerinde, gözenek dağılım modellerinin, gözeneklilik parametresinin, değiştirilmiş gerilme çifti teorisinden gelen malzeme uzunluk ölçeği parametresinin ve kuvvet yasası parametresinin etkisi tablolar ve şekiller vasıtasıyla sunulmuştur. Çalışmada, malzeme uzunluk ölçeği parametresinin nano-kirişin rijitliğini arttırıcı etkisinin olduğu ve düzensiz gözenek dağılımına sahip nanokirişlerin, düzenli gözenek dağılımına sahip olanlara göre daha rijit davrandığı sonuçlarına ulaşılmıştır.

Keywords

• Fonksiyonel derecelendirilmiş malzeme
• Gözeneklilik
• Nano-kiriş
• Değiştirilmiş gerilme çifti teorisi
• Sonlu elemanlar yöntemi

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