AĞIRLIKLI ARTIKLAR KULLANILARAK NANOÇUBUKLARIN EKSENEL STATİK ANALİZİ İÇİN KESİN ÇÖZÜMLER

Abstract

Bu çalışmada, Eringen’in yerel olmayan diferansiyel modeli kullanılarak; üçhen yayılı yüklenmiş nano çubukların eksenel statik analizi verilmiştir. Üç ağırlıklı artık tabanlı yöntem (Subdomain, Galerkin ve Least squares yöntemleri) gerçek statik deplasmanı elde etmek için kullanılmıştır. Bu yöntemler bölgenin tamamında integral hatalarını minimize etme varsayımına dayanmaktadır. Sistem denklemleri çözümü aranan bilinmeyenler ile aynı sayıda olmadır. Bu yüzden üç ağırlıklı artık yöntemi için de kübik polinomlar statik deplasmanı göstermek üzere seçilmiştir. Subdomain, Galerkin and Least squares yöntemleriyle gerçek çözümler ile aynı polinomlar olarak elde edilmiştir. Değişik sayıda bilinmeyen içeren sabitler ile grafikler çizdirilerek çözümler gösterilmiştir.Bu çalışmada, Eringen’in yerel olmayan diferansiyel modeli kullanılarak; üçhen yayılı yüklenmiş nano çubukların eksenel statik analizi verilmiştir. Üç ağırlıklı artık tabanlı yöntem (Subdomain, Galerkin ve Least squares yöntemleri) gerçek statik deplasmanı elde etmek için kullanılmıştır. Bu yöntemler bölgenin tamamında integral hatalarını minimize etme varsayımına dayanmaktadır. Sistem denklemleri çözümü aranan bilinmeyenler ile aynı sayıda olmadır. Bu yüzden üç ağırlıklı artık yöntemi için de kübik polinomlar statik deplasmanı göstermek üzere seçilmiştir. Subdomain, Galerkin and Least squares yöntemleriyle gerçek çözümler ile aynı polinomlar olarak elde edilmiştir. Değişik sayıda bilinmeyen içeren sabitler ile grafikler çizdirilerek çözümler gösterilmiştir.

Keywords

• Eksenel Statik
• Eksenel Statik
• Nanoçubuk
• Ağırlıklı Artık Yöntemleri
• Yer Değiştirme Fonksiyonu
• Gerçek Çözüm

EXACT SOLUTIONS FOR AXIAL STATIC ANALYSIS OF NANORODS USING WEIGHTED RESIDUALS

Abstract

In the present work, axial static analysis of nanorods under triangular loading is presented via Eringen’s nonlocal differential model. Three weighted residual methods (Subdomain, Galerkin and Least squares methods) are used to obtain the exact static deflection. These methods require that the integral of the error with different assumptions over the domain be set to zero. The number of equations have to be equal to unknown terms. A cubic displacement function has been chosen for three weighted residual methods. Subdomain, Galerkin and Least squares methods yield identical solution as the exact solution. The plots of the solution are shown for different number of unknown coefficients.

Keywords

• Axial Static
• Nanorod
• Weighted Residual Methods
• Displacement Function
• Exact Solution

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