Tabakalı Kompozit Malzemelerin Gerilme Analizleri için Peridinamik ve Timoşenko Kiriş Teorisinin Birleştirilmesi

Bu çalışmada, Peridinamik En Küçük Kareler Minimizasyonu (PEKKM) yaklaşımı ve Timoşenko Kiriş Teorisi (TKT) kullanılarak tabakalı kompozit yapıya sahip kirişlerin eğilme davranışı incelenmiştir. PEKKM, bir fonksiyonun herhangi mertebeden türevini yerel olmayan integral formlarında doğru bir şekilde hesaplamaktadır. Bu sebepted dolayı, PEKKM, TKT denge denklemlerinin çözümü için oldukça uygun bir yaklaşımdır. Tabakalı yapıya sahip kirişlerin en-boy oranlarının, yükleme ve sınır koşullarının yanı sıra fiber açılarının bu yapılardaki gerilme ve şekil değiştirme alanlarına etkisi ayrıntılı olarak incelenmiştir. Ayrıca, PEKKM yaklaşımı, kayma gerilme değerlerinin, gerilme denge denklemlerini kullanılarak elde edilmesi için kullanılmıştır. Mevcut yaklaşımın tabakalı yapıya sahip kompozit kirişlerdeki şekil değiştirme ve gerilme dağılımlarını başarıyla tahmin ettiği gösterilmiştir.

Coupling of Peridynamics and Timoshenko Beam Theory for the Stress Analysis of Laminated Composite Materials

This study investigates the bending behavior of laminated composite beams by using Peridynamic Least Squares Minimization (PDLSM) approach and Timoshenko Beam Theory (TBT). The PDLSM converts any arbitrary order derivatives of a function in their nonlocal forms with high accuracy. Therefore, it is highly suitable for the solution of TBT equilibrium equations. The influence of span-to-thickness ratios, loading and boundary conditions, as well as laminations on the stress and deformation fields of laminated composite beams, were investigated in detail. Also, the PDLSM was used for the transverse shear stress calculations from the stress equilibrium equations. It was demonstrated that the PD-TBT successfully predicted the deformation and stress fields in the laminated beams.

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