Ankastre Kirişlerin Doğrusal Olmayan Statik Analizi ve Analitik Çözüm ile Mukayesesi

Öz

Hafiflik ve yüksek dayanım gereksinimlerinin ön planda olduğu endüstriyel uygulamalarda, gelişmiş yapı elemanlarına duyulan ihtiyaç giderek artmaktadır. Malzeme teknolojisindeki ilerlemeler ile mühendislik tasarımlarının bütünleşmesi; özellikle makine, havacılık ve uzay alanlarında yenilikçi çözümlerin geliştirilmesine olanak sağlamıştır. Bu kapsamda, ankastre mesnetli kirişler yapısal sistemlerde sıkça tercih edilmekte; ancak geleneksel doğrusal analiz yöntemleri, doğrusal olmayan davranışların tam olarak modellenmesinde yetersiz kalmaktadır. Gerilme-birim şekil değiştirme ilişkilerinin doğrusal olmaması ve yükleme altında meydana gelen büyük yer değiştirmeler, bu yapıların analizinde dikkate alınması gereken önemli unsurlar olarak ön plana çıkmaktadır. Bu çalışmada, bir ucu ankastre olan kirişe uygulanan momentlerin neden olduğu yatay ve düşey yer değiştirmeler, doğrusal olmayan malzeme davranışı ve büyük şekil değiştirmeler temel alınarak analiz edilmiştir. Analizler sonlu elemanlar yazılımı ile gerçekleştirilmiş; çözüm sürecinin farklı geometrilere ve malzeme türlerine uygulanabilirliğini sağlamak amacıyla parametrik bir kodlama yaklaşımı benimsenmiştir. Ayrıca fonksiyonel gradyanlı malzemelerin modellenmesi ve analizi hakkında yaklaşım ortaya konmuştur. Analiz sonuçları teorik yaklaşımlar ve elde edilen analitik sonuçlar ile mukayese edilerek farkların sebepleri değerlendirilmiştir.

Anahtar Kelimeler

• Ankastre Kiriş
• Doğrusal olmayan
• Yer değiştirme

Nonlinear Static Analysis of Cantilever Beams and Comparison with Analytical Solution

Abstract

In industrial applications where lightweight structures and high strength requirements are of paramount importance, the demand for advanced structural elements is steadily increasing. The integration of advancements in material technology with engineering design has enabled the development of innovative solutions, particularly in the fields of mechanical, aerospace, and space engineering. In this context, cantilever beams are frequently preferred in structural systems; however, traditional linear analysis methods are often inadequate for accurately modeling nonlinear behaviors. The nonlinearity of stress–strain relationships and the occurrence of large displacements under loading emerge as critical factors that must be considered in the analysis of such structures. In this study, the horizontal and vertical displacements caused by the applied moments on a cantilever beam were analyzed based on nonlinear material behavior and large deformations. The analyses were carried out using finite element software, and a parametric coding approach was adopted to ensure the applicability of the solution process to various geometries and material types. Furthermore, a modeling and analysis approach for functionally graded materials (FGMs) was proposed. The results of the analyses were compared with theoretical approaches and analytical results, and the causes of the discrepancies were evaluated.

Keywords

• Cantilever Beam
• Displacement
• Nonlinear

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