Hiperstatik eksenel yüklü viskoelastik çubukların analizi için yeni enerji fonksiyoneli

Elastik cisimlerde gerilme sadece şekil değiştirmenin bir fonksiyonudur, viskoelastik cisimlerde ise gerilme hem şekil değiştirmeye hem de şekil değiştirme hızına bağlıdır. Maddesel sabitleri farklı olan yayların ve sönüm kutularının çeşitli kombinasyonları yapılarak, yüksek polimerler, naylon lifler, beton vb. malzemelerin mekanik davranışlarını temsil etme olanağı vardır. Maxwell modeli kullanılarak mekanik davranışı temsil edilen statikçe belirsiz eksenel yüklü çubuk probleminin ele alındığı bu çalışmada, toplam potansiyel enerji (TPE) teoremi kullanılarak en karmaşık yapı sistemlerine bile kolaylıkla uygulanabilecek bir çözüm yolu önerilmiştir. Düğüm noktalarının yer değiştirmeleri cinsinden bulunan TPE ifadesi Laplace uzayında elde edilmiştir. TPE ifadesini minimum yapan çözümler gerçek yer değiştirmeler olup, Laplace uzayında elde edilen çözümlerden zaman uzayına geçmek için Ters Laplace dönüşümü yöntemi uygulanmıştır. Yöntem örnek problem üzerinde test edilmiş ve sonuçlar sunulmuştur. Bu yöntem, viskoelastik malzeme modelinin, sistemi oluşturan eleman sayısının ve yükleme tipinin değişmesinden bağımsız olarak birkaç basit işlem adımının takibi ile doğrudan çözüme ulaşmada büyük kolaylık sağlar.

Anahtar Kelimeler:

Hiperstatik Sistemler, Viskoelastik, Toplam Potansiyel Enerji, Laplace Dönüşümü, Ters Laplace Dönüşümü, Statically ındeterminate systems, Viscoelastic, Total potential energy, Laplace transform, Inverse Laplace transform

New energy functional for analysis of statically indeterminate axially loaded viscoelastic bars

In elastic bodies, stress is only a function of strain, while in viscoelastic bodies, stress depends on both strain and strain rate. By making various combinations of springs and dashpots with different material constants, it is possible to represent the mechanical behavior of materials such as high polymers, nylon fibers, concrete etc. In this study, which discusses the statically indeterminate axially loaded bar problem, whose mechanical behavior is represented using the Maxwell model, a solution technique that can be easily applied to even the most complex structural systems is proposed by using the total potential energy (TPE) theorem. The TPE expression in terms of the displacement of the nodes is obtained in the Laplace space. The solutions that minimize the TPE expression are the real displacements, and the Inverse Laplace transform method is applied to return to the time domain. The method has been tested on the sample problem and the results are presented. This method provides great convenience in obtaining the solution directly by following a few simple process steps, regardless of the change in the viscoelastic material model, the number of elements of the system and the type of loading.

Keywords:

Statically ındeterminate systems, Viscoelastic, Total potential energy, Laplace transform, Inverse Laplace transform,

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