The purpose of this study is to extend a new mixed-type finite element (MFE) model, developed earlier by the present authors for the analysis of viscoelastic Kirchhoff plates [Aköz, A. Y., Kadıoğlu, F. and Tekin, G. [2015] “Quasi-static and dynamic analysis of viscoelastic plates”, Mechanics of Time-Dependent Materials 19(4), 483–503], to study the quasi-static and dynamic responses of first-order shear-deformable (FSD) linear viscoelastic Mindlin–Reissner plates. In this context, various viscoelastic material models are discussed for the plate structure to read from them possible patterns of viscoelastic behavior. The developed MFE named VPLT32 is C0-continuous four-node linear isoparametric plate element with eight degrees of freedom per node. Hereditary integral form of the constitutive law with constant Poisson’s ratio is used. A new functional in the Laplace–Carson domain suitable for MFE formulation in the same domain is developed by employing Gâteaux differential (GD) method. The unique aspects of this study and the possible contributions of the proposed method to the literature can be summarized as follows: by using this new functional, moment and shear force values that are important for engineers can be obtained directly without any mathematical operation. In addition, geometric and dynamic boundary conditions can be obtained easily and a field variable can be included to the functional systematically. Moreover, shear-locking problem can be eliminated by using the GD method. Dubner and Abate numerical Laplace inversion technique is adopted to transform the obtained solution from the Laplace–Carson domain into the real-time domain. A set of numerical examples are presented not only to demonstrate the validity and accuracy of the proposed MFE formulation but also to examine the effects of load, geometry and material parameters on the viscoelastic response of FSD Mindlin–Reissner plates and to give a better insight into time-dependent behavior of engineering thick plate problems.
The buckling behavior of sandwich shells with functionally graded (FG) coatings operating under different external pressures was generally investigated under simply supported boundary conditions. Since it is very difficult to determine the approximation functions satisfying clamped boundary conditions and to solve the basic equations analytically within the framework of first order shear deformation theory (FOST), the number of publications on this subject is very limited. An analytical solution to the buckling problem of FG-coated cylindrical shells under clamped boundary conditions subjected to uniform hydrostatic pressure within the FOST framework is presented for the first time. By mathematical modeling of the FG coatings, the constitutive relations and basic equations of sandwich cylindrical shells within the FOST framework are obtained. Analytical solutions of the basic equations in the framework of the Donnell shell theory, obtained using the Galerkin method, is carried out using new approximation functions that satisfy clamped boundary conditions. Finally, the influences of FG models and volume fractions on the hydrostatic buckling pressure within the FOST and classical shell theory (CT) frameworks are investigated in detail.
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 minumum 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.
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