An Efficient Dynamic Analysis of Planar Arches

European Mechanical Science

2020

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The bending response of Functionally Graded (FG) beams is carried out by the Complementary Functions Method (CFM). The mechanical properties of the material, Young's modulus, of the straight beams are considered to be graded only in the thickness direction. Poisson's ratio is supposed to be constant. Governing equations of the considered problem are obtained with the aid of minimum total potential energy principle based on Timoshenko's beam theory (FSDT). The main purpose of this paper is the infusion of the CFM to the bending analysis of FG straight beams. The effectiveness and accuracy of the proposed scheme are confirmed by comparing its numerical results with those of the available literature. The application of this efficient method provides accurate results of static response for FGM beams with different variations of material properties.

Section: Introductionmentioning

confidence: 99%

Static Analysis of FG Beams via Complementary Functions Method

European Mechanical Science

2020

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“…Karaca [32] studied the static and dynamic analysis of circular Timoshenko rods which are loaded in-plane and out-ofplane, theoretically. Temel et al [33] investigated the forced vibration of isotropic-elastic planar curved rods in Laplace domain with the CFM. The dynamic and static analysis of in-plane and out-of-plane loaded curved structural elements is examined by Aslan [34] in the Laplace domain, while RK5 algorithm is used for the solution of differential equations based on the CFM.…”

Section: Introductionmentioning

confidence: 99%

Damped transient response of in-plane and out-of-plane loaded stepped curved rods

J Braz. Soc. Mech. Sci. Eng.

2018

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This paper focuses on the damped and undamped transient response of in-plane and out-of-plane loaded stepped curved rods. A unified approach combining the complementary functions method with the Laplace transform is applied to examine the dynamic behavior of above structural elements, while the materials are assumed to be isotropic and homogeneous. The effect of shear deformation is also taken into account. As examples, the forced vibration analysis of a stepped circular arch subjected to step, triangular impulsive and rectified sinusoidal wave in-plane loads and a stepped circular rod under the step, pulse and square wave out-of-plane loads are presented. To validate and compare the results of the present study, two computer programs are coded in Fortran. Verification and exactness of the written programs are performed by comparing the results of the present method and results of ANSYS which is a conventional finite element program. It has emerged that present method is highly accurate and efficient compared to conventional step-by-step integration methods.

“…Karaca [19], düzlemi içinde ve düzlemine dik yüklü daire eksenli Timoshenko çubukların statik ve dinamik analizlerini teorik olarak incelemiştir. Temel ve arkadaşları [20], izotropik ve elastik malzemeden yapılmış olan eğri eksenli düzlemsel çubukların zorlanmış titreşimini TFY yardımıyla Laplace uzayında araştırmışlardır. Aslan [21], düzlemi içinde ve düzlemine dik yüklü eğri eksenli çubukların statik ve dinamik yükler altında davranışını Laplace uzayında TFY ile analiz etmiştir.…”

Section: Introductionunclassified

Forced Vibration of Viscoelastic Cycloidal Bars with Rectangular Cross-Sections

Çukurova Üniversitesi Mühendislik-Mimarlık Fakültesi Dergisi

2018

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ÖzBu çalışmada, lineer elastik veya viskoelastik malzemeye sahip dikdörtgen kesitli sikloid çubukların burulma etkisindeki dinamik davranışı Tamamlayıcı Fonksiyonlar Yöntemi (TFY) ile Laplace uzayında incelenmiştir. Elde edilen adi diferansiyel denklemlerin sayısal çözümleri için 5. Derece Runge-Kutta (RK5) algoritması kullanılmıştır. Formülasyonda, kayma deformasyon ve sönüm etkileri göz önüne alınmıştır. Çubuk malzemesi homojen, izotrop, lineer elastik veya viskoelastik olarak kabul edilmiştir. Bununla beraber, viskoelastik durumda Kelvin tipi sönüm modeli kullanılmıştır. Laplace uzayında elde edilen çözümlerden zaman uzayına geçmek için uygun bir ters dönüşüm yöntemi kullanılmıştır. Bu amaçla dikdörtgen kesitli sikloid çubukların dinamik analizi için Fortran dilinde bir bilgisayar programı hazırlanmıştır. Hazırlanan bilgisayar programın sonuçları, ANSYS sonlu eleman paket programı kullanılarak hesaplanan sonuçlar ile karşılaştırılıp, bu yöntemin doğruluğu ve üstünlüğü gösterilmiştir. AbstractIn the present study, the dynamic response of cycloid bars with rectangular cross-sections subjected to torsional load is examined by the Complementary Functions Method (CFM) in the Laplace domain. The fifth-order Runge-Kutta (RK5) algorithm has been applied for the numerical solution of the obtained ordinary differential equations. Effects of shear deformation and damping are taken into consideration. Material of the rods is assumed to be homogenous, isotropic, linear elastic or visco-elastic. In viscoelastic modeling the Kelvin model is employed. The solutions obtained in the Laplace domain are transformed to the time domain by an appropriate inverse numerical Laplace transform method. A computer program is coded in Fortran for the forced vibration of the considered structures. Verification and exactness of the written program is performed by comparing the results of the present methods and results of ANSYS which is a finite element software.