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Analytical solutions for static bending of edge cracked micro beams
(Techno-Press, 2016) Akbaş, Şeref Doğuşcan
In this study, static bending of edge cracked micro beams is studied analytically under uniformly distributed transverse loading based on modified couple stress theory. The cracked beam is modelled using a proper modification of the classical cracked-beam theory consisting of two sub-beams connected through a massless elastic rotational spring. The deflection curve expressions of the edge cracked microbeam segments separated by the rotational spring are determined by the Integration method. The elastic curve functions of the edge cracked micro beams are obtained in explicit form for cantilever and simply supported beams. In order to establish the accuracy of the present formulation and results, the deflections are obtained, and compared with the published results available in the literature. Good agreement is observed. In the numerical study, the elastic deflections of the edge cracked micro beams are calculated and discussed for different crack positions, different lengths of the beam, different length scale parameter, different crack depths, and some typical boundary conditions. Also, the difference between the classical beam theory and modified couple stress theory is investigated for static bending of edge cracked microbeams. It is believed that the tabulated results will be a reference with which other researchers can compare their results.
Axially Forced Vibration Analysis of Cracked a Nanorod
(Univ Tehran, Danishgah-I Tihran, 2019) Akbaş, Şeref Doğuşcan
This study presents axially forced vibration of a cracked nanorod under harmonic external dynamically load. In constitutive equation of problem, the nonlocal elasticity theory is used. The Crack is modelled as an axial spring in the crack section. In the axial spring model, the nonrod separates two sub-nanorods and the flexibility of the axial spring represents the effect of the crack. Boundary condition of the nanorod is selected as fixed-free and a harmonic load is subjected at the free end of the nanorod. Governing equation of the problem is obtained by using equilibrium conditions. In the solution of the governing equation, analytical solution is presented and exact expressions are obtained for the forced vibration problem. On the solution method, the separation of variable is implemented and the forced vibration displacements are obtained exactly. In the open literature, the forced vibration analysis of the cracked nanorod has not been investigated broadly. The objective of this study is to fill this blank for cracked nanorods. In numerical results, influences of the crack parameter, position of crack, the nonlocal parameter and dynamic load parameters on forced vibration responses of the cracked nanorod are presented and discussed.
Bending of a cracked functionally graded nanobeam
(Techno-Press, 2018) Akbaş, Şeref Doğuşcan
In this study, static bending of an edge cracked cantilever nanobeam composed of functionally graded material (FGM) subjected to transversal point load at the free end of the beam is investigated based on modified couple stress theory. Material properties of the beam change in the height direction according to exponential distributions. The cracked nanobeam is modelled using a proper modification of the classical cracked-beam theory consisting of two sub-nanobeams connected through a massless elastic rotational spring. The inclusion of an additional material parameter enables the new beam model to capture the size effect. The new non-classical beam model reduces to the classical beam model when the length scale parameter is set to zero. The considered problem is investigated within the Euler-Bernoulli beam theory by using finite element method. In order to establish the accuracy of the present formulation and results, the deflections are obtained, and compared with the published results available in the literature. Good agreement is observed. In the numerical study, the static deflections of the edge cracked FGM nanobeams are calculated and discussed for different crack positions, different lengths of the beam, different length scale parameter, different crack depths, and different material distributions. Also, the difference between the classical beam theory and modified couple stress theory is investigated for static bending of edge cracked FGM nanobeams. It is believed that the tabulated results will be a reference with which other researchers can compare their results.
Çatlak içeren bir çerçeve taşıyıcı sistemin zorlanmış titreşim analizi
(2020) Koçyiğit, Kemal; Akbaş, Şeref Doğuşcan
Bu çalışmada, kenarında çatlaklar bulunan tek açıklıklı bir çerçeve taşıyıcının sönümsüz ve sönümlü zorlanmış titreşim cevaplarıincelenmiştir. Çatlaklı çerçevenin titreşim analizleri, Euler-Bernoulli çubuk teorisi çerçevesinde incelenmiştir. Çatlak etkisindendolayı ortaya çıkan yerel esneklik, çatlak kesiti veya bölgesinde, kütlesiz ve boyutsuz bir çubuk sonlu eleman ile modellenmiştir.Çatlaktan dolayı ortaya çıkan yerel esneklik, lineer elastik kırılma mekaniği teorisi baz alınarak açılma modu (Mod1) ile düzlemiçi kayma modu (Mod2) kullanılmasıyla birlikte elde edilen gerilme yığılma faktörü ve şekil değiştirme enerjisi salıverininimoranlarına bağlı olarak elde edilmiştir. Çatlak esnekliğinin tersi alınarak elde edilen çatlak rijitliğinin sonlu elemanlar modelineeklenmesiyle birlikte birleştirilmiş sonlu elemanlar formülasyonları elde edilmiştir.Zorlanmış titreşim çözümlerinde zaman tanım aralığında doğrudan integrasyon yöntemlerinden biri olan merkezi farklar yöntemikullanılmıştır. Çalışmada farklı değerlerdeki çatlak derinliğinin, farklı çatlak konumunun ve farklı değerlerdeki çerçeve yapınıngeometrik boyutlarına bağlı olarak dinamik cevaplar elde edilmiş ve yorumlanmıştır. Elde edilen formülasyon ve sonuçlarındoğruluğu için, literatürdeki benzer çalışmaların özel sonuçları ile kıyaslama çalışmaları yapılmıştır.
Comparison study between layered and functionally graded composite beams for static deflection and stress analyses
(Univ Tehran, Danishgah-I Tihran, 2020) Kirlangic, Okan; Akbaş, Şeref Doğuşcan
The aim of this paper is to compare the static deflections and stress results of layered and functionally graded composite beams under static load. In the comparison study, the results obtained for a cantilever beam under point load. The Timoshenko beam and the Euler-Bernoulli beam theories are used in the beam model. The energy based Ritz method is used for the solution of the problem and algebraic polynomials are used with the trivial functions for the Ritz method. Two different materials are considered as layered and functionally graded distribution in a cantilever beam and their static deflections, stress distributions are compared under a point load at free end of the beam. For two different distributions, the formulations of Ritz method are obtained and solved numerically. In the numerical results, the effects of material distribution parameter, aspect ratio on the static deflections and stress distribution of functionally graded beams are obtained and compared with the results of the layered composite beam. Difference among of beam theories are compared for functionally graded and layered beams. Also, some comparison studies are performed in order to validate the using formulations.
Damped dynamic responses of a layered functionally graded thick beam under a pulse load
(Techno-Press, 2020) Asiri, Saeed A.; Akbaş, Şeref Doğuşcan; Eltaher, Mohamed A.
This article aims to illustrate the damped dynamic responses of layered functionally graded (FG) thick 2D beam under dynamic pulse sinusoidal load by using finite element method, for the first time. To investigate the response of thick beam accurately, two-dimensional plane stress problem is assumed to describe the constitutive behavior of thick beam structure. The material is distributed gradually through the thickness of each layer by generalized power law function. The Kelvin-Voigt viscoelastic constitutive model is exploited to include the material internal damping effect. The governing equations are obtained by using Lagrange's equations and solved by using finite element method with twelve -node 2D plane element. The dynamic equation of motion is solved numerically by Newmark implicit time integration procedure. Numerical studies are presented to illustrate stacking sequence and material gradation index on the displacement-time response of cantilever beam structure. It is found that, the number of waves increases by increasing the graduation distribution parameter. The presented mathematical model is useful in analysis and design of nuclear, marine, vehicle and aerospace structures those manufactured from functionally graded materials (FGM).
Dynamic analysis of a laminated composite beam under harmonic load
(Techno-Press, 2020) Akbaş, Şeref Doğuşcan
Dynamic responses of a laminated composite cantilever beam under a harmonic are investigated in this study. The governing equations of problem are derived by using the Lagrange procedure. The Timoshenko beam theory is considered and the Ritz method is implemented in the solution of the problem. The algebraic polynomials are used with the trivial functions for the Ritz method. In the solution of dynamic problem, the Newmark average acceleration method is used in the time history. In the numerical examples, the effects of load parameter, the fiber orientation angles and stacking sequence of laminas on the dynamic responses of the laminated beam are investigated.
Dynamic Analysis of Layered Functionally Graded Viscoelastic Deep Beams with Different Boundary Conditions Due to a Pulse Load
(World Scientific Publ Co Pte Ltd, 2020) Asiri, Saeed A.; Akbaş, Şeref Doğuşcan; Eltaher, M. A.
This paper studies the dynamic viscoelastic response of functionally graded (FG) thick 2D cantilever and simply supported beams under dynamic pulse load, for the first time. A point load applied at a specific spatial point is described as a time-pulse sinusoidal load. Two-dimensional plane-stress constitutive equation is exploited to describe the local stress-strain relation through the beam. The gradation of material is depicted by generalized power law function through the layer thickness across beam thickness. The Kelvin-Voigt viscoelastic model is proposed to describe material damping of structure. Lagrange's equation is employed to derive governing motion equation. A finite element method (FEM) is exploited to discretize the spatial domain of 2D beam structure by using 12-node 2D plane element. Numerical Newmark implicit time integration method is proposed to solve the equation of motion incrementally and get the response of beam structure. Two types of boundary conditions are considered in the numerical examples. In numerical results, effects of stacking sequence, geometry parameters and material gradation index and viscoelasticity coefficients on the displacement-time response of layered functionally graded viscoelastic deep beams for different boundary conditions.
Dynamic analysis of thick beams with functionally graded porous layers and viscoelastic support
(Sage Publications Ltd, 2021) Akbaş, Şeref Doğuşcan; Bashiri, Abdullateef H.; Assie, Amr E.; Eltaher, Mohamed A.
This study presents dynamic responses of a composite thick beam with a functionally graded porous layer under dynamic sine pulse load. The boundary conditions of the composite beam are considered as viscoelastic supports. Three layers are considered, and face sheet layers have porous functionally graded materials in which the distribution of material gradation through the graded layer is described by the power law function, and the porosity is depicted by three different distributions (i.e., symmetric distribution, X distribution, and LOZENGE distribution). The layered composite thick beam is modeled as a two-dimensional plane stress problem. The equation of motion is obtained by Lagrange's equations. In formation of the problem, the finite element method is used with a 12-node 2D plane element. In the solution process of the dynamic problem, a numerical time integration method of the Newmark method is used. In numerical analyses, influences of stiffness and damping coefficients of viscoelastic supports, material gradation index, porosity parameter, and porosity models on the dynamic response of thick functionally graded porous beam are investigated under the pulse load.
Dynamic analysis of viscoelastic functionally graded porous thick beams under pulse load
(Springer, 2022) Akbaş, Şeref Doğuşcan; Fageehi, Y. A.; Assie, A. E.; Eltaher, M. A.
Due to the significant effect of porosity on the mechanical response of functionally graded (FG) structures, this paper presents a comprehensive model to investigate the vibration response of FG porous thick beam under the dynamic sine pulse load including the damping effect by using adopted finite element model, for the first time. The multilayer thick beam is modeled as two-dimensional plane stress problem. The distribution of material gradation through the graded layer is described by the power law function, and the porosity is depicted by three different distributions (i.e., symmetric-distribution, X-distribution and O-distribution). The damping effect is included in the model by using the Kelvin-Voigt viscoelastic constitutive model. Constitutive equations, gradation and porosity functions are described in detail. Forced motion equations are derived by using Lagrange energy principles. Twelve-node 2D plane element with 3 x 3 integration points is proposed to discretize the beam and get the element matrices and force vectors. The numerical time integration method of Newmark is proposed to solve the system numerical and get the displacement response of the structure. Effects of layer stacking sequence, material gradation index and porosity parameter on the dynamic's response of thick FG porous damped beam are presented. The presented mathematical model is useful in analysis and design of nuclear, marine, vehicle and aerospace structures those manufactured from functionally graded materials.
Dynamic responses of functionally graded and layered composite beams
(Techno-Press, 2021) Kirlangic, O.; Akbaş, Şeref Doğuşcan
This paper presents and compares the free and damped forced vibrations of layered and functionally graded composite beams. In the considered study, a cantilever beam subjected to a harmonic point load at the free end is investigated with layered and functionally graded materials. In the kinematics of the beam, the Timoshenko beam theory is used. The governing equations of problem are derived by using the Lagrange procedure. In the solution of the problem, the Ritz method is used. Algebraic polynomials are used with the trial functions for the Ritz method. In the obtaining of free vibration results, the eigenvalue procedure is implemented. In the solution of the damped forced vibration problem, the Newmark average acceleration method is used in the time history. In the damping effect, the Kelvin-Voigt viscoelastic model is used with the constitutive relations. In the numerical examples, the effects of material distribution parameter and dynamic parameters on the natural frequencies and forced vibration responses of functionally graded beams are obtained and compared with the results of the layered composite beam. Also, comparison studies are performed in order to validate the used formulations.
Dynamic responses of laminated beams under a moving load in thermal environment
(Techno-Press, 2020) Akbaş, Şeref Doğuşcan
The goal of this study is to investigate dynamic responses of laminated composite beams under a moving load with thermal effects. The governing equations of problem are derived by using the Lagrange procedure. The transverse -shear strain and rotary inertia are considered within the Timoshenko beam theory. The material properties of laminas are considered as the temperature dependent physical property. The differential equations of the problem are solved by the Ritz method. The solution step of dynamic problem, the Newmark average acceleration method is used in the time history. A compassion study is performed for accuracy of used formulations and method. In the numerical results, the effects of velocity of moving load, temperature values, the fiber orientation angles and the stacking sequence of laminas on the dynamic responses of the composite laminated beam are investigated.
Fonksiyonel derecelendirilmiş ortotropik bir kirişin statik ve titreşim davranışlarının incelenmesi
(2018) Akbaş, Şeref Doğuşcan
Bu çalışmada, fonksiyonel derecelendirilmiş konsol bir kirişin statik ve serbest titreşim davranışları ortotropik malzeme modeli kullanılarak incelenmiştir. Fonksiyonel derecelendirilmiş kirişin incelenmesinde düzlem parçalı sürekli ortam modeli kullanılmış olup, sonlu elemanlar yöntemi uygulanmıştır. Probleme ait yönetici denklemleri, virtüel yer değiştirmeler prensibi ile elde edilmiştir. Kirişin malzeme özellikleri, kiriş yüksekliği boyunca belli bir fonksiyona bağlı olarak belirlenmiştir. Ele alınan kirişin boyutları, levha modeli olacak biçimde seçilerek düzlem gerilme problemi uygulanmıştır. Söz konusu problemin, sonlu elemanlar formülasyonları elde edilip, sonlu eleman çözümü için MATLAB programında algoritma ve program yazılarak sonuçlar elde edilmiştir. Ele alınan çalışmada, farklı malzeme dağılımlarının, kirişin statik ve titreşim davranışına olan etkileri incelenmiştir. Değişik malzeme dağılımlarına göre, en büyük yer değiştirmeler ve doğal frekanslar elde edilip, yorumlanmıştır.
Forced Vibration Analysis of a Cracked Frame
(Gazi Univ, 2020) Koçyiğit, Kemal; Akbaş, Şeref Doğuşcan
In this study, undamped and damped forced vibration responses of a single span frame with cracks are investigated. The vibration analysis of the cracked frame is examined by using the Euler-Bernoulli beam theory. The local flexibility resulting from the crack effect is modeled with a massless and dimensionless finite element beam in the crack section. The local flexibility is obtained by using the stress intensity factor and strain energy release rates according to the opening mode (Mode 1) and the in-plane shear mode (Mode 2) based on the linear elastic fracture mechanics theory. The crack stiffness is obtained by taking the inverse of the flexibility of the crack. Assembly of global finite element matrices are obtained by adding the crack stiffness to the finite element model. In solution of the forced vibration problem, the central difference method is used in the time history. In the numerical results, the effects of the crack depth, the crack location and dimension of the frame on the undamped and damped forced vibration responses of the cracked frame are investigated. Also, the validation studies are performed in order to accuracy of the presented method.
Forced vibration analysis of composite beams reinforced by carbon nanotubes
(MDPI AG, 2021) Civalek, Ö.; Akbaş, Şeref Doğuşcan; Akgöz, B.; Dastjerdi, S.
This paper presents forced vibration analysis of a simply supported beam made of carbon nanotube-reinforced composite material subjected to a harmonic point load at the midpoint of beam. The composite beam is made of a polymeric matrix and reinforced the single-walled carbon nano-tubes with their various distributions. In the beam kinematics, the first-order shear deformation beam theory was used. The governing equations of problem were derived by using the Lagrange procedure. In the solution of the problem, the Ritz method was used, and algebraic polynomials were employed with the trivial functions for the Ritz method. In the solution of the forced vibration problem, the Newmark average acceleration method was applied in the time history. In the numerical examples, the effects of carbon nanotube volume fraction, aspect ratio, and dynamic parameters on the forced vibration response of carbon nanotube-reinforced composite beams are investigated. In addition, some comparison studies were performed, with special results of published papers to validate the using formulations. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.
Forced vibration analysis of cracked functionally graded microbeams
(Techno-Press, 2018) Akbaş, Şeref Doğuşcan
Forced vibration analysis of a cracked functionally graded microbeam is investigated by using modified couple stress theory with damping effect. Mechanical properties of the functionally graded beam change vary along the thickness direction. The crack is modelled with a rotational spring. The Kelvin-Voigt model is considered in the damping effect. In solution of the dynamic problem, finite element method is used within Timoshenko beam theory in the time domain. Influences of the geometry and material parameters on forced vibration responses of cracked functionally graded microbeams are presented.
Forced vibration analysis of cracked nanobeams
(Springer Heidelberg, 2018) Akbaş, Şeref Doğuşcan
Forced vibration responses of a cantilever nanobeam with crack are presented for modified couple stress theory with damping effect. The crack is modeled with a rotational spring. The Kelvin-Voigt model is considered in the damping effect. In solution of the dynamic problem, finite element method is used within Timoshenko beam theory in the time domain. Influences of the geometry, crack and material parameters on forced vibration responses of cracked nanobeams are examined and discussed. Also, different beam theories are compared in the forced vibration results.
Forced Vibration Analysis of Functionally Graded Nanobeams
(Imperial College Press, 2017) Akbaş, Şeref Doğuşcan
In this paper, forced vibration responses of functionally graded (FG) nanobeams are presented for modified couple stress theory (MCST) with damping effect. The FG nanobeam is excited by a transverse triangular force impulse modulated by a harmonic motion. Mechanical properties of FG beam depends on the position. The Kelvin-Voigt model is considered in the damping effect. In solution of the dynamic problem, finite element method is used within Timoshenko beam theory. The obtained system of differential equations is reduced to a linear algebraic equation system and solved in the time domain by using Newmark average acceleration method. Influences of the geometry and material parameters on forced vibration responses of FG nanobeams are examined and discussed.
Forced vibration analysis of functionally graded porous deep beams
(Elsevier Sci Ltd, 2018) Akbaş, Şeref Doğuşcan
The purpose of this study is to investigate forced vibration analysis of functionally graded porous deep beams under dynamically load. Mechanical properties of the functionally graded deep beam change in the thickness direction with porosity. The beam theories fail to satisfy in the calculation and the boundary conditions of deep beams. So, the plane solid continua model is used in the calculation of deep beams in order to obtain more realistic results. The governing equations of the problems are obtained by using the Hamilton procedure. In the solution of the problem, finite element method is used within the plane solid continua model. The effects of porosity parameters, material distribution and porosity models on the forced vibration responses of functionally graded deep beams are examined and discussed with porosity effects. Numerical results show that porosity plays very important role in the dynamic responses of the functionally graded deep beam. Choosing the suitable functionally graded material distribution, negative effects of the porosity can be decreased. It is necessary to use the plane solid continua model in modelling the deep beams.
Forced vibration analysis of functionally graded sandwich deep beams
(Techno-Press, 2019) Akbaş, Şeref Doğuşcan
This paper presents forced vibration analysis of sandwich deep beams made of functionally graded material (FGM) in face layers and a porous material in core layer. The FGM sandwich deep beam is subjected to a harmonic dynamic load. The FGM in the face layer is graded though the layer thickness. In order to get more realistic result for the deep beam problem, the plane solid continua is used in the modeling of The FGM sandwich deep beam. The equations of the problem are derived based the Hamilton procedure and solved by using the finite element method. The novelty in this paper is to investigate the dynamic responses of sandwich deep beams made of FGM and porous material by using the plane solid continua. In the numerical results, the effects of different material distributions, porosity coefficient, geometric and dynamic parameters on the dynamic responses of the FGM sandwich deep beam are investigated and discussed.

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