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Mesut şimsek - One of the best experts on this subject based on the ideXlab platform.
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nonlinear static and free vibration analysis of microBeams based on the nonlinear elastic foundation using modified couple stress theory and he s variational method
Composite Structures, 2014Co-Authors: Mesut şimsekAbstract:Abstract In the present manuscript, a non-Classical Beam theory is developed for the static and nonlinear vibration analysis of microBeams based on a three-layered nonlinear elastic foundation within the framework of the modified couple stress theory and Euler–Bernoulli Beam theory together with the von-Karman’s geometric nonlinearity. This non-Classical Beam model incorporates the length scale parameter which can account for the small size effect. By using the Hamilton’s principle, the equations of motion and the boundary conditions of the problem are derived. The nonlinear partial differential equation governing the motion of the system is reduced to the nonlinear ordinary differential equation with the help of the Galerkin discretization technique. He’s variational method is then applied for the first time to obtain approximate analytical expressions for the nonlinear frequency of the microBeams with pinned–pinned and clamped–clamped end conditions. Static analysis is also performed for uniformly distributed load. Some illustrative numerical examples are presented in order to investigate the influences of the length scale parameter and the stiffness coefficients of the nonlinear foundation on the static deflection and the ratio of nonlinear frequency to linear frequency (the nonlinear frequency ratio). Comparison studies are also performed to verify the present formulation and solutions. Close agreement is observed.
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a unified higher order Beam theory for buckling of a functionally graded microBeam embedded in elastic medium using modified couple stress theory
Composite Structures, 2013Co-Authors: Mesut şimsek, Jn ReddyAbstract:Abstract Based on the modified couple stress theory (MCST), a unified higher order Beam theory which contains various Beam theories as special cases is proposed for buckling of a functionally graded (FG) microBeam embedded in elastic Pasternak medium. This non-Classical microBeam model incorporates the material length scale parameter which can capture the size effect. The non-Classical Beam model reduces to the Classical Beam model when the material length scale parameter is set to zero. The material properties of the FG microBeam are assumed to vary in the thickness direction and are estimated through the Mori–Tanaka homogenization technique and the Classical rule of mixture. The governing equations and the related boundary conditions are derived using the principal of the minimum total potential energy. The Navier-type solution is developed for simply-supported boundary conditions, and explicit expressions related to each type of Beam theory are proposed for the critical buckling load. Numerical results are presented to investigate the influences the material length scale parameter, aspect ratio, different estimation method of material properties, various material compositions, and the parameters of the elastic medium on the critical buckling load. Comparison study is also performed to verify the present formulation.
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static bending of a functionally graded microscale timoshenko Beam based on the modified couple stress theory
Composite Structures, 2013Co-Authors: Mesut şimsek, Turgut Kocaturk, şeref Doguscan AkbasAbstract:Abstract A microscale functionally graded Timoshenko Beam model is developed for the static bending analysis based on the modified couple stress theory (MCST). The material properties of the FG microBeams are assumed to vary in the thickness direction and are estimated through the Mori–Tanaka homogenization technique and the Classical rule of mixture. The equilibrium equations and the related boundary conditions are derived by using the principal of the minimum total potential energy. The governing equations are solved analytically for a simply-supported Beam subjected to a point and uniformly distributed load. 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 influences of the volume fraction index, the different estimation method of the material properties, length scale parameter, the aspect ratio and the Poisson effect on the static bending behavior are examined. Some of the present results are compared with the previously published results to establish the validity of the present formulation. It is found that the deflections of the microBeam by the Classical Beam theory are always larger than those by the modified couple stress theory.
Jn Reddy - One of the best experts on this subject based on the ideXlab platform.
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HOMOGENIZED AND NON-Classical Beam THEORIES IN SHIP STRUCTURAL DESIGN - CHALLENGES AND OPPORTUNITIES
2019Co-Authors: Romanoff Jani, Karttunen Anssi, Goncalves, Bruno Reinaldo, Jn ReddyAbstract:The paper gives an overview of the recent developments on the application of homogenized, non-Classical Beam theories used to predict the micro- and macrostructural stresses in the design of marine structures. These theories become important when ultralight-weight marine structures are developed and one needs to explore the regions where the length scales of Beam openings are in the range of the characteristic lengths of the Beams or when lattice/frame-type Beams are used to reduce the weight of ship structures. The homogenized Beam models are based on non-Classical continuum mechanics that allow local bending inside the Beams. This added feature allows the treatment of size effects with great accuracy. The resulting analytical and finite element models have special features in terms of shape functions and iterative solutions in non-linear problems. Non-Classical Beam models enable localization processes that recover the microstructural effects from homogenized solutions accurately and the models are able to handle limit states of serviceability and ultimate strength. The non-Classical models are validated by experiments and 3D FE simulations of periodic Beams and plates. The non-Classical Beam theories converge to the physically correct solutions for wider range of Beam parameters than the Classical Beam theories do.Peer reviewe
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a unified higher order Beam theory for buckling of a functionally graded microBeam embedded in elastic medium using modified couple stress theory
Composite Structures, 2013Co-Authors: Mesut şimsek, Jn ReddyAbstract:Abstract Based on the modified couple stress theory (MCST), a unified higher order Beam theory which contains various Beam theories as special cases is proposed for buckling of a functionally graded (FG) microBeam embedded in elastic Pasternak medium. This non-Classical microBeam model incorporates the material length scale parameter which can capture the size effect. The non-Classical Beam model reduces to the Classical Beam model when the material length scale parameter is set to zero. The material properties of the FG microBeam are assumed to vary in the thickness direction and are estimated through the Mori–Tanaka homogenization technique and the Classical rule of mixture. The governing equations and the related boundary conditions are derived using the principal of the minimum total potential energy. The Navier-type solution is developed for simply-supported boundary conditions, and explicit expressions related to each type of Beam theory are proposed for the critical buckling load. Numerical results are presented to investigate the influences the material length scale parameter, aspect ratio, different estimation method of material properties, various material compositions, and the parameters of the elastic medium on the critical buckling load. Comparison study is also performed to verify the present formulation.
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Bending solutions of Levinson Beams and plates in terms of the Classical theories
International Journal of Solids and Structures, 2001Co-Authors: Jn Reddy, Chien Ming Wang, G. T. LimAbstract:Using the mathematical similarity of the governing equations of the Classical Beam and plate theories and the Levinson Beam and plate theories, and the basis of load equivalence, exact relationships between the bending solutions of the two theories for Beams and plates are derived. These relationships enable the conversion of the well-known Classical (Euler-Bernoulli) Beam and (Kirchhoff) plate solutions to their shear deformable counterparts using the Levinson Beam and plate theories. Examples are given to illustrate the use of these relationships.
Mohammad Taghi Ahmadian - One of the best experts on this subject based on the ideXlab platform.
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Effect of size dependency on in-plane vibration of circular micro-rings
Scientia Iranica, 2017Co-Authors: A. Karimzadeh, Mohammad Taghi Ahmadian, M. RahaeifardAbstract:In this paper, based on the modied couple stress theory, the size-dependent dynamic behavior of circular rings on elastic foundation is investigated. The ring is modeled by Euler-Bernoulli and Timoshenko Beam theories, and Hamilton's principle is utilized to derive the equations of motion and boundary conditions. The formulation derived is a general form of the equation of motion of circular rings and can be reduced to the Classical form by eliminating the size-dependent terms. On this basis, the size-dependent natural frequencies of a circular ring are calculated based on the non-Classical Euler-Bernoulli and Timoshenko Beam theories. The ndings are compared with Classical Beam theories. Response of the micro-ring under application of static and dynamic loads is investigatedand compared with the Classical theories. Results show that when the thickness of the ring is in the order of the length scale of the ring material, the natural frequencies evaluated using the modied couple stress are considerably more than those predicted based on the Classical Beam theories, while the defection and natural frequencies of the Classical and non-Classical Beam theories approach one another for the rings with thickness much larger than the material length scale.
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Strain gradient Beam element
Finite Elements in Analysis and Design, 2013Co-Authors: M. H. Kahrobaiyan, Mohsen Asghari, Mohammad Taghi AhmadianAbstract:The Classical continuum theory is neither able to accurately model the mechanical behavior of micro/nano-scale structures nor capable of justifying the size-dependent behavior observed in these structures; so the non-Classical continuum theories such as the strain gradient theory have been emerged and developed. In order to enable the finite element method (FEM) to more accurately deal with the problems in micro/nano-scale structures, a size-dependent Euler-Bernoulli Beam element is developed based on the strain gradient theory. Compared to the Classical Euler-Bernoulli Beam element, the nodal displacement vector of the new Euler-Bernoulli Beam element has an additional component, i.e. the nodal curvature, associated with the additional kinematic parameter existing at the boundaries of strain gradient Beams. The mass and stiffness matrices of the new non-Classical Beam element are derived based on the Galerkin's method. In some examples, it is shown that how the new element can be employed to solve a real-case problem and the results are compared to the analytical and available experimental data as well as the results obtained by employing the Classical Beam elements. It is observed that there is a good agreement between the experimental and the strain gradient based FEM results while the difference between the experimental and the Classical FEM results is significant. In addition, it is indicated that the new Beam element can successfully capture the size-dependency and the structures modeled by this element show stiffer behavior than those modeled by the Classical Beam element. Moreover, by setting some material length scale parameters to zero the new Beam element is able to recover the results of the Classical theory and the modified couple stress theory (another non-Classical continuum theory).
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A Size-Dependent Beam Element Based on the Modified Couple Stress Theory
Volume 8: Mechanics of Solids Structures and Fluids; Vibration Acoustics and Wave Propagation, 2011Co-Authors: M. H. Kahrobaiyan, M. Khajehpour, Mohammad Taghi AhmadianAbstract:In this paper, the modified couple stress theory is employed to develop a size-dependent Beam element able to predict the size-dependency observed in microBeams. The stiffness matrix is obtained for the aforementioned Beam element. As an example, the deflection of a microcantilever is evaluated using the proposed Beam elements and the results of the finite element method are compared to the analytical results obtained by the Classical Beam theory. The maximum deflection of the Beam is depicted versus the ratio of the Beam thickness to the material length scale parameter, the parameter appearing in non-Classical continuum theories. The results show that when the characteristic size of the Beam (thickness, diameter, etc) is small, like the Beam used in MEMS and NEMS, the difference between the results of the current model and those obtained by the Classical Beam theory is significant but it diminishes as the characteristic size increases.Copyright © 2011 by ASME
H Rafiitabar - One of the best experts on this subject based on the ideXlab platform.
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computational modelling of a non viscous fluid flow in a multi walled carbon nanotube modelled as a timoshenko Beam
Nanotechnology, 2008Co-Authors: Narjes Khosravian, H RafiitabarAbstract:In the design of nanotube-based fluidic devices, a critical issue is the effect of the induced vibrations in the nanotube arising from the fluid flow, since these vibrations can promote structural instabilities, such as buckling transitions. It is known that the induced resonant frequencies depend on the fluid flow velocity in a significant manner. We have studied, for the first time, the flow of a non-viscous fluid in stubby multi-walled carbon nanotubes, using the Timoshenko Classical Beam theory to model the nanotubes as a continuum structure. We have obtained the variations of the resonant frequencies with the fluid flow velocity under several experimentally interesting boundary conditions and aspect ratios of the nanotube. The main finding from our work is that, compared to an Euler–Bernoulli Classical Beam model of a nanotube, the Timoshenko Beam predicts the loss of stability at lower fluid flow velocities.
şeref Doguscan Akbas - One of the best experts on this subject based on the ideXlab platform.
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Wave propagation in a microBeam based on the modified couple stress theory
Structural Engineering and Mechanics, 2013Co-Authors: Turgut Kocaturk, şeref Doguscan AkbasAbstract:This paper presents responses of the free end of a cantilever micro Beam under the effect of an impact force based on the modified couple stress theory. The Beam is excited by a transverse triangular force impulse modulated by a harmonic motion. The Kelvin-Voigt model for the material of the Beam is used. The considered problem is investigated within the Bernoulli-Euler Beam theory by using energy based finite element method. The system of equations of motion is derived by using Lagrange`s equations. The obtained system of linear differential equations is reduced to a linear algebraic equation system and solved in the time domain by using Newmark average acceleration method. In the study, the difference of the modified couple stress theory and the Classical Beam theory is investigated for the wave propagation. A few of the obtained results are compared with the previously published results. The influences of the material length scale parameter on the wave propagation are investigated in detail. It is clearly seen from the results that the Classical Beam theory based on the modified couple stress theory must be used instead of the Classical theory for small values of Beam height.
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static bending of a functionally graded microscale timoshenko Beam based on the modified couple stress theory
Composite Structures, 2013Co-Authors: Mesut şimsek, Turgut Kocaturk, şeref Doguscan AkbasAbstract:Abstract A microscale functionally graded Timoshenko Beam model is developed for the static bending analysis based on the modified couple stress theory (MCST). The material properties of the FG microBeams are assumed to vary in the thickness direction and are estimated through the Mori–Tanaka homogenization technique and the Classical rule of mixture. The equilibrium equations and the related boundary conditions are derived by using the principal of the minimum total potential energy. The governing equations are solved analytically for a simply-supported Beam subjected to a point and uniformly distributed load. 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 influences of the volume fraction index, the different estimation method of the material properties, length scale parameter, the aspect ratio and the Poisson effect on the static bending behavior are examined. Some of the present results are compared with the previously published results to establish the validity of the present formulation. It is found that the deflections of the microBeam by the Classical Beam theory are always larger than those by the modified couple stress theory.