scholarly journals Formulation and experimental validation of space-fractional Timoshenko beam model with functionally graded materials effects

2021 ◽  
Author(s):  
Paulina Stempin ◽  
Wojciech Sumelka
Keyword(s):  
Functionally Graded Materials ◽  
Timoshenko Beam ◽  
Functionally Graded ◽  
Beam Model ◽  
Material Parameter Identification ◽  
Graded Materials ◽  
Size Dependent ◽  
Non Local ◽  
Thick Beam ◽  
Euler Bernoulli Beam

AbstractIn this study, the static bending behaviour of a size-dependent thick beam is considered including FGM (Functionally Graded Materials) effects. The presented theory is a further development and extension of the space-fractional (non-local) Euler–Bernoulli beam model (s-FEBB) to space-fractional Timoshenko beam (s-FTB) one by proper taking into account shear deformation. Furthermore, a detailed parametric study on the influence of length scale and order of fractional continua for different boundary conditions demonstrates, how the non-locality affects the static bending response of the s-FTB model. The differences in results between s-FTB and s-FEBB models are shown as well to indicate when shear deformations need to be considered. Finally, material parameter identification and validation based on the bending of SU-8 polymer microbeams confirm the effectiveness of the presented model.

Nonlinear Pull-In Instability of Strain Gradient Microplates Made of Functionally Graded Materials

2019 ◽  
Vol 19 (02) ◽  
pp. 1950007 ◽  
Author(s):  
R. Gholami ◽  
R. Ansari ◽  
H. Rouhi
Keyword(s):  
Functionally Graded Materials ◽  
Strain Gradient ◽  
Scale Effects ◽  
Functionally Graded ◽  
Strain Gradient Theory ◽  
Small Scale ◽  
Gradient Theory ◽  
Graded Materials ◽  
First Order ◽  
Size Dependent

In this paper, the size-dependent nonlinear pull-in behavior of rectangular microplates made from functionally graded materials (FGMs) subjected to electrostatic actuation is numerically studied using a novel approach. The small scale effects are taken into account according to Mindlin’s first-order strain gradient theory (SGT). The plate model is formulated based on the first-order shear deformation theory (FSDT) using the virtual work principle. The size-dependent relations are derived in general form, which can be reduced to those based on different elasticity theories, including the modified strain gradient, modified couple stress and classical theories (MSGT, MCST and CT). The solution of the problem is arrived at by employing an efficient matrix-based method called the variational differential quadrature (VDQ). First, the quadratic form of the energy functional including the size effects is obtained. Then, it is discretized by the VDQ method using a set of matrix differential and integral operators. Finally, the achieved discretized nonlinear equations are solved by the pseudo arc-length continuation method. In the numerical results, the effects of material length scale parameters, side length-to-thickness ratio and FGM’s material gradient index on the nonlinear pull-in instability of microplates with different boundary conditions are investigated. A comparison is also made between the predictions by the MSGT, MCST and CT.

The Material Parameter Identification for Functionally Graded Materials by the Isoparametric Graded Finite Element

2012 ◽  
Vol 446-449 ◽  
pp. 3609-3614 ◽  
Author(s):  
Li Xin Huang ◽  
Lin Wang ◽  
Yue Chen ◽  
Qi Yao ◽  
Xiao Jun Zhou
Keyword(s):  
Parameter Identification ◽  
Functionally Graded Materials ◽  
Material Parameter ◽  
Identification Problem ◽  
Optimization Method ◽  
Functionally Graded ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Material Parameter Identification ◽  
Graded Materials

A material parameter identification method is proposed for functionally graded materials (FGMs) which are modeled by the isoparametric graded finite elements (IGFE). The material parameter identification problem is formulated as the problem of minimizing the objective function defined as a square sum of differences between the measured displacement and the computed displacement by the IGFE. Levenberg-Marquardt optimization method, in which the sensitivity analysis of displacements with respect to the material parameters is based on the finite difference approximation method, is used to solve the minimization problem. Numerical example is given to illustrate the validity of the proposed method for parameter identification.

Interaction Between Thermal Field and Two-Dimensional Functionally Graded Materials: A Structural Mechanical Example

2019 ◽  
Vol 11 (10) ◽  
pp. 1950099 ◽  
Author(s):  
Ye Tang ◽  
Shun Zhong ◽  
Tianzhi Yang ◽  
Qian Ding
Keyword(s):  
Boundary Conditions ◽  
Functionally Graded Materials ◽  
Material Properties ◽  
Thermal Environment ◽  
Differential Quadrature Method ◽  
Functionally Graded ◽  
Graded Materials ◽  
Promising Strategy ◽  
Generalized Differential ◽  
Euler Bernoulli Beam

The buckling and free vibration of a Euler–Bernoulli beam composed of two-directional functionally graded materials (FGMs) in thermal environment are analyzed. The material properties and temperature distributions are considered to be continuously varied along both axial and thickness directions. Such two-directional FGMs provide the basis of a promising strategy to tune the dynamic behavior of a structure in a controlled fashion, achieving tunable response as desired. The dynamic equation of the beam and relevant boundary conditions are derived based on Hamilton’s principle. The generalized differential quadrature method is used for determining the exact buckling configuration and the natural frequencies of the beam with different boundary conditions. Numerical results are presented to examine the effects of material gradations on the critical buckling temperature. It is concluded that both temperature change and material properties have significant influences on the natural frequency, which suggests that it is possible to tailor or tune the dynamic behaviors of a beam by using man-made FGMs in a complex environment.

scholarly journals Transverse Vibration of Axially Moving Functionally Graded Materials Based on Timoshenko Beam Theory

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Suihan Sui ◽  
Ling Chen ◽  
Cheng Li ◽  
Xinpei Liu
Keyword(s):  
Power Law ◽  
Timoshenko Beam ◽  
Natural Frequencies ◽  
Beam Theory ◽  
Functionally Graded ◽  
Beam Model ◽  
Vibration Modes ◽  
Graded Materials ◽  
Power Law Exponent ◽  
Axially Moving

The transverse free vibration of an axially moving beam made of functionally graded materials (FGM) is investigated using a Timoshenko beam theory. Natural frequencies, vibration modes, and critical speeds of such axially moving systems are determined and discussed in detail. The material properties are assumed to vary continuously through the thickness of the beam according to a power law distribution. Hamilton’s principle is employed to derive the governing equation and a complex mode approach is utilized to obtain the transverse dynamical behaviors including the vibration modes and natural frequencies. Effects of the axially moving speed and the power-law exponent on the dynamic responses are examined. Some numerical examples are presented to reveal the differences of natural frequencies for Timoshenko beam model and Euler beam model. Moreover, the critical speed is determined numerically to indicate its variation with respect to the power-law exponent, axial initial stress, and length to thickness ratio.

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