Size-dependent electro-magneto-elastic bending analyses of the shear-deformable axisymmetric functionally graded circular nanoplates

2017 ◽  
Vol 132 (10) ◽  
Author(s):  
Mohammad Arefi ◽  
Ashraf M. Zenkour
Keyword(s):  
Functionally Graded ◽  
Elastic Bending ◽  
Size Dependent ◽  
Shear Deformable

Nonlinear forced vibration analysis of higher order shear-deformable functionally graded microbeam resting on nonlinear elastic foundation based on modified couple stress theory

2018 ◽  
Vol 233 (9) ◽  
pp. 1773-1790 ◽  
Author(s):  
Debabrata Das
Keyword(s):  
Couple Stress Theory ◽  
Modified Couple Stress Theory ◽  
Functionally Graded ◽  
Stress Theory ◽  
Size Dependent ◽  
Modified Couple Stress ◽  
Nonlinear Forced Vibration ◽  
Forced Vibration Analysis ◽  
Nonlinear Elastic ◽  
Shear Deformable

Geometrically nonlinear forced vibration analysis of higher order shear-deformable functionally graded microbeam is presented, where the beam is supported on a three-parameter Winkler–Pasternak-type nonlinear elastic foundation and subjected to a harmonically varying distributed load. The modified couple stress theory of elasticity is employed in the formulation to address the size-dependent effect. Hamilton’s principle is used to derive the displacement-based governing equations considering Reddy’s third-order shear deformation theory. Ritz method is followed to convert the governing equations to nonlinear algebraic form in the frequency domain by approximating the displacement fields. A mixed algorithm for nonlinear equations based on the iterative substitution method with successive relaxation and Broyden’s method is successfully employed to solve the stable regions of the frequency-response curves. The results are presented for hinged and clamped beams, and the effects of different parameters such as size-dependent thickness, load amplitude, foundation parameters, and gradation-profile parameter are studied. The effect of thermal loading due to uniform temperature rise is also studied considering temperature-dependent material properties.

On size-dependent bending behaviors of shape memory alloy microbeams via nonlocal strain gradient theory

2021 ◽  
pp. 1045389X2098699
Author(s):  
Bo Zhou ◽  
Zetian Kang ◽  
Xiao Ma ◽  
Shifeng Xue
Keyword(s):  
Shape Memory Alloy ◽  
Shape Memory ◽  
Functionally Graded ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Size Dependent ◽  
Material Length Scale Parameter ◽  
Material Length Scale ◽  
Material Length ◽  
Nonlocal Strain Gradient

This paper focuses on the size-dependent behaviors of functionally graded shape memory alloy (FG-SMA) microbeams based on the Bernoulli-Euler beam theory. It is taken into consideration that material properties, such as austenitic elastic modulus, martensitic elastic modulus and critical transformation stresses vary continuously along the longitudinal direction. According to the simplified linear shape memory alloy (SMA) constitutive equations and nonlocal strain gradient theory, the mechanical model was established via the principle of virtual work. Employing the Galerkin method, the governing differential equations were numerically solved. The functionally graded effect, nonlocal effect and size effect of the mechanical behaviors of the FG-SMA microbeam were numerically simulated and discussed. Results indicate that the mechanical behaviors of FG-SMA microbeams are distinctly size-dependent only when the ratio of material length scale parameter to the microbeam height is small enough. Both the increments of material nonlocal parameter and ratio of material length-scale parameter to the microbeam height all make the FG-SMA microbeam become softer. However, the stiffness increases with the increment of FG parameter. The FG parameter plays an important role in controlling the transverse deformation of the FG-SMA microbeam. This work can provide a theoretical basis for the design and application of FG-SMA microstructures.

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