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A Micromorphic Beam Theory for Beams with Elongated Microstructures
Faculty
Engineering
Year:
2020
Type of Publication:
ZU Hosted
Pages:
Authors:
Samer Abdelrahman Mohamed Emam
Staff Zu Site
Abstract In Staff Site
Journal:
Scientific Reports Nature
Volume:
Keywords :
, Micromorphic Beam Theory , Beams with Elongated
Abstract:
A novel micromorphic beam theory that considers the exact shape and size of the beam’s microstructure is developed. The new theory complements the beam theories that are based on the classical mechanics by modeling the shape and size of the beam’s microstructure. This theory models the beam with a microstructure that has shape and size and exhibits microstrains that are independent of the beam’s macroscopic strains. This theory postulates six independent degrees of freedom to describe the axial and transverse displacements and the axial and shear microstrains of the beam. The detailed variational formulation of the beam theory is provided based on the reduced micromorphic model. For the first time, the displacement and microstrain fields of beams with elongated microstructures are developed. In addition, six material constants are defined to fully describe the beam’s microscopic and macroscopic stiffnesses, and two length scale parameters are used to capture the beam size effect. A case study of clamped-clamped beams is analytically solved to show the influence of the beam’s microstructural stiffness and size on its mechanical deformation. The developed micromorphic beam theory would find many important applications including the mechanics of advanced beams such as meta-, phononic, and photonic beams.
Author Related Publications
Samer Abdelrahman Mohamed Emam, "Exploiting the subharmonic parametric resonances of a buckled beam for vibratory energy harvesting", Springer دولي, 2018
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Samer Abdelrahman Mohamed Emam, "Free vibration analysis of functionally graded size-dependent nanobeam", international, 2012
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Samer Abdelrahman Mohamed Emam, "Static and stability analysis of nonlocal functionally graded nanobeams", i, 2013
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Samer Abdelrahman Mohamed Emam, "Approximate analytical solutions for the nonlinear free vibrations of composite beams in buckling", international, 2013
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Samer Abdelrahman Mohamed Emam, "Nonlinear response of buckled beams to 1:1 and 3:1 internal resonances", international, 2013
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Department Related Publications
Soliman Soliman Soliman Alieldien, "A first-order shear deformation finite element model for elastostatic analysis of laminated composite plates and the equivalent functionally graded plates", Ain Shams Engineering Journal, 2011
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Soliman Soliman Soliman Alieldien, "Size-dependent analysis of functionally graded ultra-thin films", Structural Engineering and Mechanics, Vol. 44, No. 4 (2012) 431-448, 2012
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Soliman Soliman Soliman Alieldien, "Bending Analysis of Ultra-thin Functionally Graded Mindlin Plates Incorporating Surface Energy Effects", International Journal of Mechanical Sciences, 2013
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Soliman Soliman Soliman Alieldien, "Finite element analysis of functionally graded nano-scale films", Finite Elements in Analysis and Design, 2013
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Soliman Soliman Soliman Alieldien, "Finite Element Analysis of the Deformation of Functionally Graded Plates under Thermomechanical Loads", Mathematical Problems in Engineering, 2013
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