Journal ArticleDOI
A Timoshenko beam element based on the modified couple stress theory
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In this article, a new comprehensive Timoshenko beam element has been developed on the basis of the modified couple stress theory, and the shape functions of the new element are derived by solving the governing equations of modified couple-stress Timoshenko beams.About:Â
This article is published in International Journal of Mechanical Sciences.The article was published on 2014-02-01. It has received 93 citations till now. The article focuses on the topics: Timoshenko beam theory & Beam (structure).read more
Citations
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A review of continuum mechanics models for size-dependent analysis of beams and plates
TL;DR: In this paper, a comprehensive review on the development of higher-order continuum models for capturing size effects in small-scale structures is presented, mainly focusing on the size-dependent beam, plate and shell models developed based on the nonlocal elasticity theory, modified couple stress theory and strain gradient theory.
Journal ArticleDOI
Free vibration analysis of size-dependent shear deformable functionally graded cylindrical shell on the basis of modified couple stress theory
TL;DR: In this paper, size-dependent equations of motion for functionally graded cylindrical shell were developed using shear deformation model and rotation inertia, where material properties of the shell were assumed as continuously variable along thickness, consistent with the variation in the component's volume fraction based on power law distribution.
Journal ArticleDOI
Size-dependent vibration of bi-directional functionally graded microbeams with arbitrary boundary conditions
Luan C. Trinh,Luan C. Trinh,Thuc P. Vo,Thuc P. Vo,Huu-Tai Thai,Huu-Tai Thai,Trung-Kien Nguyen +6 more
TL;DR: In this article, the free vibration behavior of bi-dimensional functionally graded (BDFG) microbeams under arbitrary boundary conditions (BCs) is studied using a quasi-3D theory.
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A geometrically nonlinear beam model based on the second strain gradient theory
TL;DR: In this article, the geometrically nonlinear governing differential equation of motion and corresponding boundary conditions of small-scale Euler-Bernoulli beams are achieved using the second strain gradient theory.
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A size-dependent FG micro-plate model incorporating higher-order shear and normal deformation effects based on a modified couple stress theory
TL;DR: In this paper, a modified couple stress theory was proposed to account for both shear and normal deformation effects by a parabolic variation of all displacements across the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the micro-plate.
References
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Journal ArticleDOI
Strain gradient plasticity: Theory and experiment
TL;DR: In this paper, a deformation theory of plasticity is introduced to represent in a phenomenological manner the relative roles of strain hardening and strain gradient hardening, which is a non-linear generalization of Cosserat couple stress theory.
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Couple stress based strain gradient theory for elasticity
TL;DR: In this paper, an equilibrium relation is developed to govern the behavior of the couples, which constrained the couple stress tensor to be symmetric, and the symmetric curvature tensor became the only properly conjugated high order strain measures in the theory to have a real contribution to the total strain energy of the system.
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Experiments and theory in strain gradient elasticity
TL;DR: In this paper, a new set of higher-order metrics is developed to characterize strain gradient behaviors in small-scale structures and a strain gradient elastic bending theory for plane-strain beams is developed.
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Effects of couple-stresses in linear elasticity
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A microbend test method for measuring the plasticity length scale
TL;DR: In this paper, a microbend test method for determining the plasticity length scale has been developed and described, which involves the bending of a thin annealed foil around a small diameter cylindrical mandril, followed by measurement of the unloaded and loaded radii of curvature.
Related Papers (5)
A microstructure-dependent Timoshenko beam model based on a modified couple stress theory
H. M. Ma,Xin-Lin Gao,J. N. Reddy +2 more