Journal ArticleDOI
Bending and vibration of functionally graded microbeams using a new higher order beam theory and the modified couple stress theory
Mesut Şimşek,J. N. Reddy +1 more
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TLDR
In this article, a non-classical microbeam model incorporating the material length scale parameter was proposed to capture the size effect of the FG microbeams and the governing equations and the related boundary conditions were derived using Hamilton's principle.About:
This article is published in International Journal of Engineering Science.The article was published on 2013-03-01. It has received 424 citations till now. The article focuses on the topics: Functionally graded material & Microbeam.read more
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Free vibration analysis of nonlocal strain gradient beams made of functionally graded material
Li Li,Xiaobai Li,Yujin Hu +2 more
TL;DR: In this article, a size-dependent Timoshenko beam model, which accounts for through-thickness power-law variation of a two-constituent functionally graded (FG) material, is derived in the framework of the nonlocal strain gradient theory.
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Nonlinear free vibration of a functionally graded nanobeam using nonlocal strain gradient theory and a novel Hamiltonian approach
TL;DR: In this paper, a size-dependent beam model is proposed for nonlinear free vibration of a functionally graded (FG) nanobeam with immovable ends based on the nonlocal strain gradient theory (NLSGT) and Euler-Bernoulli beam theory in conjunction with the von-Karman's geometric nonlinearity.
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Nonlocal elasticity in nanobeams: the stress-driven integral model
TL;DR: In this article, the bending field is placed in the proper position of input variable, giving to the elastic curvature field the role of output of the constitutive law, evaluated by convolution between the bending fields and an averaging kernel.
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Buckling analysis of size-dependent nonlinear beams based on a nonlocal strain gradient theory
TL;DR: In this paper, a size-dependent nonlinear Euler-Bernoulli beam is considered in the framework of the nonlocal strain gradient theory and the geometric nonlinearity due to the stretching effect of the midplane of the size dependent beam was considered, and the governing equations and boundary conditions were derived by employing the Hamilton principle.
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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.
References
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A Simple Higher-Order Theory for Laminated Composite Plates
TL;DR: In this paper, a higher-order shear deformation theory of laminated composite plates is developed, which accounts for parabolic distribution of the transverse shear strains through the thickness of the plate.
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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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Elastic materials with couple-stresses
TL;DR: HAL as discussed by the authors is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not, which may come from teaching and research institutions in France or abroad, or from public or private research centers.
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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.