Abstract null null In this paper, we present an efficient and accurate numerical approach for static bending and free vibration analyses of microstructure-dependent Bernoulli-Euler beams. The current approach includes strain gradient, couple stress (rotation gradient) and velocity gradient effects simultaneously through a reformulated strain gradient elasticity, which applies only one material parameter for each gradient effect. Based on the Hamilton’s principle and an Isogeometric Analysis (IGA) approach, the governing equations are derived and solved, respectively, which effectively fulfills the higher continuity requirements in the present microstructure-dependent Bernoulli-Euler beam formulation. The static bending and free vibration analyses of simply supported microstructure-dependent beams are studied by directly applying the current approach and compared with the corresponding analytical solutions. The physical mesh convergence and numerical results prove the high performance and accuracy of the present numerical approach. In addition, the cantilever and clamped microbeams are also carried out to show the applicability of the present approach.

Last. Xin-Lin Gao(SMU: Southern Methodist University)H-Index: 41

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A new microstructure-dependent non-classical model for Kirchhoff plates is developed by using a reformulated strain gradient elasticity theory that incorporates both the strain gradient and couple ...

Nonlocal strain gradient continuum mechanics is a methodology widely employed in the literature to assess size effects in nano-structures. Notwithstanding this, improper higher-order boundary conditions (HOBC) are prescribed to close the corresponding elastostatic problems. In the present study, it is proven that HOBC have to be replaced with univocally determined boundary conditions of constitutive type, established by a consistent variational formulation. The treatment, developed in the framew...

A new non-classical Bernoulli–Euler beam model is developed using a reformulated strain gradient elasticity theory that incorporates both couple stress and strain gradient effects. This reformulate...

Abstract In this article, a refined modified couple stress theory based on isogeomeric analysis to capture the small-scale effect on laminated composite micro-plates is developed for the first time. Based on Hamilton's principle, the weak form for composite plate is established by using the Reddy's third order shear deformation theory without shear correction factor and the refined modified couple stress theory. Unlike the modified couple stress theory, which contains only one material length sc...

Nonlocal strain gradient continuum mechanics is a methodology widely employed in literature to assess size effects in nanostructures. Notwithstanding this, improper higher-order boundary conditions (HOBC) are prescribed to close the corresponding elastostatic problems. In the present study, it is proven that HOBC have to be replaced with univocally determined boundary conditions of constitutive type, established by a consistent variational formulation. The treatment, developed in the framework o...

Last. M. Abdel-Wahab(Ton Duc Thang University)H-Index: 4

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Abstract In this article, we present for the first time a research analysis for the size-dependent effects on thermal buckling and post-buckling behaviors of functionally graded material micro-plates with porosities (imperfect FGM) using isogeometric analysis. A seventh-order shear deformation plate theory associated with the modified couple stress theory (MCST) is particularly imposed to capture the size-dependent phenomenon within imperfect FGM micro-plates. The material properties of imperfec...

Last. M. Abdel-Wahab(UGent: Ghent University)H-Index: 11

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The use of modified couple stress theory to simulate the size-dependent phenomenon of composite laminate microplate is commonly limited to simple boundary conditions and mechanical bending load. The small-scale effects on bending and buckling on composite laminate microplate under complex boundary conditions in thermal environment have not been understood fully in the literature. Hence, this research develops, for the first time, a model to overcome the above limitation through the combination o...

In Part I of this study, a variational formulation was presented for the large elastic deformation problem of micromorphic shells. Using the novel matrix-vector format presented for the kinematic m...

Last. Tinh Quoc Bui(TITech: Tokyo Institute of Technology)H-Index: 54

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Abstract A novel and effective computational approach within the context of isogeometric analysis (IGA) is developed for analyzing size-dependent mechanical behaviors of functionally graded (FG) microbeams. To capture the size effects, an extension of quasi-3D theory is established to integrate with the modified couple stress theory. The nonuniform rational B-spline (NURBS) basis functions are employed and can directly meet the first-order derivative demand of the quasi-3D theory, where four var...

Abstract The size-dependent bending behavior of nano-beams is investigated by the modified nonlocal strain gradient elasticity theory. According to this model, the bending moment is expressed by integral convolutions of elastic flexural curvature and of its derivative with the special bi-exponential averaging kernel. It has been recently proven that such a relation is equivalent to a differential equation, involving bending moment and flexural curvature fields, equipped with natural higher-order...

#1Lan Hoang That Ton(University of Architecture, Civil Engineering and Geodesy)

In this article, the bending behaviors of functionally graded porous (FGP) beams are determined associated with uniform load. The simple beam theory is carried out with various boundary conditions. Two types of porosity are also applied to study the influences of material properties on bending behaviors. The results obtained in this article are presented and compared with other results in the references to verify the correctness in implementing the formula and writing the Matlab code. Last but n...