scholarly journals On well-posedness of two-phase nonlocal integral models for higher-order refined shear deformation beams

2021 ◽  
Author(s):  
Pei Zhang ◽  
Hai Qing
Keyword(s):  
Shear Deformation ◽  
Scale Effects ◽  
Differential Quadrature Method ◽  
Higher Order ◽  
Functionally Graded ◽  
Integral Model ◽  
Well Posedness ◽  
Curved Beams ◽  
Two Phase ◽  
Constitutive Requirements

AbstractDue to the conflict between equilibrium and constitutive requirements, Eringen’s strain-driven nonlocal integral model is not applicable to nanostructures of engineering interest. As an alternative, the stress-driven model has been recently developed. In this paper, for higher-order shear deformation beams, the ill-posed issue (i.e., excessive mandatory boundary conditions (BCs) cannot be met simultaneously) exists not only in strain-driven nonlocal models but also in stress-driven ones. The well-posedness of both the strain- and stress-driven two-phase nonlocal (TPN-StrainD and TPN-StressD) models is pertinently evidenced by formulating the static bending of curved beams made of functionally graded (FG) materials. The two-phase nonlocal integral constitutive relation is equivalent to a differential law equipped with two restriction conditions. By using the generalized differential quadrature method (GDQM), the coupling governing equations are solved numerically. The results show that the two-phase models can predict consistent scale-effects under different supported and loading conditions.

Well-posed two-phase nonlocal integral models for free vibration of nanobeams in context with higher-order refined shear deformation theory

2021 ◽  
pp. 107754632110399
Author(s):  
Pei Zhang ◽  
Hai Qing
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Shear Deformation ◽  
Differential Quadrature Method ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Well Posedness ◽  
Governing Equations ◽  
Two Phase

In this article, the well-posedness of several common nonlocal models for higher-order refined shear deformation beams is studied. Unlike the case of classic beams models, both strain-driven and stress-driven purely nonlocal theories lead to an ill-posed issue (i.e., there are excessive mandatory boundary conditions) when considering higher-order shear deformation assumption. As an effective remedy, the well-posedness of strain-driven and stress-driven two-phase nonlocal (StrainDTPN and StressDTPN) models is pertinently evidenced by studying the free vibration problem of nanobeams. The governing equations of motion and standard boundary conditions are derived from Hamilton’s principle. The integral constitutive relation is transformed equivalently to a differential form equipped with two constitutive boundary conditions. Using the generalized differential quadrature method (GDQM), the governing equations in terms of displacements are solved numerically. Numerical results show that both the StrainDTPN and StressDTPN models can predict consistent size-effects of beams with different boundary conditions.

FROUDE’S LAW OF SIMILITUDE – CONTEMPORARY AND FUTURE SEAKEEPING TESTING

2021 ◽  
Vol 153 (A2) ◽  
Author(s):  
R P Dallinga ◽  
R H M Huijsmans
Keyword(s):  
Model Test ◽  
Scale Effects ◽  
Higher Order ◽  
Air Pressure ◽  
Test Results ◽  
Viscous Effects ◽  
Two Phase ◽  
Scale Models ◽  
Non Linear

Historically “scale effects” in the interpretation of tests with scale models in waves using Froude’s Law of Similitude are mostly associated with viscous effects. Nowadays, with a much more complete modelling of reality and a focus on higher order non-linear phenomena, scaling of model test results implies a wider range of assumptions than the validity of Froude’s Law. Our contribution to the conference is a visionary review of contemporary and future problems in the interpretation of these tests. In this context we will discuss the developments in test techniques, including the development of a new Two-Phase Laboratory facilitating seakeeping and sloshing tests at reduced air pressure.

Bending and free vibration analyses of functionally graded material nanoplates via a novel nonlocal single variable shear deformation plate theory

2020 ◽  
pp. 095440622096452
Author(s):  
Le Kha Hoa ◽  
Pham Van Vinh ◽  
Nguyen Dinh Duc ◽  
Nguyen Thoi Trung ◽  
Le Truong Son ◽  
...  
Keyword(s):  
Shear Deformation ◽  
Functionally Graded Material ◽  
Numerical Solutions ◽  
Scale Effects ◽  
Plate Thickness ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Small Scale ◽  
Parameter Study ◽  
Graded Material

A novel nonlocal shear deformation theory is established to investigate functionally graded nanoplates. The significant benefit of this theory is that it consists of only one unknown variable in its displacement formula and governing differential equation, but it can take into account both the quadratic distribution of the shear strains and stresses through the plate thickness as well as the small-scale effects on nanostructures. The numerical solutions of simply supported rectangular functionally graded material nanoplates are carried out by applying the Navier procedure. To indicate the accuracy and convergence of this theory, the present solutions have been compared with other published results. Furthermore, a deep parameter study is also carried out to exhibit the influence of some parameters on the response of the functionally graded material nanoplates.

Nonlinear thermo-mechanical buckling of higher-order shear deformable porous functionally graded material plates reinforced by orthogonal and/or oblique stiffeners

2019 ◽  
Vol 233 (17) ◽  
pp. 6177-6196 ◽  
Author(s):  
Vu Hoai Nam ◽  
Nguyen Thi Phuong ◽  
Dang Thuy Dong ◽  
Nguyen Thoi Trung ◽  
Nguyen Van Tue
Keyword(s):  
Shear Deformation ◽  
Elastic Foundation ◽  
Functionally Graded Material ◽  
Thermal Environment ◽  
Plate Theory ◽  
Higher Order ◽  
Functionally Graded ◽  
Shear Deformation Plate Theory ◽  
Graded Material ◽  
Post Buckling

In this paper, an analytical approach for nonlinear buckling and post-buckling behavior of stiffened porous functionally graded plate rested on Pasternak's elastic foundation under mechanical load in thermal environment is presented. The orthogonal and/or oblique stiffeners are attached to the surface of plate and are included in the calculation by improving the Lekhnitskii's smeared stiffener technique in the framework of higher-order shear deformation plate theory. The complex equilibrium and stability equations are established based on the Reddy's higher-order shear deformation plate theory and taken into account the geometrical nonlinearity of von Kármán. The solution forms of displacements satisfying the different boundary conditions are chosen, the stress function method and the Galerkin procedure are used to solve the problem. The good agreements of the present analytical solution are validated by making the comparisons of the present results with other results. In addition, the effects of porosity distribution, stiffener, volume fraction index, thermal environment, elastic foundation… on the critical buckling load and post-buckling response of porous functionally graded material plates are numerically investigated.

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