scholarly journals A non-classical Mindlin plate model incorporating microstructure, surface energy and foundation effects

2016 ◽  
Vol 472 (2191) ◽  
pp. 20160275 ◽  
Author(s):  
X.-L. Gao ◽  
G. Y. Zhang
Keyword(s):  
Surface Energy ◽  
Classical Model ◽  
Surface Elasticity ◽  
Mindlin Plate ◽  
Beam Model ◽  
Plate Model ◽  
Energy Effect ◽  
Special Cases ◽  
Microstructure Effect ◽  
Surface Energy Effect

A non-classical model for a Mindlin plate resting on an elastic foundation is developed in a general form using a modified couple stress theory, a surface elasticity theory and a two-parameter Winkler–Pasternak foundation model. It includes all five kinematic variables possible for a Mindlin plate. The equations of motion and the complete boundary conditions are obtained simultaneously through a variational formulation based on Hamilton's principle, and the microstructure, surface energy and foundation effects are treated in a unified manner. The newly developed model contains one material length-scale parameter to describe the microstructure effect, three surface elastic constants to account for the surface energy effect, and two foundation parameters to capture the foundation effect. The current non-classical plate model reduces to its classical elasticity-based counterpart when the microstructure, surface energy and foundation effects are all suppressed. In addition, the new model includes the Mindlin plate models considering the microstructure dependence or the surface energy effect or the foundation influence alone as special cases, recovers the Kirchhoff plate model incorporating the microstructure, surface energy and foundation effects, and degenerates to the Timoshenko beam model including the microstructure effect. To illustrate the new Mindlin plate model, the static bending and free vibration problems of a simply supported rectangular plate are analytically solved by directly applying the general formulae derived.

A non-classical model for first-ordershear deformation circular cylindrical thin shells incorporating microstructure and surface energy effects

2021 ◽  
pp. 108128652097848
Author(s):  
GY Zhang ◽  
X-L Gao
Keyword(s):  
Surface Energy ◽  
Shell Model ◽  
Shear Deformation ◽  
Thin Shell ◽  
Classical Model ◽  
Thin Shells ◽  
Energy Effect ◽  
First Order ◽  
Microstructure Effect ◽  
Surface Energy Effect

A new non-classical model for first-order shear deformation circular cylindrical thin shells is developed by using a modified couple stress theory and a surface elasticity theory. Through a variational formulation based on Hamilton’s principle, the equations of motion and boundary conditions are simultaneously obtained, and the microstructure and surface energy effects are treated in a unified manner. The newly developed non-classical shell model contains one material length-scale parameter to account for the microstructure effect and three surface elastic constants to capture the surface energy effect. The new model includes shell models considering the microstructure effect only or the surface energy effect alone as special cases and recovers the first-order shear deformation circular cylindrical thin shell model based on classical elasticity as a limiting case. In addition, the current shell model reduces to the non-classical model for Mindlin plates incorporating the microstructure and surface energy effects when the thin shell radius tends to infinity. To illustrate the new model, the static bending and free vibration problems of a simply supported circular cylindrical thin shell are analytically solved. The numerical results reveal that the inclusion of the microstructure and surface energy effects leads to reduced shell deflections and rotation angles and increased natural frequencies. The differences are significant when the shell is very thin, but they diminish as the shell thickness increases. These predicted size effects at the micron scale agree with the general trends observed in experiments.

A new isogeometric Timoshenko beam model incorporating microstructures and surface energy effects

2020 ◽  
Vol 25 (10) ◽  
pp. 2005-2022 ◽  
Author(s):  
Shuohui Yin ◽  
Yang Deng ◽  
Gongye Zhang ◽  
Tiantang Yu ◽  
Shuitao Gu
Keyword(s):  
Surface Energy ◽  
Elasticity Theory ◽  
Timoshenko Beam ◽  
Couple Stress Theory ◽  
Surface Elasticity ◽  
Numerical Results ◽  
Beam Model ◽  
Timoshenko Beam Model ◽  
Order Continuity ◽  
Microstructure Effect

A new isogeometric Timoshenko beam model is developed using a modified couple stress theory (MCST) and a surface elasticity theory. The MCST is wildly used to capture microstructure effects that includes only one material length scale parameter, while the Gurtin–Murdoch surface elasticity theory containing three surface elasticity constants is employed to approximate the nature of surface energy effects. A new effective computational approach is presented for the current nonclassical Timoshenko beam model based on isogeometric analysis with high-order continuity basis functions of non-uniform rational B-splines, which effectively fulfills the higher continuity requirements in MCST. To validate the new approach and quantitatively illustrate both the microstructure and surface energy effects, the numerical results obtained from the developed approach for static deflection and natural frequencies of beams are compared with the analytical results available in the literature. Numerical results reveal that both the microstructure effect and surface energy effect should be considered in very thin beams, which also explains the size-dependent behavior.

Surface energy effect on boiling heat transfer

2005 ◽  
Vol 41 (12) ◽  
pp. 1043-1047 ◽  
Author(s):  
Atul P. Patil ◽  
Vijaya C. B. Vittala
Keyword(s):  
Heat Transfer ◽  
Surface Energy ◽  
Boiling Heat Transfer ◽  
Energy Effect ◽  
Surface Energy Effect

A Surface Energy Density-Based Theory of Nanoelastic Dynamics and Its Application in the Scattering of P-Wave by a Cylindrical Nanocavity

2020 ◽  
Vol 87 (10) ◽  
Author(s):  
Ning Jia ◽  
Zhilong Peng ◽  
Yin Yao ◽  
Shaohua Chen
Keyword(s):  
Surface Energy ◽  
Surface Effect ◽  
P Wave ◽  
Wave Frequency ◽  
Inertial Effect ◽  
Inertia Force ◽  
Energy Effect ◽  
Classical Counterpart ◽  
Surface Energy Effect ◽  
Effect Of Surface

Abstract The scattering of elastic waves in nanoporous materials is inevitably influenced by the surface effect of nanopores. In order to investigate such a dynamic problem with surface effect of nanomaterials, a new theory of nanoelastic dynamics is proposed, in which both the effect of surface free energy and the effect of surface inertia force are included. With the new theory, a scattering of plane compressional waves (P-wave) by a cylindrical nanocavity is analyzed, and the corresponding dynamic stress concentration factor (DSCF) around the nanocavity is analytically solved. It is found that, when the size of cavity is at a nanoscale, the surface energy effect leads to a reduction of the maximum DSCF comparing with the classical counterpart without surface effect, while the surface inertial effect enlarges the maximum DSCF. The surface inertial effect gradually becomes dominant over the surface energy effect with an increasing incident wave frequency. Although both kinds of surface effects tend to vanish with an increasing cavity radius, the surface inertial effect can exist in a submicron-sized cavity if the wave frequency is sufficiently high. All these results should be of guiding value not only for an optimal design of porous structure possessing a better dynamic load bearing capacity but also for the non-destructive detection of nano-defects.

Sign in / Sign up

Export Citation Format

Share Document