Reissner-Mindlin Plate Theory

2017 ◽  
pp. 67-82
Author(s):  
Anh Le van
Keyword(s):  
Plate Theory ◽  
Mindlin Plate ◽  
Mindlin Plate Theory

Coupled Extensional and Flexural Motions of a Two-Layer Plate With Interface Slip

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Peng Li ◽  
Feng Jin ◽  
Weiqiu Chen ◽  
Jiashi Yang
Keyword(s):  
Plate Theory ◽  
Cutoff Frequency ◽  
Great Influence ◽  
Imperfect Interface ◽  
Mindlin Plate ◽  
Finite Plate ◽  
Mindlin Plate Theory ◽  
Interface Elasticity ◽  
Propagating Shear ◽  
Perfect Interface

The effect of imperfect interface on the coupled extensional and flexural motions in a two-layer elastic plate is investigated from views of theoretical analysis and numerical simulations. A set of full two-dimensional equations is obtained based on Mindlin plate theory and shear-slip model, which concerns the interface elasticity and tangential discontinuous displacements across the bonding imperfect interface. Some numerical examples are processed, including the propagation of straight-crested waves in an unbounded plate, the buckling of a finite plate, as well as the deflection of a finite plate under uniform load. It is revealed that the bending-evanescent wave in the composites with a perfect interface eventually cuts-on to a propagating shear-like wave with cutoff frequency when the two sublayers imperfectly bonded. The similar phenomenon has been verified once again for coupled face-shear and thickness-shear waves. It also has been pointed out that the interfacial parameter has a great influence on the performance of static buckling, in which the outcome can be reduced to classical buckling load of a simply supported plate when the interface is perfect.

Sharp Corner Functions for Mindlin Plates

2005 ◽  
Vol 72 (1) ◽  
pp. 1-9 ◽  
Author(s):  
O. G. McGee ◽  
J. W. Kim ◽  
A. W. Leissa
Keyword(s):  
Plate Theory ◽  
Thin Plates ◽  
Mode Shapes ◽  
Mindlin Plate ◽  
Transverse Displacement ◽  
Thick Plates ◽  
Thin Plate Theory ◽  
Mindlin Plate Theory ◽  
Moderately Thick Plates ◽  
Sharp Corners

Transverse displacement and rotation eigenfunctions for the bending of moderately thick plates are derived for the Mindlin plate theory so as to satisfy exactly the differential equations of equilibrium and the boundary conditions along two intersecting straight edges. These eigenfunctions are in some ways similar to those derived by Max Williams for thin plates a half century ago. The eigenfunctions are called “corner functions,” for they represent the state of stress currently in sharp corners, demonstrating the singularities that arise there for larger angles. The corner functions, together with others, may be used with energy approaches to obtain accurate results for global behavior of moderately thick plates, such as static deflections, free vibration frequencies, buckling loads, and mode shapes. Comparisons of Mindlin corner functions with those of thin-plate theory are made in this work, and remarkable differences are found.

Nonlinear vibration of piezoelectric nanoplates using nonlocal Mindlin plate theory

2016 ◽  
Vol 25 (15-16) ◽  
pp. 1252-1264 ◽  
Author(s):  
Chen Liu ◽  
Liao-Liang Ke ◽  
Jie Yang ◽  
Sritawat Kitipornchai ◽  
Yue-Sheng Wang
Keyword(s):  
Nonlinear Vibration ◽  
Plate Theory ◽  
Mindlin Plate ◽  
Mindlin Plate Theory

Nonlinear free vibration of orthotropic graphene sheets using nonlocal Mindlin plate theory

2011 ◽  
Vol 226 (7) ◽  
pp. 1896-1906 ◽  
Author(s):  
AR Setoodeh ◽  
P Malekzadeh ◽  
AR Vosoughi
Keyword(s):  
Free Vibration ◽  
Virtual Work ◽  
Plate Theory ◽  
Differential Quadrature Method ◽  
Nonlinear Partial Differential Equations ◽  
Mindlin Plate ◽  
Small Scale ◽  
Graphene Sheets ◽  
Nonlinear Free Vibration ◽  
Mindlin Plate Theory

This article deals with the small-scale effect on the nonlinear free vibration of orthotropic single-layered graphene sheets using the nonlocal elasticity plate theory. The formulations are based on the Mindlin plate theory, and von Karman-type nonlinearity is considered in strain displacement relations. Virtual work principle is used to derive the nonlinear nonlocal plate equations in which the effects of rotary inertia and transverse shear are included. The differential quadrature method is employed to reduce the governing nonlinear partial differential equations to a system of nonlinear algebraic eigenvalue equations. The efficiency and accuracy of the method are demonstrated by comparing the developed result with those available in literature. The methodology is capable of studying large-amplitude vibration characteristics of nanoplates with different sets of boundary conditions. The effects of various parameters on the nonlinear vibrations of nanoplates are presented.

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