New Mindlin Plate Theory Converging on the Phase Velocities of Transverse Waves and That of Rayleigh Waves.

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.

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The validity range of CPT and Mindlin plate theory in comparison with 3-D vibrational analysis of circular plates on the elastic foundation

European Journal of Mechanics - A/Solids ◽

10.1016/j.euromechsol.2008.07.012 ◽

2009 ◽

Vol 28 (2) ◽

pp. 289-304 ◽

Cited By ~ 14

Author(s):

Sh. Hosseini-Hashemi ◽

M. Omidi ◽

H. Rokni Damavandi Taher

Keyword(s):

Elastic Foundation ◽

Plate Theory ◽

Vibrational Analysis ◽

Mindlin Plate ◽

Circular Plates ◽

Validity Range ◽

Mindlin Plate Theory

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Reissner-Mindlin Plate Theory

Nonlinear Theory of Elastic Plates ◽

10.1016/b978-1-78548-227-4.50004-6 ◽

2017 ◽

pp. 67-82

Author(s):

Anh Le van

Keyword(s):

Plate Theory ◽

Mindlin Plate ◽

Mindlin Plate Theory

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Sharp Corner Functions for Mindlin Plates

Journal of Applied Mechanics ◽

10.1115/1.1795221 ◽

2005 ◽

Vol 72 (1) ◽

pp. 1-9 ◽

Cited By ~ 19

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.

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