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.

A Mindlin–Reissner Variational Principle to Analyze the Behavior of Moderately Thick Plates

1989 ◽  
Vol 42 (11S) ◽  
pp. S32-S38
Author(s):  
Roberto S. Carnicer ◽  
Stefano Alliney
Keyword(s):  
Finite Element ◽  
Variational Principle ◽  
Plate Theory ◽  
Mindlin Plate ◽  
General Boundary Conditions ◽  
Thick Plates ◽  
Numerical Examples ◽  
Simple Support ◽  
Mindlin Plate Theory ◽  
Moderately Thick Plates

In the present work a method to solve the plate behavior under the assumption of the Mindlin plate theory is analyzed by means of finite element techniques, avoiding the tendency of the thin element to lock when the thickness of the plates becomes very small. A different formulation is developed from the Mindlin–Reissner principle for general boundary conditions. Numerical examples to evaluate the noninfluence of locking on clamped and simple support plates are calculated.

ACCURATE FREQUENCIES AND MODE SHAPES FOR MODERATELY THICK, CANTILEVERED, SKEW PLATES

2007 ◽  
Vol 07 (03) ◽  
pp. 425-440 ◽  
Author(s):  
A. W. LEISSA ◽  
C. S. HUANG ◽  
M. J. CHANG
Keyword(s):  
Plate Theory ◽  
Ritz Method ◽  
The Other ◽  
Mode Shapes ◽  
Mindlin Plate ◽  
Transverse Displacement ◽  
Algebraic Polynomials ◽  
Stress Singularities ◽  
Dependent Variables ◽  
Mindlin Plate Theory

Accurate free vibration frequencies and mode shapes are presented for complete sets of moderately thick, cantilevered skew plates of triangular, trapezoidal and parallelogram shape. These accurate results are obtained by using the Ritz method applied to the Mindlin plate theory. Two sets of functions are employed simultaneously for each of the three dependent variables: transverse displacement (w) and bending rotations (ϕx and ϕy). One set is the widely used algebraic polynomials. The other is the set of corner functions which provide the proper stress singularities in the reentrant clamped-free corner, and accelerates the convergence of the solutions. The extensive frequencies presented are exact to the four digits shown. Corresponding mode shapes are also shown, by means of nodal patterns, most of which are novel in the published literature.

scholarly journals Static and dynamic analyses of stiffened folded laminate composite plate

2013 ◽  
Vol 35 (1) ◽  
pp. 31-50
Author(s):  
Bui Van Binh ◽  
Tran Ich Thinh ◽  
Tran Minh Tu
Keyword(s):  
Composite Plate ◽  
Laminate Composite ◽  
Plate Theory ◽  
Mode Shapes ◽  
Mindlin Plate ◽  
Laminate Composite Plate ◽  
Dynamic Analyses ◽  
Mindlin Plate Theory ◽  
Matlab Programming ◽  
Good Agreement

This paper presents some numerical results of bending and vibration analyses of an unstiffened and stiffened folded laminate composite plate using finite element method. The effects of fiber orientations, boundary conditions, stiffener conditions of the plates for deflections, natural frequencies, and the corresponding mode shapes, transient displacement responses were considered. The Matlab programming using rectangular isoparametric plate element with five degree of freedom per node based on Mindlin plate theory was built to solve the problems. A good agreement is found between the results of this technique and other published results available in the literature.

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.

Sign in / Sign up

Export Citation Format

Share Document