Shortening Effect on Buckling Behavior of Reddy Plates and Prismatic Plate Structures

2019 ◽  
Vol 19 (04) ◽  
pp. 1950048 ◽  
Author(s):  
E. Ruocco ◽  
J. N. Reddy
Keyword(s):  
Plate Theory ◽  
Strain Tensor ◽  
Closed Form Solution ◽  
Form Solution ◽  
Stiffened Plates ◽  
Flat Plates ◽  
Buckling Mode ◽  
Von Karman ◽  
Kirchhoff Stress Tensor ◽  
Von Kármán

A closed-form solution based on the Reddy third-order shear deformation plate theory is proposed for the buckling of both flat and stiffened plates, simply supported on two opposite edges. The effect of the nonlinear strain–displacement terms, usually neglected under the von Kármán hypothesis, on the buckling of thick plates is investigated, and the equations governing the critical behavior considering the full Green–Lagrange strain tensor and the second Piola–Kirchhoff stress tensor are derived using the principle of minimum potential energy. The general Levy-type approach is employed, and the accuracy and effectiveness of the proposed formulation is validated through direct comparison with analytical and numerical results available in the literature. The parametric analyses performed for different geometrical ratios show that the von Kármán hypothesis holds only for thin flat plates whereas it can significantly overestimate buckling loads for stiffened plates, for which the buckling mode entails comparable in-plane and out-of-plane displacements.

Design and finite element assessment of fully uncoupled multi-directional layups for delamination tests

2019 ◽  
Vol 54 (6) ◽  
pp. 773-790 ◽  
Author(s):  
Torquato Garulli ◽  
Anita Catapano ◽  
Daniele Fanteria ◽  
Julien Jumel ◽  
Eric Martin
Keyword(s):  
Finite Element ◽  
Crack Closure ◽  
Plate Theory ◽  
Closed Form Solution ◽  
Standard Test ◽  
Form Solution ◽  
Virtual Crack Closure Technique ◽  
Test Procedures ◽  
Closure Technique ◽  
Double Cantilever Beam Test

In this paper, a procedure to obtain fully uncoupled multi-directional stacking sequences for delamination specimens is outlined. For such sequences, in-plane, membrane-bending and torsion–bending coupling terms are null (in closed-form solution in the framework of classical laminated plate theory) for the entire stack and for both its halves, which form two arms in the pre-cracked region of a typical delamination specimen. This is achieved exploiting the superposition of quasi-trivial quasi-homogeneous stacking sequences, according to appropriate rules. Any pair of orientations of the plies embedding the delamination plane can be obtained. To assess the effectiveness of the proposed approach, a fully uncoupled multi-directional sequence is designed and compared to other relevant sequences proposed in the literature. Finite element simulations of double cantilever beam test are performed using classic virtual crack closure technique and a revised state-of-the-art virtual crack closure technique formulation too. Some interesting conclusions regarding proper design of multidirectional stacks for delamination tests are drawn. Moreover, the results confirm the suitability of fully uncoupled multi-directional sequences for delamination tests. Thanks to their properties, these sequences might lay the foundations for the development of standard test procedures for delamination in angle-ply interfaces.

scholarly journals Elastohydrodynamics of a pre-stretched finite elastic sheet lubricated by a thin viscous film with application to microfluidic soft actuators

2019 ◽  
Vol 862 ◽  
pp. 732-752 ◽  
Author(s):  
Evgeniy Boyko ◽  
Ran Eshel ◽  
Khaled Gommed ◽  
Amir D. Gat ◽  
Moran Bercovici
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Finite Domain ◽  
Viscous Film ◽  
Elastic Sheet ◽  
Von Karman ◽  
Von Kármán Equations ◽  
Wide Range ◽  
Soft Actuators ◽  
Von Kármán

The interaction of a thin viscous film with an elastic sheet results in coupling of pressure and deformation, which can be utilized as an actuation mechanism for surface deformations in a wide range of applications, including microfluidics, optics and soft robotics. Implementation of such configurations inherently takes place over finite domains and often requires some pre-stretching of the sheet. Under the assumptions of strong pre-stretching and small deformations of the lubricated elastic sheet, we use the linearized Reynolds and Föppl–von Kármán equations to derive closed-form analytical solutions describing the deformation in a finite domain due to external forces, accounting for both bending and tension effects. We provide a closed-form solution for the case of a square-shaped actuation region and present the effect of pre-stretching on the dynamics of the deformation. We further present the dependence of the deformation magnitude and time scale on the spatial wavenumber, as well as the transition between stretching- and bending-dominant regimes. We also demonstrate the effect of spatial discretization of the forcing (representing practical actuation elements) on the achievable resolution of the deformation. Extending the problem to an axisymmetric domain, we investigate the effects arising from nonlinearity of the Reynolds and Föppl–von Kármán equations and present the deformation behaviour as it becomes comparable to the initial film thickness and dependent on the induced tension. These results set the theoretical foundation for implementation of microfluidic soft actuators based on elastohydrodynanmics.

A closed form solution for bending/stretching analysis of functionally graded circular plates under asymmetric loading using the Green function

2010 ◽  
Vol 224 (6) ◽  
pp. 1153-1163 ◽  
Author(s):  
A R Saidi ◽  
A Naderi ◽  
E Jomehzadeh
Keyword(s):  
Green Function ◽  
Closed Form ◽  
Volume Fraction ◽  
Plate Theory ◽  
Closed Form Solution ◽  
Form Solution ◽  
Functionally Graded ◽  
Transverse Displacement ◽  
Circular Plates ◽  
Equilibrium Equations

In this article, a closed-form solution for bending/stretching analysis of functionally graded (FG) circular plates under asymmetric loads is presented. It is assumed that the material properties of the FG plate are described by a power function of the thickness variable. The equilibrium equations are derived according to the classical plate theory using the principle of total potential energy. Two new functions are introduced to decouple the governing equilibrium equations. The three highly coupled partial differential equations are then converted into an independent equation in terms of transverse displacement. A closed-form solution for deflection of FG circular plates under arbitrary lateral eccentric concentrated force is obtained by defining a new coordinate system. This solution can be used as a Green function to obtain the closed-form solution of the FG plate under arbitrary loadings. Also, the solution is employed to solve some different asymmetric problems. Finally, the stress and displacement components are obtained exactly for each problem and the effect of volume fraction is also studied.

NONLINEAR BENDING ANALYSIS OF FUNCTIONALLY GRADED PLATES UNDER PRESSURE LOADS USING A FOUR VARIABLE REFINED PLATE THEORY

2014 ◽  
Vol 11 (04) ◽  
pp. 1350062 ◽  
Author(s):  
MOHAMED ATIF BENATTA ◽  
ABDELHAKIM KACI ◽  
ABDELOUAHED TOUNSI ◽  
MOHAMMED SID AHMED HOUARI ◽  
KARIMA BAKHTI ◽  
...  
Keyword(s):  
Shear Stress ◽  
Shear Deformation ◽  
Transverse Shear ◽  
Plate Theory ◽  
Functionally Graded ◽  
Shear Stresses ◽  
Functionally Graded Plates ◽  
Refined Plate Theory ◽  
Von Karman ◽  
Von Kármán

The novelty of this paper is the use of four variable refined plate theory for nonlinear analysis of plates made of functionally graded materials. The plates are subjected to pressure loading and their geometric nonlinearity is introduced in the strain–displacement equations based on Von–Karman assumptions. Unlike any other theory, the theory presented gives rise to only four governing equations. Number of unknown functions involved is only four, as against five in case of simple shear deformation theories of Mindlin and Reissner (first shear deformation theory). The plate properties are assumed to be varied through the thickness following a simple power law distribution in terms of volume fraction of material constituents. The theory presented is variationally consistent, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. The fundamental equations for functionally graded plates are obtained using the Von–Karman theory for large deflection and the solution is obtained by minimization of the total potential energy. Numerical results for functionally graded plates are given in dimensionless graphical forms; and the effects of material properties on deflections and stresses are determined. The results obtained for plate with various thickness ratios using the theory are not only substantially more accurate than those obtained using the CPT, but are almost comparable to those obtained using higher order theories having more number of unknown functions.

scholarly journals A Novel Higher-Order Shear and Normal Deformable Plate Theory for the Static, Free Vibration and Buckling Analysis of Functionally Graded Plates

2017 ◽  
Vol 2017 ◽  
pp. 1-20 ◽  
Author(s):  
Shi-Chao Yi ◽  
Lin-Quan Yao ◽  
Bai-Jian Tang
Keyword(s):  
Natural Frequencies ◽  
Plate Theory ◽  
Closed Form Solution ◽  
Higher Order ◽  
Form Solution ◽  
Functionally Graded ◽  
The Novel ◽  
Functionally Graded Plates ◽  
Graded Materials ◽  
Different Shapes

Closed-form solution of a special higher-order shear and normal deformable plate theory is presented for the static situations, natural frequencies, and buckling responses of simple supported functionally graded materials plates (FGMs). Distinguished from the usual theories, the uniqueness is the differentia of the new plate theory. Each individual FGM plate has special characteristics, such as material properties and length-thickness ratio. These distinctive attributes determine a set of orthogonal polynomials, and then the polynomials can form an exclusive plate theory. Thus, the novel plate theory has two merits: one is the orthogonality, where the majority of the coefficients of the equations derived from Hamilton’s principle are zero; the other is the flexibility, where the order of the plate theory can be arbitrarily set. Numerical examples with different shapes of plates are presented and the achieved results are compared with the reference solutions available in the literature. Several aspects of the model involving relevant parameters, length-to-thickness, stiffness ratios, and so forth affected by static and dynamic situations are elaborate analyzed in detail. As a consequence, the applicability and the effectiveness of the present method for accurately computing deflection, stresses, natural frequencies, and buckling response of various FGM plates are demonstrated.

scholarly journals Nonlinear Donati compatibility conditions for the nonlinear Kirchhoff–von Kármán–Love plate theory

2013 ◽  
Vol 351 (9-10) ◽  
pp. 405-409 ◽  
Author(s):  
Philippe G. Ciarlet ◽  
Giuseppe Geymonat ◽  
Françoise Krasucki
Keyword(s):  
Plate Theory ◽  
Compatibility Conditions ◽  
Von Karman ◽  
Von Kármán

Nonlinear Vibration of Rotating Thin Disks

2000 ◽  
Vol 122 (4) ◽  
pp. 376-383 ◽  
Author(s):  
Albert C. J. Luo ◽  
C. D. Mote,
Keyword(s):  
Nonlinear Vibration ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Nonlinear Effects ◽  
Linear Vibration ◽  
Rotating Disks ◽  
Nodal Diameter ◽  
Von Karman ◽  
Thin Disks ◽  
Von Kármán

The response and natural frequencies for the linear and nonlinear vibrations of rotating disks are given analytically through the new plate theory proposed by Luo in 1999. The results for the nonlinear vibration can reduce to the ones for the linear vibration when the nonlinear effects vanish and for the von Karman model when the nonlinear effects are modified. They are applicable to disks experiencing large-amplitude displacement or initial flatness and waviness. The natural frequencies for symmetric and asymmetric responses of a 3.5-inch diameter computer memory disk as an example are predicted through the linear theory, the von Karman theory and the new plate theory. The hardening of rotating disks occurs when nodal-diameter numbers are small and the softening of rotating disks occurs when nodal-diameter numbers become larger. The critical speeds of the softening disks decrease with increasing deflection amplitudes. [S0739-3717(00)02004-3]

Thermoelastic Fields in Boundary Layers of Isotropic Laminates

2005 ◽  
Vol 72 (1) ◽  
pp. 86-101 ◽  
Author(s):  
Christian Mittelstedt ◽  
Wilfried Becker
Keyword(s):  
Closed Form ◽  
Edge Effects ◽  
Plate Theory ◽  
Closed Form Solution ◽  
Laminate Plate ◽  
Free Edge ◽  
Linear Displacement ◽  
Form Solution ◽  
State Variables ◽  
Layered Plates

An approximate approach to the calculation of displacements, strains, and stresses near edges and corners in symmetric rectangular layered plates of dissimilar isotropic materials under thermal load is presented. In the thickness direction the plate is discretized into an arbitrary number of sublayers/mathematical layers. A layerwise linear displacement field is formulated such that the terms according to classical laminate plate theory are upgraded with unknown in-plane functions and a linear interpolation scheme through the layer thickness in order to describe edge and corner perturbations. By virtue of the principle of minimum potential energy the governing coupled Euler–Lagrange differential equations are derived, which in the case of free-edge effects allow a closed-form solution for the unknown inplane functions. Free-corner effects are investigated by combining the displacement formulations of the two interacting free-edge effects. Hence, all state variables in the plate are obtained in a closed-form manner. Boundary conditions of traction free plate edges are satisfied in an integral sense. The present methodology is easily applied and requires only reasonable computational expenses.

Sign in / Sign up

Export Citation Format

Share Document