scholarly journals An inverse problem for a functionally graded elliptical plate with large deflection and slightly disturbed boundary

2006 ◽  
Vol 43 (20) ◽  
pp. 5981-5993 ◽  
Author(s):  
June-Jye Hsieh ◽  
Lin-Tsang Lee
Keyword(s):  
Inverse Problem ◽  
Large Deflection ◽  
Functionally Graded ◽  
Elliptical Plate

Large Deflections of Elliptical Plates

1956 ◽  
Vol 23 (1) ◽  
pp. 21-26
Author(s):  
N. A. Weil ◽  
N. M. Newmark
Keyword(s):  
Circular Plate ◽  
Maximum Stress ◽  
Large Deflection ◽  
Ritz Method ◽  
Constant Thickness ◽  
Infinite Strip ◽  
Elliptical Plate ◽  
Arbitrary Dimensions ◽  
Center Deflection ◽  
Large Deflection Problem

Abstract A solution is obtained by means of the Ritz method for the “large-deflection” problem of a clamped elliptical plate of constant thickness, subjected to a uniformly distributed load. Two shapes of elliptical plate are treated, in addition to the limiting cases of the circular plate and infinite strip, for which the exact solutions are known. Center deflections as well as total stresses at the center and edge decrease as one proceeds from the infinite strip through the elliptical shapes to the circular plate, holding the width of the plates constant. The relation between edge-stress at the semiminor axis (maximum stress in the plate) and center deflection is found to be practically independent of the proportions of the elliptical plate. Hence the governing stress may be determined from a single curve for a given load on an elliptical plate of arbitrary dimensions, if the center deflection is known.

Analytical Solutions for Large Deflections of Functionally Graded Beams Based on Layer-Graded Beam Model

2018 ◽  
Vol 10 (09) ◽  
pp. 1850098 ◽  
Author(s):  
Peng Zhou ◽  
Ying Liu ◽  
Xiaoyan Liang
Keyword(s):  
Intensity Factor ◽  
Analytical Solutions ◽  
Large Deflection ◽  
Yield Criterion ◽  
Functionally Graded ◽  
Beam Model ◽  
Large Deflections ◽  
Transverse Loading ◽  
Functionally Graded Beam ◽  
Gradient Variation

The objective of this paper is to investigate the large deflection of a slender functionally graded beam under the transverse loading. Firstly, by modeling the functionally graded beam as a layered structure with graded yield strength, a unified yield criterion for a functionally graded metallic beam is established. Based on the proposed yielding criteria, analytical solutions (AS) for the large deflections of fully clamped functionally graded beams subjected to transverse loading are formulated. Comparisons between the present solutions with numerical results are made and good agreements are found. The effects of gradient profile and gradient intensity factor on the large deflections of functionally graded beams are discussed in detail. The reliability of the present analytical model is demonstrated, and the larger the gradient variation ratio near the loading surface is, the more accurate the layer-graded beam model will be.

Nonlinear Analysis of a Thin Circular Functionally Graded Plate and Large Deflection Effects on the Forces and Moments

2008 ◽  
Vol 130 (1) ◽  
Author(s):  
A. Allahverdizadeh ◽  
A. Rastgo ◽  
M. H. Naei
Keyword(s):  
Nonlinear Analysis ◽  
Large Deflection ◽  
Volume Fraction ◽  
Plate Thickness ◽  
Functionally Grade ◽  
Functionally Graded ◽  
Governing Equations ◽  
Temperature Dependent ◽  
Harmonic Vibrations ◽  
Graded Material

Nonlinear analysis of a thin circular functionally grade plate is formulated in terms of von Karman’s dynamic equations. The plate thickness is constant and temperature-dependent functionally graded material (FGM) properties vary through the thickness of the plate. Forces and moments of the plate, due to large vibration amplitudes, are developed in this paper by solving the governing equations for harmonic vibrations. Corresponding results are illustrated in the case of steady-state free vibration. The results show that the variation of volume fraction index is influential in forces, moments, and FGM properties.

scholarly journals LARGE DEFLECTION OF CANTILEVER FUNCTIONALLY GRADED SANDWICH BEAM UNDER END FORCES BASED ON A TOTAL LAGRANGE FORMULATION

2020 ◽  
Vol 57 (6A) ◽  
pp. 32
Author(s):  
Hoai Bui Thi Thu
Keyword(s):  
Large Deflection ◽  
Control Method ◽  
Sandwich Beam ◽  
Point Load ◽  
Functionally Graded ◽  
Linear Functions ◽  
Element Formulation ◽  
Material Inhomogeneity ◽  
Lagrange Formulation ◽  
Layer Thickness Ratio

A two-node beam element for large deflection analysis of cantilever functionally graded sandwich (FGSW) beams subjected to end forces is formulated in the context of total Lagrange formulation. The beams consist of three layers, a homogeneous core and two functionally graded layers with material properties varying in the thickness direction by a power gradation law. Linear functions are adopted to interpolate the displacement field and reduced integral technique is applied to evaluate the element formulation. Newton-Raphson based iterative algorithm is employed in combination with arc-length control method to compute equilibrium paths of the beams. Numerical investigations are given for the beam under a transverse point load and a moment to show the accuracy of the element and to illustrate the effects of material inhomogeneity and the layer thickness ratio on the large deflection behavior of the FGSW beams.

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