The Large Elastic-Plastic Deflection With Springback of a Circular Plate Subjected to Circumferential Moments

1982 ◽  
Vol 49 (3) ◽  
pp. 507-515 ◽  
Author(s):  
T. X. Yu ◽  
W. Johnson
Keyword(s):  
Circular Plate ◽  
Large Deflection ◽  
Computer Programs ◽  
Bending Moments ◽  
Plastic Bending ◽  
Elastic Plastic ◽  
Small Deflection ◽  
Deflection Theory

The large deflection elastic-plastic bending of a circular plate subjected to radially outward acting bending moments uniformly distributed around its circumference is analyzed, and computer programs are given to facilitate the determination of the distributions of bending moments, in-plane forces, and displacements during the bending and after unloading or springback. Computed examples are given, and the errors developed by small deflection theory are discussed.

Bending of a Cylindrically Aeolotropic Circular Plate With Eccentric Load

1952 ◽  
Vol 19 (1) ◽  
pp. 9-12
Author(s):  
A. M. Sen Gupta
Keyword(s):  
Boundary Conditions ◽  
Circular Plate ◽  
Uniform Thickness ◽  
Eccentric Load ◽  
Concentrated Load ◽  
Different Boundary Conditions ◽  
Small Deflection ◽  
Deflection Theory ◽  
Clamped Edge

Abstract The problem of small-deflection theory applicable to plates of cylindrically aeolotropic material has been developed, and expressions for moments and deflections produced have been found by Carrier in some symmetrical cases under uniform lateral loadings and with different boundary conditions. The author has also found the moments and deflection in the case of an unsymmetrical bending of a plate loaded by a distribution of pressure of the form p = p0r cos θ, with clamped edge. The object of the present paper is to investigate the problem of the bending of a cylindrically aeolotropic circular plate of uniform thickness under a concentrated load P applied at a point A at a distance b from the center, the edge being clamped.

Buckling of Circular Plate on Elastic Foundation

1965 ◽  
Vol 87 (3) ◽  
pp. 323-324 ◽  
Author(s):  
L. V. Kline ◽  
J. O. Hancock
Keyword(s):  
Circular Plate ◽  
Middle Surface ◽  
Elastic Plates ◽  
Buckling Loads ◽  
Simply Supported ◽  
Small Deflection ◽  
Edge Conditions ◽  
Deflection Theory ◽  
Plate On Elastic Foundation ◽  
Clamped Edge

The buckling loads are found for the simply supported and clamped-edge conditions for a circular plate on a springy foundation under the action of edge loading in the middle surface of the plate. The small deflection theory of bending of thin elastic plates has been used.

Elastoplastic Bending of Rectangular Plates With Large Deflection

1972 ◽  
Vol 39 (4) ◽  
pp. 978-982 ◽  
Author(s):  
T. H. Lin ◽  
S. R. Lin ◽  
B. Mazelsky
Keyword(s):  
Plastic Strain ◽  
Large Deflection ◽  
Rectangular Plates ◽  
Elastic Plates ◽  
Fiber Stress ◽  
Plate Deformation ◽  
Small Deflection ◽  
External Forces ◽  
Deflection Theory ◽  
Elastoplastic Bending

An analytical method for predicting the elastoplastic bending of rectangular plates with large deflection is studied. The effects of plastic strain and large deflection on plate deformation are shown to be the same as a set of applied external forces on the plate in the classical elastic small deflection theory. The calculated deflection for purely elastic plates compares well with previous existing solutions. For the plates considered, the deflection is increased only slightly by plastic strain; however, the maximum extreme fiber stress is considerably relieved by plastic yielding.

Design and Analysis of a Nano-Probe of the AFM Based on the Small/Large Deflection Theory

2004 ◽  
Author(s):  
Chun-Te Lin ◽  
Wei-Chuan Liao ◽  
Jen-Yi Chen ◽  
Hui-Chi Su ◽  
Kuo-Ning Chiang
Keyword(s):  
High Resolution ◽  
Resonant Frequency ◽  
Physical Properties ◽  
Large Deflection ◽  
Spring Constant ◽  
The Finite Element Method ◽  
Small Deflection ◽  
Supporting Base ◽  
Deflection Theory ◽  
Large Deflection Theory

The atomic force microscope (AFM) is a newly developed high resolution microscopy technique which is capable of measuring of nano-scale pattern, nanofabrication, data storage and material analysis in the mechanical, chemical and biological fields. The nano-probe is the most critical component of the AFM, and it consists of three parts: a sharp tip, a cantilever beam and a supporting base. The tip must be sharp enough to measure the surface topography with a high resolution. The cantilever beam must have the appropriate spring constant and resonant frequency for the type of operation selected. The supporting base must be of a suitable size for loading into the probe head. Therefore, depending on the various applications, the nano-probe structures used in the AFM should must meet the following criteria: (1) good tip sharpness with a small radius apex, (2) small spring constant and (3) high resonant frequency. This research will propose the design rule for three types of nano-probes, including the rectangular-shaped, V-shaped and chamfer V-shaped nano-probe for the AFM using the finite element method. The fundamental mechanical parameters of a nano-probe for an AFM are its spring constant, its resonant frequency and its physical dimensions. Research of the relevant literatures indicates that numerous researchers only consider the small deflection theory when analyzing the above-mentioned physical properties of the nano-probe. However, the small deflection theory is suitable only when the behavior of nonlinear geometry has not taken place in the structure. But, the applications of the nano-probe are increasing at a rapid rate, and the geometric dimensions or physical properties of nano-probe are changing from the traditional applications. The measuring of the red corpuscle requires a small size probe, but the ultra-high resolution topography is demanding an ever increasing applied force. The phenomenon of nonlinear geometry is occurring in the structure at present, and as a result the small deflection theory is no longer suitable for analyzing the nano-probe. This research introduces the large deflection theory in the finite element method (FEM) to investigate the geometrical size and the physical properties of the nano-probe.

Dynamic Buckling of a Thin Cylindrical Shell Under Axial Impact

1966 ◽  
Vol 33 (1) ◽  
pp. 105-112 ◽  
Author(s):  
H. E. Lindberg ◽  
R. E. Herbert
Keyword(s):  
High Speed ◽  
Large Deflection ◽  
Normal Modes ◽  
Thin Cylindrical Shell ◽  
Axial Impact ◽  
Initial Imperfections ◽  
Small Deflection ◽  
Deflection Theory ◽  
Circumferential Wave ◽  
Very High

Buckling of thin cylindrical shells from axial impact is studied under the assumption that initial imperfections can be approximated by “white noise.” Linear small-deflection theory is used to calculate the resulting growth of the normal modes, and a statistical analysis gives the expected values for the “preferred” axial and circumferential wave-lengths. Very high-speed photographs (240,000 frames/sec) of shells buckling under axial impact show excellent agreement with the theory and demonstrate that large-deflection buckling follows the pattern established by the early linear motion.

Displacements and Stresses of a Laterally Loaded Semicircular Plate With Clamped Edges

1959 ◽  
Vol 26 (2) ◽  
pp. 224-226
Author(s):  
W. H. Jurney
Keyword(s):  
Circular Plate ◽  
Normal Load ◽  
Constant Thickness ◽  
Small Deflection ◽  
Deflection Theory ◽  
Laterally Loaded ◽  
Superposition Of Solutions ◽  
Clamped Edges

Abstract A solution is obtained for the case of the clamped semicircular plate of constant thickness, subjected to a uniformly distributed normal load. The method employed is superposition of solutions for a circular plate with fixed edges. The technique involved could be extended to study more general types of loading of the clamped semicircular plate. Results are based on the assumption that the Kirchhoff, or small deflection, theory applies.

Analysis of Deeply Buried Flexible Pipes

2003 ◽  
Vol 1849 (1) ◽  
pp. 124-134 ◽  
Author(s):  
M. T. Suleiman ◽  
R. A. Lohnes ◽  
T. J. Wipf ◽  
F. W. Klaiber
Keyword(s):  
Large Deflection ◽  
Soil Cover ◽  
Constitutive Models ◽  
Pipe Material ◽  
Vertical Deflection ◽  
Finite Element Program ◽  
Pipe System ◽  
Small Deflection ◽  
Deflection Theory ◽  
Large Deflection Theory

CANDE is one of the most commonly used programs for analysis of buried pipe; however, CANDE is limited to applications with small deflections. This limitation is typically not problematic, but there are some instances in which analysts may be interested in large-deflection behavior. This limitation led to the consideration of other analysis tools. In this study ANSYS, a general finite element program, was used to model the soil-pipe system. Small- and large-deflection theories of ANSYS were used in the analysis of several case studies, and the results were compared with those of CANDE. Also, a code was written to run within ANSYS to include the following soil constitutive models: the hyperbolic tangent modulus with both power and hyperbolic bulk modulus. Results obtained using ANSYS with the modified soil models were in good agreement, with less than 10% difference, except in one case: CANDE results for 6.1 m of soil cover above the springline for 610-mm pipe diameter with SM and ML soils. Use of large-deflection theory resulted in an insignificant effect, less than 5%, when compared with ANSYS small-deflection theory results for soil heights up to 6.1 m above the springline, which proves that small-deflection theory is adequate for these cases. Comparing CANDE and ANSYS for 1,200-mm-diameter polythylene (PE) pipes with experimental results showed that ANSYS more accurately describes the PE pipe behavior for cases of 9 m of soil cover or more and that large-deflection theory describes the PE pipe behavior better than small-deflection theory for a vertical deflection of 4% or more. The pipe material effect was investigated by comparing the results of ANSYS small- and large-deflection theories for both PE and polyvinyl chloride pipes. The difference between the small- and large-deflection theories for both pipe materials becomes significant, more than 10%, at a vertical deflection of 4%.

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