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.

Application of large-deflection theory to normally loaded rectangular plates with clamped edges

1970 ◽  
Vol 5 (2) ◽  
pp. 140-144 ◽  
Author(s):  
A Scholes
Keyword(s):  
Large Deflection ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Aspect Ratios ◽  
Non Linear ◽  
Deflection Theory ◽  
Large Deflection Theory ◽  
Clamped Edges ◽  
Clamped Edge ◽  
Good Agreement

A previous paper (1)∗described an analysis for plates that made use of non-linear large-deflection theory. The results of the analysis were compared with measurements of deflections and stresses in simply supported rectangular plates. In this paper the analysis has been used to calculate the stresses and deflections for clamped-edge plates and these have been compared with measurements made on plates of various aspect ratios. Good agreement has been obtained for the maximum values of these stresses and deflections. These maximum values have been plotted in such a form as to be easily usable by the designer of pressure-loaded clamped-edge rectangular plates.

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.

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.

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%.

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.

On the Occurrence of Simultaneous Resonances in Parametrically-Excited Rectangular Plates

1993 ◽  
Vol 115 (3) ◽  
pp. 344-352 ◽  
Author(s):  
G. L. Ostiguy ◽  
L. P. Samson ◽  
H. Nguyen
Keyword(s):  
Large Deflection ◽  
Rectangular Plates ◽  
Temporal Response ◽  
Governing Equations ◽  
Parametrically Excited ◽  
Damped System ◽  
Simultaneous Resonances ◽  
Deflection Theory ◽  
New Phenomena ◽  
Large Deflection Theory

The present work deals primarily with the problem of the occurrence of simultaneous resonances in parametrically-excited rectangular plates. The analysis is based on the dynamic analog of the von Karman’s large-deflection theory and the governing equations are satisfied using the orthogonality properties of the assumed functions. The temporal response of the damped system is determined by the generalized asymptotic method and various types of simultaneous resonances are investigated. An experimental investigation is performed to verify the analytical predictions and to possibly discover new phenomena not predicted by the theory. Experiments are conducted for four different sets of boundary conditions. Analytically defined simultaneous resonances are experimentally observed and isolated.

Dynamic Model of Mechanisms With Highly Compliant Members

2005 ◽  
Author(s):  
Chao-Chieh Lan ◽  
Kok-Meng Lee
Keyword(s):  
Dynamic Model ◽  
Large Deflection ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Wide Spectrum ◽  
Geometrical Nonlinearity ◽  
Geometric Constraints ◽  
Axial Deformation ◽  
Small Deflection ◽  
Deflection Theory

The dynamic model for links in most mechanisms has often based on small deflection theory without considering geometrical nonlinearity. For applications like light-weight links or high-precision elements, it is necessary to capture the large deflection caused by bending forces. A complete dynamic model is presented here to characterize the motion of a compliant mechanism capable of large deflection with shear and axial deformation. We derive the governing equations from Hamilton’s principle along with the essential geometric constraints that relate deformation and coordinate variables, and solve them using a semi-discrete method based on the Newmark scheme and shooting method. The dynamic model has been validated experimentally. We also extend the model for analyzing compliant mechanisms. It is expected that the dynamic model will serve as a basis for analyzing a wide spectrum of compliant multi-link mechanisms.

Stresses in Largely Deflected Cantilever Beams Subjected to Gravity

1969 ◽  
Vol 36 (2) ◽  
pp. 323-325 ◽  
Author(s):  
Han-Chow Lee ◽  
A. J. Durelli ◽  
V. J. Parks
Keyword(s):  
Large Deflection ◽  
Beam Theory ◽  
Cantilever Beams ◽  
Small Deflection ◽  
Deflection Theory ◽  
Large Deflection Theory

Stresses and displacements in largely deflected cantilever beams subjected to gravity were analyzed by means of photoelasticity. The results obtained for stresses and moments are normalized and presented parametrically for increasing amounts of deflection. For comparison purposes the results obtained using elementary beam theory (small deflection) and large deflection theory are also included.

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