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.

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.

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 Mixed-Body Model: A Method for Predicting Large Deflections in Stepped Cantilever Beams

2021 ◽  
pp. 1-18
Author(s):  
Brandon Sargent ◽  
Collin Ynchausti ◽  
Todd G Nelson ◽  
Larry L Howell
Keyword(s):  
Large Deflections ◽  
Cantilever Beams ◽  
Element Analysis ◽  
Body Model ◽  
Minimal Error ◽  
Small Deflection ◽  
Rigid Body Model ◽  
Expected Values ◽  
Deflection Theory ◽  
Sample Set

Abstract This paper presents a method for predicting endpoint coordinates, stress, and force to deflect stepped cantilever beams under large deflections. This method, the Mixed-Body Model or MBM, combines small deflection theory and the Pseudo-Rigid-Body Model for large deflections. To analyze the efficacy of the model, the MBM is compared to a model that assumes the first step in the beam to be rigid, to finite element analysis, and to the numerical boundary value solution over a large sample set of loading conditions, geometries, and material properties. The model was also compared to physical prototypes. In all cases, the MBM agrees well with expected values. Optimization of the MBM parameters yielded increased agreement, leading to average errors of <0.01 to 3%. The model provides a simple, quick solution with minimal error that can be particularly helpful in design.

Benchmark of Plate Forming and Weld Distortion Process

2005 ◽  
Vol 128 (3) ◽  
pp. 414-419
Author(s):  
James Gombas
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Cylindrical Shell ◽  
Large Deflection ◽  
Element Analysis ◽  
Manufacturing Simulation ◽  
Simulation Process ◽  
Weld Distortion ◽  
Deflection Theory ◽  
Large Deflection Theory

A circular flat plate with a perforated central region is to be formed by dies into a dome and then welded onto a cylindrical shell. After welding, the dome must be spherical within a narrow tolerance band. This plate forming and welding is simulated using large deflection theory elastic-plastic finite element analysis. The manufacturing assessment is performed so that the dies may be designed to compensate for plate distortions that occur during various stages of manufacturing, including the effects of weld distortion. The manufacturing simulation benchmarks against measurements taken at several manufacturing stages from existing hardware. The manufacturing simulation process can then be used for future applications of similar geometries.

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.

Large Deflections and Buckling Loads of Cantilever Columns with Constant Volume

2017 ◽  
Vol 17 (08) ◽  
pp. 1750091 ◽  
Author(s):  
Joon Kyu Lee ◽  
Byoung Koo Lee
Keyword(s):  
Differential Equations ◽  
Cross Section ◽  
Large Deflection ◽  
Nonlinear Differential Equations ◽  
Constant Volume ◽  
Large Deflections ◽  
Buckling Loads ◽  
Geometrical Nonlinear ◽  
Deflection Theory ◽  
Large Deflection Theory

This paper deals with the large deflections and buckling loads of tapered cantilever columns with a constant volume. The column member has a solid regular polygonal cross-section. The depth of this cross-section is functionally varied along the column axis. Geometrical nonlinear differential equations, which govern the buckled shape of the column, are derived using the large deflection theory, considering the effect of shear deformation. The buckling load of the column is approximately equivalent to the load under which a very small tip deflection occurs. In regard to the numerical results, both the elastica and buckling loads with varying column parameters are discussed. The configurations of the strongest column are also presented.

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