Fracture in Straight Pipes Under Large Deflection Conditions—Part I: Structural Deformations

1977 ◽  
Vol 99 (1) ◽  
pp. 122-127 ◽  
Author(s):  
A. F. Emery ◽  
W. J. Love ◽  
A. S. Kobayashi
Keyword(s):  
Large Deflection ◽  
Pressure Profile ◽  
Stress Fields ◽  
Large Deflections ◽  
Crack Shape ◽  
Dynamic Motion ◽  
Structural Deformations ◽  
Pressurized Cylinder ◽  
Plastic Stress

The dynamic motion of an axially oriented through crack in a pressurized cylinder was studied numerically. Both small and large deflection theories were used, with the results suggesting that large deflections may be important for elastic, but not for plastic stress fields. Computations were also made with pressures predicted by consideration of fluid outflow through the crack and indicate that the crack shape near the tip is independent of the pressure profile.

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.

scholarly journals A Seminalytical Approach to Large Deflections in Compliant Beams under Point Load

2009 ◽  
Vol 2009 ◽  
pp. 1-13 ◽  
Author(s):  
N. Tolou ◽  
J. L. Herder
Keyword(s):  
Cantilever Beam ◽  
Large Deflection ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Geometrical Nonlinearity ◽  
Adomian Decomposition Method ◽  
Analytical Form ◽  
Point Load ◽  
Large Deflections ◽  
Adomian Decomposition

The deflection of compliant mechanism (CM) which involves geometrical nonlinearity due to large deflection of members continues to be an interesting problem in mechanical systems. This paper deals with an analytical investigation of large deflections in compliant mechanisms. The main objective is to propose a convenient method of solution for the large deflection problem in CMs in order to overcome the difficulty and inaccuracy of conventional methods, as well as for the purpose of mathematical modeling and optimization. For simplicity, an element is considered which is a cantilever beam out of linear elastic material under vertical end point load. This can further be used as a building block in more complex compliant mechanisms. First, the governing equation has been obtained for the cantilever beam; subsequently, the Adomian decomposition method (ADM) has been utilized to obtain a semianalytical solution. The vertical and horizontal displacements of a cantilever beam can conveniently be obtained in an explicit analytical form. In addition, variations of the parameters that affect the characteristics of the deflection have been examined. The results reveal that the proposed procedure is very accurate, efficient, and convenient for cantilever beams, and can probably be applied to a large class of practical problems for the purpose of analysis and optimization.

The effect of complex crack shape on crack driving forces and crack tip stress fields: Experiment and FE analysis

2020 ◽  
Vol 185 ◽  
pp. 104135
Author(s):  
Seung-Jae Kim ◽  
Kyung-Dong Bae ◽  
Yun-Jae Kim ◽  
Ho-Wan Ryu ◽  
Jin-Weon Kim ◽  
...  
Keyword(s):  
Driving Forces ◽  
Crack Tip ◽  
Fe Analysis ◽  
Stress Fields ◽  
Crack Shape ◽  
Complex Crack ◽  
Crack Tip Stress

Large Deflections of Circular Plates of Variable Thickness

1982 ◽  
Vol 49 (1) ◽  
pp. 243-245 ◽  
Author(s):  
B. Banerjee
Keyword(s):  
Circular Plate ◽  
Variable Thickness ◽  
Large Deflection ◽  
Numerical Results ◽  
Large Deflections ◽  
Circular Plates ◽  
Uniform Load ◽  
Plate Of Variable Thickness ◽  
Plates Of Variable Thickness

The large deflection of a clamped circular plate of variable thickness under uniform load has been investigated using von Karman’s equations. Numerical results obtained for the deflections and stresses at the center of the plate have been given in tabular forms.

Large deflection analysis of clamped annular sector plates

1984 ◽  
Vol 19 (1) ◽  
pp. 1-8 ◽  
Author(s):  
R S Srinivasan ◽  
V Thiruvenkatachari
Keyword(s):  
Integral Equation ◽  
Parametric Study ◽  
Large Deflection ◽  
Large Deflections ◽  
Lateral Loads ◽  
Bending Stresses ◽  
Deflection Analysis ◽  
Annular Sector ◽  
Newton Raphson ◽  
Sector Angle

Thin annular sector plates undergoing large deflections due to lateral loads are considered in this paper. For such plates exact solutions are not available. A matrix method using integral equation of beams and the Newton Raphson procedure has been adopted for the analysis of clamped annular sector plates. Numerical values for the deflection, the membrane and the bending stresses at the interior of the plate, and the bending stresses at the edges of the plate are obtained. A parametric study has been carried out by varying the sector angle from 30 to 90 degrees in steps of 30 degrees, and the ratio of the inner and outer radii from 0 to 0.6 in steps of 0.2. The results are presented in non-dimensional graphical format.

Advancements in Machinery Management Using the Measurement of Rotor Torsional Response

1997 ◽  
Author(s):  
Alan S. Thomson
Keyword(s):  
Dynamic Stiffness ◽  
Management Tool ◽  
Large Deflections ◽  
Dynamic Motion ◽  
Torsional Response ◽  
Machine Failure ◽  
Shaft System ◽  
Lateral Forces ◽  
Torsional Excitation ◽  
Many Sources

Rotor torsional (angular, steady and dynamic) motion, in response to the interaction of torque and torsional/lateral cross coupled forces with torsional dynamic stiffness, exist in rotating and reciprocating machinery for many reasons. The dynamic torsional response however, is commonly not measured on a continual basis. In the torsional dynamic stiffness, damping parameters are generally several magnitudes weaker than their lateral counterpart. This yields the opportunity for torsional responses, especially when exciting a resonance, to produce relatively large deflections and corresponding stresses, sometimes large enough to cause machine failure. Due to their rigid coupling, long shaft system lengths (a series of shafts coupled together), and large polar moments of inertia, the turbomachinery used in the power generation industry are particularly sensitive to forced torsional excitation. The forcing can come from many sources, including lateral forces which cross couple into torsional forces. Recent research introduces new sources of cross coupled excitation and a method to indirectly measure their and other effects on the mechanical integrity of the mechanical system. A modified and a prototype technique for continuously measuring directly and indirectly the rotor torsional response, and using it to evaluate rotor torsional dynamic stiffness as a machinery management tool is discussed in this paper.

Large deflection of plates and beams obeying non-linear stress—strain laws

1974 ◽  
Vol 9 (3) ◽  
pp. 178-184 ◽  
Author(s):  
K R Rushton ◽  
P M Hook
Keyword(s):  
Finite Difference ◽  
Large Deflection ◽  
Experimental Results ◽  
Large Deflections ◽  
Rectangular Plates ◽  
Dynamic Relaxation ◽  
Stress Strain ◽  
Finite Difference Technique ◽  
Non Linear ◽  
Alternative Solutions

The large deflections of rectangular plates and beams obeying a non-linear stress-strain law are examined. Solutions are obtained by use of dynamic relaxation, a numerical finite-difference technique. Comparisons are made with alternative solutions and experimental results. The effects of varying parameters in the non-linear expressions are considered.

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.

Large Deflection 3DOF Piezoelectric Microrobotic Manipulator With Positional Sensing and Self-Calibration

2012 ◽  
Author(s):  
Xing Jin ◽  
Jason V. Clark
Keyword(s):  
Dynamic Response ◽  
Frequency Response ◽  
Range Of Motion ◽  
Data Storage ◽  
Scanning Probe Microscopy ◽  
Large Deflection ◽  
Scanning Probe ◽  
Large Deflections ◽  
Self Calibration ◽  
Aqueous Environments

In this paper, we propose a large deflection piezoelectric microrobotic manipulator with the ability to self-calibrate displacement and sense its position. Such a manipulator should be applicable to scanning probe microscopy, nanolithography, data storage, biological probing in murky aqueous environments, and the like. Previous devices for such applications are limited in dexterity, range of motion, frequency response, positional calibration, or require environmental cleanliness. Our device has a three novel attributes, which are: an ability to achieve large deflections with greater than one degree of freedom (DOF); an ability to self-calibrate it displacement; and an ability to sense its position after actuation or prescribed displacement. Through simulation we demonstrate independent 3 DOF motional control (validated experimentally), positional sensing and self-calibration, and dynamic response.

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