Plane Deformation of the Loaded Straight Edge of a Semi-Infinite Linearly Elastic Body Suspended on a Winkler Layer

1970 ◽  
Vol 37 (2) ◽  
pp. 524-526 ◽  
Author(s):  
M. F. Kanninen
Keyword(s):  
Crack Propagation ◽  
Elastic Body ◽  
Elastic Foundation ◽  
Finite Interval ◽  
Plane Deformation ◽  
Fourier Method ◽  
Elastic Solid ◽  
Cleavage Crack ◽  
Uniform Load ◽  
Concentrated Force

A solution for an edge loaded, semi-infinite elastic solid on an elastic foundation is presented. This solution, arising in the development of a nonlinear atomic model for cleavage crack propagation, was obtained by the Fourier method. Example results are given for a uniform load on a finite interval and for a concentrated force, Fig. 1, in terms of the sine and cosine integral functions and their auxiliary forms.

scholarly journals Dynamic crack propagation in a 2D elastic body. The out-of plane case

PAMM ◽  
2007 ◽  
Vol 7 (1) ◽  
pp. 1090801-1090802
Author(s):  
A.-M. Sändig ◽  
A. Lalegname ◽  
S. Nicaise
Keyword(s):  
Crack Propagation ◽  
Elastic Body ◽  
Dynamic Crack Propagation ◽  
Dynamic Crack ◽  
Plane Case ◽  
Out Of Plane

Dispersive properties of a fluid layer overlying a semi-infinite elastic solid*

1954 ◽  
Vol 44 (3) ◽  
pp. 493-512
Author(s):  
Ivan Tolstoy
Keyword(s):  
Elastic Body ◽  
Group Velocity ◽  
Normal Mode ◽  
Fundamental Mode ◽  
Fluid Layer ◽  
Elastic Solid ◽  
Numerical Results ◽  
Stoneley Wave ◽  
Wave Velocities ◽  
Minimum Group

Abstract The dispersive properties of waves propagating in a system consisting of a fluid layer overlying a semi-infinite elastic body are investigated by means of new formulas for the group velocity. The distribution of stationary values of the group velocity is examined in the light of these formulas and of numerical results. Also it is shown that the minimum group velocity of the fundamental mode may belong either to the normal-mode branch or to the Stoneley-wave branch, depending on the contrast in wave velocities between the two media.

Effect of the Gravity Force on the Propagation of a Rotating Flexible Rod After Impact

1997 ◽  
Author(s):  
Wei-Hsin Gau
Keyword(s):  
Elastic Waves ◽  
Virtual Work ◽  
Impact Load ◽  
Equations Of Motion ◽  
Fourier Method ◽  
Gravity Force ◽  
Principle Of Virtual Work ◽  
Shape Functions ◽  
Concentrated Force ◽  
The Impact

Abstract The aim of this paper is to analyze the effect of the gravity force on the impact-induced elastic waves which propagate on a radially rotating rod. The equations of motion of the system are developed using the principle of virtual work in dynamics. The impact load is included by the use of the generalized impulse momentum equations, involving the coefficient of restitution. The system is solved using the Fourier method. The deformation of the rod is supposed to be at any instant a linear combination of a set of shape functions. These shape functions are, in this investigation, the modes of a cantilever beam. The weight of the rod is modeled as a concentrated force applied at any instant at the center of the rod.

scholarly journals Three Dimensional Simulation of Polycrystalline Cleavage Crack Propagation in Steel

2009 ◽  
Vol 95 (6) ◽  
pp. 498-505 ◽  
Author(s):  
Kei Sugimoto ◽  
Shuji Aihara ◽  
Yoichi Tanaka
Keyword(s):  
Crack Propagation ◽  
Three Dimensional ◽  
Cleavage Crack ◽  
Dimensional Simulation

Study of Shear Deformation's Influence on Deflection of Continuous Composite Box-Girder Bridge with Corrugated Steel Webs

2013 ◽  
Vol 275-277 ◽  
pp. 961-965
Author(s):  
Ming Min Tang ◽  
Li Chao Su ◽  
Shui Wan
Keyword(s):  
Shear Deformation ◽  
Water Diversion ◽  
Uniform Load ◽  
Box Girders ◽  
Concentrated Force ◽  
Element Analysis ◽  
Box Girder ◽  
North Water ◽  
Box Girder Bridge ◽  
Girder Bridge

Taking South-to-North Water Diversion Bridge, a continuous composite box-girder bridge with corrugated steel webs, as the engineering background, the cantilever beam end’s deflection calculation formulae considering shear deformation were deduced by using energy method. Comparing with finite-element analysis (FEA) values and measured values, the formulae which considered both concentrated force and uniform load have enough accuracy. Results show that, shear deformation’s proportion is more obvious in overall deflection of such box-girders which have smaller span ratio, and it’s more than 30%. For continuous composite box-girder bridge with corrugated steel webs, contribution of shear deformation to overall deflection should not be ignored.

scholarly journals Research on Biomimetic Models and Nanomechanical Behaviour of Membranous Wings of Chinese Bee Apis cerana cerana Fabricius

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Yanru Zhao ◽  
Dongsheng Wang ◽  
Jin Tong ◽  
Jiyu Sun ◽  
Jin Zhang
Keyword(s):  
Finite Element ◽  
Apis Cerana ◽  
Element Model ◽  
Apis Cerana Cerana ◽  
Technical Innovation ◽  
Uniform Load ◽  
Load Bearing Capacity ◽  
Concentrated Force ◽  
Stress States ◽  
The Finite Element Model

The structures combining the veins and membranes of membranous wings of the Chinese bee Apis cerana cerana Fabricius into a whole have excellent load-resisting capacity. The membranous wings of Chinese bees were taken as research objects and the mechanical properties of a biomimetic model of membranous wings as targets. In order to understand and learn from the biosystem and then make technical innovation, the membranous wings of Chinese bees were simulated and analysed with reverse engineering and finite element method. The deformations and stress states of the finite element model of membranous wings were researched under the concentrated force, uniform load, and torque. It was found that the whole model deforms evenly and there are no unusual deformations arising. The displacements and deformations are small and transform uniformly. It was indicated that the veins and membranes combine well into a whole to transmit loads effectively, which illustrates the membranous wings of Chinese bees having excellent integral mechanical behaviour and structure stiffness. The realization of structure models of the membranous wings of Chinese bees and analysis of the relativity of structures and performances or functions will provide an inspiration for designing biomimetic thin-film materials with superior load-bearing capacity.

Acoustic Emission From a Brief Crack Propagation Event

1979 ◽  
Vol 46 (1) ◽  
pp. 107-112 ◽  
Author(s):  
J. D. Achenbach ◽  
J. G. Harris
Keyword(s):  
Acoustic Emission ◽  
Brittle Fracture ◽  
Crack Propagation ◽  
Acoustic Emissions ◽  
Elastic Solid ◽  
Propagation Speed ◽  
Crack Edge ◽  
Arbitrary Distribution ◽  
Canonical Solution ◽  
Phase Functions

Acoustic emissions produced by elementary processes of deformation and fracture at a crack edge are investigated on the basis of elastodynamic ray theory. To obtain a two-dimensional canonical solution we analyze wavefront motions generated by an arbitrary distribution of climbing edge dislocations emanating from the tip of a semi-infinite crack in an unbounded linearly elastic solid. These wavefront results are expressed in terms of emission coefficients which govern the variation with angle, and phase functions which govern the intensity of the wavefront signals. Explicit expressions for the emission coefficients are presented. The coefficients have been plotted versus the angle of observation, for various values of the crack propagation speed. The phase functions are in the form of integrals over the emanating dislocation distributions. Specific dislocation distributions correspond to brittle fracture and plastic yielding at the crack tip, respectively. Acoustic emission is most intense for brittle fracture, when the particle velocities experience wavefront jumps which are proportional to the stress-intensity factors prior to fracture. An appropriate adjustment of the canonical solution accounts for curvature of a crack edge. Such effects as focussing, finite duration of the propagation event, and finite dimensions of the crack are briefly discussed. As a specific example, the first signals generated by brittle Mode I propagation of an elliptical crack are calculated.

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