A 2d hypersingular timedomain traction bem for transient. Mode iii stress intensity factors for edge cracked circular shafts, bonded wedges, bonded half planes and dcbs. It is found that the deformation fields near the notch tip are modeii dominant. Aoki s, kishimoto k 1978 elastodynamic analysis of crack by finite. Antiplane elastodynamic analysis of cracked graded orthotropic layers with viscous damping. Numerical simulation of loading edge cracks by edge impact using the extended. Elastodynamic analysis for slow tectonic loading with spontaneous rupture episodes on faults with rate and statedependent friction the harvard community has made this article openly available. Analysis of elastodynamic deforn1ations near a cracknotch tip by the mlpg method 719 parameters ci and k control its shape. Different variational formulations of unilateral contact problems with friction based on boundary variational principle are considered. Wavefront fields in the scattering of elastic waves by. The mode mixity parameter can be changed in an orthotropic plate by adjusting the ratio of the youngs moduli in the axial and the transverse direction.
In this work a fast solver for largescale threedimensional elastodynamic crack problems is presented, implemented, and tested. This article derives the elastodynamic image forces experienced by both straight screw and edge dislocations, moving and quiescent, in the presence of a planar free surface. However, having the solutions to the corresponding direct problems is a prerequisite to the inverse problems. Elastodynamic fracture analysis of multiple cracks by. Contact mechanics and wear of railwheel systems, ed. Thus, a crankrodslider mechanism its considered for this elastodynamic analysis which is performed in two stages, respectively the modal analysis where the natural frequencies are established and eigen vibrations forms computation, which suppose to. Interfacial cracking in a graded coatingsubstrate system. Solution of the 3d elastodynamic contact problem for body with. In each case the plate edges parallel to the crack are loaded in a. It is a simplification of the more general nonlinear theory of elasticity and a branch of continuum mechanics the fundamental linearizing assumptions of linear elasticity are. Based on the finite element software abaqus and graded element method, we developed a dummy node fracture element, wrote the user subroutines umat and uel, and solved the energy release rate component of functionally graded material fgm plates with cracks. Antiplane harmonic elastodynamic stress analysis of an infinite wedge with a circular cavity gang liu. Abstract an accurate hybrid displacement elastodynamic finite element.
Linear elasticity is a mathematical model of how solid objects deform and become internally stressed due to prescribed loading conditions. The dual boundary element method in the laplace transform domain is used for the accurate dynamic analysis of cracked bodies. The effect of geometric configurations on the elastic. The simplest configuration is the twodimensonal normal edgecrack in an elastic half plane. Graduate thesis or dissertation elastodynamic analysis. The corresponding quasistatic problem is also examined and it is. A numerical solution procedure is developed for solving the. A threedimensional analysis of a half plane crack in a transversely isotropic solid is performed. Perturbation analysis of eulerbernoulil beam vibration using a nonlinear spring for damage representation, journal of the mechanics.
The magnetoelastic analysis of a soft ferromagnetic strip with a singleedge crack was also performed. An orthotropic fgm layer with an edge or embedded crack perpendicular to the boundary under impact. Several methodologies of analysis have been developed in the research field of geometric continuum mechanics 14, 15, limit analysis 1619, homogenization 20, elastodynamics 2125, thermal problems 2628, random composites 2932, and nonlocal and gradient formulations 3338. Timedomain traction boundary integral equations bies are applied for this purpose, to both crackfaces and external boundaries of the cracked solid. Elastodynamic analysis of crack emanating from the vertex. Pretschner, md a main goal of surgical simulators is the creation of virtual training environments for prospective surgeons. This paper studies the effect of magnetic fields on the fracture toughness in nickel iron soft ferromagnetic materials. Elastodynamic analysis of a mechanism with flexible links. The method is based on the observation that the particle velocity is selfsimilar. Kasaeian elastodynamic analysis of a functionally graded halfplane with multiple subsurface crack acta mechanica solida sinica issue 1 2012 pp.
R2 is a bounded domain with boundary we consider the following twodimensional elastodynamic problem. In addition, the range of variation of sif at crack tip l 2 in orthotropic layer is higher than that in isotropic one. The index of stress singularity is ascertained from a plot of log stress vs. Louca 1 sep 20 engineering fracture mechanics, vol. Analysis of elastodynamic deformations near a cracknotch. Solution for the stress intensity factor history around the punch corner and crack tip is found. Singh, fatigue crack growth analysis of a homogeneous plate in the presence of multiple defects using extended isogeometric analysis, journal of the brazilian society of mechanical sciences and engineering, 10. The primary objective of this book is to give the reader a basic understanding of waves and their propagation in a linear elastic continuum. Keer, 1980 solid contact and lubrication, american society of mechanical engineers special publication.
A twodimensional 2d hypersingular timedomain traction bem for transient elastodynamic crack analysis is presented in this paper. Interface cracks often initiate around the bonding freeedge corner due to the highstress concentration. The cracked half plane is subjected to a class of timeharmonic line. Tensile tests were conducted on singleedge cracked plate specimens in the bore of a superconducting magnet at room temperature, and the critical load was determined. We eated the time evolution of the stressmtenslty factor m a employ a higherorder plate theory in which both trans double edge cracked plate.
Elastodynamic analysis of an edge crack introduction among the crack configurations that are usually considered in fracture mechanics, the surfacebreaking crack is of distinct practical. Fracture initiation due to asymmetric impact loading of an. The j integral for a path outside the dissipative region is an obvious alternative, because it is uniquely determinable from the stress intensity factor through the relation 3. For the time being, the idealized crack is assumed to have no thickness, that is, in the absence of applied loads the two faces of the crack coincide with the same surface in space. Consider a body of nominally elastic material that contains a crack. Antiplane harmonic elastodynamic stress analysis of an. Quantitative modeling of coupled piezoelastodynamic. Nonsmooth optimization algorithms of udzawas type for solution of. Elastodynamic analysis of the finite punch and finite. Elastodynamic analysis of a cracked orthotropic halfplane applied mathematical modelling issue 2350 2012 pp. Department ofmathematics and systems analysis,aaltouniversity,espoo, fi00076, finland jeonghun. The analysis developed in preceding section, allows the consideration of an orthotropic halfplane with multiple curved cracks subjected to timeharmonic concentrated applied load traction. Other examples are the shear strain at a given distance ahead of the crack edge and the crack edge sliding displacement just behind the crack edge.
A tool for defining the deformation behavior of virtual tissues1 arne radetzky, dipl. Solution of linear elastostatic and elastodynamic plane. The wave equation in elastodynamic wave propagation in a nonhomogeneous anisotropic elastic medium occupying a bounded domain. The crack is subjected to a pair of suddenlyapplied normal line loadings on its faces. Analysis of an isotropic finite wedge under antiplane deformation. Transform methods are used to reduce the boundary value problem to a single integral equation that can be solved by the wienerhopf technique. Boundary element method bem along with constrained optimization algorithm which is based on variational principles and nonsmooth analysis. For a broad class of static loads the stressintensity factor for the. To simulate the asymmetric impact of a projectile on the cracked edge of the plate, a normal velocity is suddenly imposed. Request pdf elastodynamic analysis of a plane weakened by several cracks the stress fields in an infinite plane containing volterra type climb and glide edge dislocations under timeharmonic. Time domain boundary element method for dynamic stress. Beskos an improved implementation of time domain elastodynamic biem in 3d for large scale problems and its application to ultrasonic nde. An interface element tailored for the virtual crack closure technique vcct was applied.
Antiplane elastodynamic analysis of cracked graded. Seyed mahmoud mousavi, shahriar fariborz, antiplane elastodynamic analysis of cracked graded orthotropiclayers with viscous damping, applied mathematical modelling, vol. The transient elastodynamic response of the finite punch and finite crack problems in orthotropic materials is examined. Pdf antiplane elastodynamic analysis of cracked graded. This paper applies the theory for magnetoelasticity to solve the plane problem of an edge crack in a soft ferromagnetic halfplane subjected to a farfield tension and a uniform magnetic field.
The code can be used to provide useful information about the mode i fracture behavior of bodies under a combination of mechanical, thermal, and pressure loadings for materials that permit a linearelastic fracture mechanics assumption. An investigation of the elastodynamic fields for the edgecrack configuration is presented, considering only elastodynamic stressintensity factors generated by surface motion. The studies of elastodynamic theory and its application to fundamental value problems should prepare the reader to tackle many physical problems of general interest in engineering and geophysics, and of particular interest in mechanics and seismology. We set k 1, ci load vector f are given by distance to the third nearest neighboring node from the node xi with nodes equidistant from xi counted once, and mij fa p cracked body using the extended finite element method m. Elastodynamic analysis of an edge crack northwestern. Elastodynamic analysis of a plane weakened by several cracks. Sih, 9789028601567, available at book depository with free delivery worldwide. As the distance between r 1 and l 2 reduces k iii l 2 increases, at a h. Elastodynamic analysis for slow tectonic loading with. Mathematical statement of elastodynamic contact problem for cracked body with considering unilateral restrictions and friction of the crack faces is done in classical and weak forms. The boundary element method and pathindependent integrals in sensitivity analysis of structures with stress concentration. Chensingular enrichment finite element method for elastodynamic crack.
The full text of this article hosted at is unavailable due to technical difficulties. To simulate the asymmetric impact of a projectile on the cracked edge of the plate, a normal velocity is suddenly imposed on the boundary of the plate on one side of the edge crack. The stress intensity factor is calculated and is shown graphically. In a numerical analysis of dynamic fracture problems perfom1ed by chen. Laplace and fourier transforms together with the wienerhopf technique are employed to solve the equations of motion in terms of displacements. Search algorithm, and simulation of elastodynamic crack. Elastodynamic analysis of a cracked orthotropic halfplane. In what follows install examples, the ratios of the moduli of elasticity of the orthotropic plane are taken as f 0. The twodimensional elastodynamic problem of a semiinfinite plate containing an edge crack is considered. It has been observed that if a steel plate containing an edge crack is struck by a projectile on.
Derivation of element stiffness matrices by assumed stress. Antiplane elastodynamic analysis of a cracked orthotropic strip. Little, prenticehall 1973 in journal of applied mechanics, 41, 1974, p. Journal of applied mechanics, transactions asme, 47. Elastodynamic analysis of an edge crack journal of. A closed form solution is obtained giving the shear stress and particle velocity in the vicinity of the moving crack tip. Achenbach department of civil engineering, the technological institute, northwestern university, evanston, ill. Mokashi, nonlinear vibration of an edge cracked beam with a cohesive zone ii. The laplace finite element alternating method, which combines the laplace transform technique and the finite element alternating method, is developed to deal with the elastodynamic analysis of a finite plate with multiple cracks. Nonsmooth optimization algorithms in some problems of. Numerical simulation of loading edge cracks by edge impact using.
The numerical example of a rectangular plate with an edge crack is solved and. Free and forced vibrations of thick rectangular plates. Analysis of dynamic fracture parameters in functionally. Analysis of elastodynamic deformations near a cracknotch tip by. Fourier transform techniques are used to formulate the mixed boundary value problem as a singular integral equation. Elastodynamics article about elastodynamics by the free.
Description of program or function samcr is a twodimensional, elastodynamic, finite element code for the stress analysis of moving cracks. In the present paper we investigate elastodynamic fields for the edgecrack configuration. The method of homogeneous solutions is applied to the problem of elastodynamic crack propagation from the vertex of a wedge. The cracked half plane is subjected to a class of timeharmonic line loads which are applied to its free surface. The transient finite element analysis of cracked plates.