Edge crack opening in an elastic plane with a wedge-like cut in contact with a punch

The equilibrium of an elastic plane with a wedge-like cut and an internal or edge crack on the symmetry axis was studied in [1] in the case of punch indentation in the lateral faces of the cut at a distance from the cut tip. In [1], the systemof singular integral equations of the problemwas solved numerically by the mechanical quadrature method. In this paper, the generalized Wiener-Hopf method [2] is used to obtain the analytic solution of a similar problem in the case of an edge crack under punch pressure on parts of the cut lateral faces adjacent to the cut tip. Some special cases of this problem were considered earlier without a crack [3, 4] or a punch [5, 6].     

STRESS-STRAIN STATE OF ELASTOPLASTIC BODIES WITH CRACK

A physical cut model is used to describe the changes in the stress-strain state(SSS)in elastoplastic bodies weakened by cracks. The distance between the crack edges is considered to be finite in contrast to the mathematical cut. The interactive layer with a thickness limited by the possibility of using the hypothesis of continuity is distinguished on the physical cut extension.Distribution of stresses and strains over the layer thickness is constant and does not depend on the geometry of the boundary between the cut and the interactive layer. The relationship between stresses and strains is determined by the deformation plasticity theory. The problem of plane strain or plane stress state of an arbitrary finite body weakened by a physical cut is reduced to solving a system of two variational equations for displacement fields in the body parts adjacent to the interactive layer. The proposed approach eliminates the singularity in stress distribution in contrast to the mathematical cut model. Use of local strength criteria allows us to determine the time, point and direction of the fracture initiation. Possibilities of the proposed model are illustrated by solving the problems of determining the SSS of a rectangular body weakened by a physical cut under symmetric and antisymmetric loadings.     

掏槽参数对煤矿岩巷爆破效果的影响

为了提高掘进进尺,以川煤集团绿水洞矿掘进工程为背景,利用动力有限元程序LS-DYNA3D进行掏槽参数优化研究。结合井下现场实验,分析岩巷掏槽爆破不同参数动态应力、破碎范围的变化以及井下实际爆破效果。掏槽中心孔底向孔口平均有效应力峰值在有中心眼爆破较无中心眼爆破时增加了40%以上,中心眼爆破对槽腔底部的形成起主要作用。在其他条件相同的情况下单孔载荷从1.2 kg提高到1.8 kg,掏槽区中心眼底到孔口平均应力只增加20%,并且破碎范围的增加较少,实际进尺增加小于10%。现场掘进实验表明:在常规爆破载荷下,有中心眼比无中心眼爆破深度提高31%~65%,掏槽角小于78°时,随掏槽角度增加爆破进尺下降较平缓; 但掏槽角增至82°左右, 随掏槽角度增加爆破进尺下降明显。     

A discontinuous Galerkin immersed boundary solver for compressible flows: Adaptive local time stepping for artificial viscosity–based shock-capturing on cut cells

We present a higher-order cut cell immersed boundary method (IBM) for the simulation of high Mach number flows. As a novelty on a cut cell grid, we evaluate an adaptive local time stepping (LTS) scheme in combination with an artificial viscosity–based shock-capturing approach. The cut cell grid is optimized by a nonintrusive cell agglomeration strategy in order to avoid problems with small or ill-shaped cut cells. Our approach is based on a discontinuous Galerkin discretization of the compressible Euler equations, where the immersed boundary is implicitly defined by the zero isocontour of a level set function. In flow configurations with high Mach numbers, a numerical shock-capturing mechanism is crucial in order to prevent unphysical oscillations of the polynomial approximation in the vicinity of shocks. We achieve this by means of a viscous smoothing where the artificial viscosity follows from a modal decay sensor that has been adapted to the IBM. The problem of the severe time step restriction caused by the additional second-order diffusive term and small nonagglomerated cut cells is addressed by using an adaptive LTS algorithm. The robustness, stability, and accuracy of our approach are verified for several common test cases. Moreover, the results show that our approach lowers the computational costs drastically, especially for unsteady IBM problems with complex geometries.     

Finding the elastic strain limit at the tip region of a physical cut with arbitrarily loaded faces

A model describing the stress-strain state in the neighborhood of a physical cut with an arbitrary distribution of external load along its faces is presented. The stress-strain state of a material layer bounded by the continuations of the cut faces is considered. The interaction between the layer and the external half-planes leads to a closed system of integrodifferential equations for the mean stress components in the layer, which splits into two equations for the mean normal stresses and an equation for the mean shear stress. Numerical solutions of the system for the cases of symmetric and antisymmetric loading of the faces by concentrated forces are given. Conditions for the transition of the tip region of the cut to the state of plasticity and fracture are considered.     

Calculation of compressible flows about complex moving geometries using a three‐dimensional Cartesian cut cell method

A three‐dimensional Cartesian cut cell method is described for modelling compressible flows around complex geometries, which may be either static or in relative motion. A background Cartesian mesh is generated and any solid bodies cut out of it. Accurate representation of the geometry is achieved by employing different types of cut cell. A modified finite volume solver is used to deal with boundaries that are moving with respect to the stationary background mesh. The current flow solver is an unsplit MUSCL–Hancock method of the Godunov type, which is implemented in conjunction with a cell‐merging technique to maintain numerical stability in the presence of arbitrarily small cut cells and to retain strict conservation at moving boundaries. The method is applied to some steady and unsteady compressible flows involving both static and moving bodies in three dimensions. Copyright © 2000 John Wiley & Sons, Ltd.     

Load-carrying capacity of thin-walled shells with local imperfections

The load-carrying capacity of axially compressed thin-walled shells of revolution with a circular cut is studied. The problem is solved by using the numerical version of an experimental-theoretical method. The numerical experiment is performed by using the finite-element software ANSYS/LS-DYNA 11.0. The size effect of a circular cut on the load-carrying capacity of a compressed cylindrical shell is investigated.     

Computation of two‐dimensional flows past ram‐air parachutes

Computational results for flow past a two‐dimensional model of a ram‐air parachute with leading edge cut are presented. Both laminar (Re=10⁴) and turbulent (Re=10⁶) flows are computed. A well‐proven stabilized finite element method (FEM), which has been applied to various flow problems earlier, is utilized to solve the incompressible Navier–Stokes equations in the primitive variables formulation. The Baldwin–Lomax model is employed for turbulence closure. Turbulent flow computations past a Clarck‐Y airfoil without a leading edge cut, for α=7.5°, result in an attached flow. The leading edge cut causes the flow to become unsteady and leads to a significant loss in lift and an increase in drag. The flow inside the parafoil cell remains almost stagnant, resulting in a high value of pressure, which is responsible for giving the parafoil its shape. The value of the lift‐to‐drag ratio obtained with the present computations is in good agreement with those reported in the literature. The effect of the size and location of the leading edge cut is studied. It is found that the flow on the upper surface of the parafoil is fairly insensitive to the configuration of the cut. However, the flow quality on the lower surface improves as the leading edge cut becomes smaller. The lift‐to‐drag ratio for various configurations of the leading edge cut varies between 3.4 and 5.8. It is observed that even though the time histories of the aerodynamic coefficients from the laminar and turbulent flow computations are quite different, their time‐averaged values are quite similar. Copyright © 2001 John Wiley & Sons, Ltd.     

Solution of the problem of optimal cut in an elastic beam

The Kirchhoff model of an elastic beam with a transverse cut is considered. The nonpenetration condition proposed by A. M. Khludnev is formulated at the edges of the cut. The equilibrium model of a beam with a restriction on the cut is written in the form of a variational inequality. An analytical solution is obtained with the use of the projection operator. The problem of choosing optimal cuts is formulated for the criterion of minimum opening. Conditions for determining the extremum shapes of the beam are obtained and an example of the solution of the problem is given. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 5, pp. 149–157, September–October, 1999.     

Integrodifferential equations for plane filtration in the presence of cracks

A system of singular integr Differential equations is derived for the plane problem of steady-state filtration in a plate cut by a system of cracks. We consider an arbitrary set of cracks, and also monoperiodic and biperiodic systems of cracks, in an infinite plane. In the case of a system of infinite parallel rectilinear cracks, the general solution is obtained in explicit form-in quadratures. As an example, we find the complex potential and the formula for the output from a borehole for a linear system of tiered, flooded plates, cut by a system of rectilinear parallel cracks.     

A finite volume‐based high‐order,Cartesian cut‐cell method for wave propagation

Computational aeroacoustics requires numerical techniques capable of yielding low artificial dispersion and dissipation to preserve the amplitude and the frequency characteristics of the physical processes. Furthermore, for engineering applications, the techniques need to handle irregular geometries associated with realistic configurations. We address these issues by developing an optimized prefactored compact finite volume (OPC‐fv) scheme along with a Cartesian cut‐cell technique. The OPC‐fv scheme seeks to minimize numerical dispersion and dissipation while satisfying the conservation laws. The cut‐cell approach treats irregularly shaped boundaries using divide‐and‐merge procedures for the Cartesian cells while maintaining a desirable level of accuracy. We assess these techniques using several canonical test problems, involving different levels of physical and geometric complexities. Richardson extrapolation is an effective tool for evaluating solutions of no high gradients or discontinuities, and is used to evaluate the performance of the solution technique. It is demonstrated that while the cut‐cell method has a modest effect on the order of accuracy, it is a robust method. The combined OPC‐fv scheme and the Cartesian cut‐cell technique offer good accuracy as well as geometric flexibility. Copyright © 2008 John Wiley & Sons, Ltd.     

Spatially resolved observations of strain fields at necking and fracture of anisotropic hardened steel sheet material

In this work plastic strain localization, also referred to as necking, of press-hardened ultra-high strength steel is observed using digital speckle correlation. The region of the neck is studied during tensile tests of specimens specially designed to facilitate strain localization at an inner point of the material, thus avoiding edge effects on localization and fracture. By using measurements with a length scale small enough to properly resolve the neck, its growth and shape can be studied. Furthermore, the anisotropy of the material is investigated by examining specimens cut out at different angles to the rolling direction. It is seen that the local fracture strain of specimens cut out along the rolling direction is approximately twice as high as it is for specimens cut out perpendicular to the rolling direction.     

Lifting aerofoil calculation using the boundary element method

The bbundary integral formulation and boundary element method are extended to include lifting flow problems. This involves inclusion of a branch cut in the flow field and imposition of a Kutta condition to determine the circulation, Γ Additional boundary integral contributions arise from the cut surface. Techniques for calculating Γ are developed and we treat, in particular, a superposition procedure which permits very efficient computation. Numerical results are presented for an NACA0012 aerofoil at several angles of attack.     

龙滩水电站航道座滑边坡平面有限元模拟研究

基于弹塑性有限元（FEM）模型和Mohr-Cou lomb屈服准则,采用平面有限元法对龙滩水电站航道1+016¹+080开挖边坡座滑前的稳定状况进行了数值模拟研究。对座滑前边坡的应力场、位移场及塑性屈服区的模拟结果表明,边坡在座滑前存在明显的塑性区,处于临界稳定状态;开挖过程中边坡存在连续变形,特别是开挖下部时变形会突然增大;座滑前边坡塑性区支护体系已达到承载极限,边坡具备了座滑的条件。     

Flexural Vibrations of a Piezoelectric Bimorph with a Cut Internal Electrode

Stationary vibrations of a bimorph plate composed of two piezoelectric layers of equal thickness are studied. There is an infinitely thin cut electrode between the layers. A model of flexural vibrations of the bimorph that is based on the variational equation generalizing the Hamilton principle in electroelasticity is proposed. For the plane problem, a system of equations of motion is derived and the boundary conditions and the conjugate conditions at the interface of the regions of the cut electrode are formulated. For the TsTS–19 piezoceramics, resonance and antiresonance frequencies are calculated. The values obtained are compared with the calculation results obtained with the use of the Kirchhoff model and the finite–element method. It is shown that the use of a plate with a cut electrode allows one to increase the efficiency of vibration excitation compared to the case of a continuous internal electrode.     

Shallow flow simulation on dynamically adaptive cut cell quadtree grids

A computationally efficient, high‐resolution numerical model of shallow flow hydrodynamics is described, based on dynamically adaptive quadtree grids. The numerical model solves the two‐dimensional non‐linear shallow water equations by means of an explicit second‐order MUSCL‐Hancock Godunov‐type finite volume scheme. Interface fluxes are evaluated using an HLLC approximate Riemann solver. Cartesian cut cells are used to improve the fit to curved boundaries. A ghost‐cell immersed boundary method is used to update flow information in the smallest cut cells and overcome the time step restriction that would otherwise apply. The numerical model is validated through simulations of reflection of a surge wave at a wall, a low Froude number potential flow past a circular cylinder, and the shock‐like interaction between a bore and a circular cylinder. The computational efficiency is shown to be greatly improved compared with solutions on a uniform structured grid implemented with cut cells. Copyright © 2006 John Wiley & Sons, Ltd.     

A mass‐conservative staggered immersed boundary model for solving the shallow water equations on complex geometries

In this work, an approach is proposed for solving the 3D shallow water equations with embedded boundaries that are not aligned with the underlying horizontal Cartesian grid. A hybrid cut‐cell/ghost‐cell method is used together with a direction‐splitting implicit solver: Ghost cells are used for the momentum equations in order to prescribe the correct boundary condition at the immersed boundary, while cut cells are used in the continuity equation in order to conserve mass. The resulting scheme is robust, does not suffer any time step limitation for small cut cells, and conserves fluid mass up to machine precision. Moreover, the solver displays a second‐order spatial accuracy, both globally and locally. Comparisons with analytical solutions and reference numerical solutions on curvilinear grids confirm the quality of the method. Copyright © 2015 John Wiley & Sons, Ltd.     

An old elasticity problem in a unilateral setting

A limiting case of the Michell problem involving an elastic wedge is the unbounded solid with a semi-infinite cut, the tip of which is subjected to a concentrated force. For the limiting case, the classical solution leads to overlapping of material whenever the component of the force along the axis of symmetry is directed away from the cut, and the problem must be solved anew using unilateral boundary conditions. The required mathematics is simple, and the subject is suitable for classroom discussion. Two examples are solved explicitly, and additional exercise problems are suggested.     

Wedge-shaped cut in three-dimensional elastic wedge

An asymptotic solution of the integro-differential equation of the problem of describing a low-angle wedge-shaped cut in a three-dimensional elastic wedge is found. On the basis of the solution, the asymptotic behavior of the contact pressures at the apex of the punch, which in horizontal projection forms one side of an elastic wedge that includes a low-angle wedge-shaped cut, is investigated. Scientific Research Institute for Mechanics and Applied Mathematics, Rostov University, Russia. Translated from Prikladnaya Mekhanika, Vol. 35, No. 3, pp. 27–32, March, 1999.     

Experimental study of the temperature field generated during orthogonal machining of an aluminum alloy

During the machining of metals, plastic deformation and friction lead to the generation of heat in the workpiece, which results in thermomechanically coupled deformation. Recently, several numerical models of this highly coupled process have been produced in response to increased interest in high speed machining. It is important to characterize the thermal field in the cutting zone in order to completely verify these models of high speed machining and to direct further advancement in this area. In this work, HgCdTe infrared detectors are used to experimentally measure the temperature distribution at the surface of a workpiece during orthogonal cutting. From these temperature measurements, the heat generated in the primary shear zone and the friction zone can be examined and characterized. A modified Hopkinson bar technique has been developed to perform orthogonal machining at speeds ranging from 10 to 100 m/s. In the present work, a cutting velocity of 15 m/s is employed in all the tests in order to demonstrate the capability of the apparatus and characterize thermal fields during low speed machining. Temperature fields are obtained during the orthogonal cutting of aluminum as a function of depth of cut. It is seen that depth of cut can vary both the maximum temperature as well as the distribution of the temperature field in the aluminum workpiece. the maximum temperature increased with depth of cut (238°C for 1.5 mm cut, 207°C for 1.0 mm cut and 138°C for 0.5 mm cut) and the temperature field extended further beneath the cut surface with decreasing depth of cut.