Accurate modelling of rigid and soft inclusions in 2D elastic solids by the boundary element method

In this work, a particular sub-region technique that does not require traction approximations along interfaces is used to model rigid and soft inclusions. The stability and the accuracy of the formulation have been studied for several applications, including the degenerated cases where one dimension is strongly reduced to represent an embedded bar. The rigid inclusions have been modelled by increasing their elastic modulus. On the other hand thin inclusions with elastic modulus reduced to nearly zero can accurately model crack problems. In all analysed cases, the obtained results have shown that this simple strategy is reliable and can be applied to complex stress analysis problems.     

Two methods for the numerical solution of Bueckner's singular integral equation for plane elasticity crack problems

The classical collocation and Galerkin methods are used for the numerical solution of singular integral equations of the first kind involving a finite-part integral with a double pole singularity. Such equations appear in plane elasticity crack problems, where they were suggested by Bueckner, and the unknown function in them is proportional to the crack opening displacement function. An application of the proposed methods to the problem of a straight crack under an exponential normal loading distribution is also made and shows the rapid convergence of the obtained numerical results for the stress intensity factors at the crack tips to their theoretical values.     

汽轮机汽缸蠕变-疲劳耦合寿命预测

为探索汽轮机汽缸裂纹产生的原因、带裂纹汽缸的剩余寿命、汽缸延寿等问题,开展蠕变和疲劳交互作用下的汽缸寿命预测。利用有限元计算汽缸在稳态和启停工况下的应力情况。基于蠕变 疲劳耦合理论进行裂纹萌生和扩展的寿命预测,从运行方式和汽缸结构2方面开展优化。研究结果表明：该中压内缸中分面法兰的拐角处存在较大的热应力集中,其寿命损伤大导致裂纹萌生。经过结构修复,机组寿命显著延长。     

A frequency-domain BIEM combining DBIEs and TBIEs for 3-D crack-inclusion interaction analysis

The influence of a spherical elastic inclusion on a penny-shaped crack embedded in an infinite elastic matrix subjected to a time-harmonic crack-face or incident wave loading is investigated. A boundary integral equation method (BIEM) combining displacement boundary integral equations (DBIEs) on the matrix-inclusion interface and traction boundary integral equations (TBIEs) on the crack-surface is developed and applied for the numerical solution of the corresponding 3-D elastodynamic problem in the frequency domain. The singularity subtraction and mapping techniques in conjunction with a collocation scheme are implemented for the regularization and the discretization of the BIEs by taking into account the local structure of the solution at the crack-front. As numerical examples, the interaction of an elastic inclusion and a neighboring penny-shaped crack subjected to a tensile crack-surface loading or an incident plane longitudinal wave loading is investigated. The effects of the inclusion are assessed by the analysis of mixed-mode dynamic stress intensity factors (DSIFs) in dependence on the wave number, the material combination of the matrix and the inclusion, and the crack-inclusion orientation, size and distance.     

A numerical scheme for mixed boundary value problems in elasticity

A numerical scheme, based upon the Kobayashi-Tranter method with certain modifications, is given for axisymmetric punch and crack problems in elasticity. The problems are reduced to solving a system of linear algebraic equations instead of a Fredholm integral equation of the second kind. A standard program thus allows the treatment of a range of different cases.The indentation of a rigid punch on an elastic layer overlying an elastic foundation is formulated in this fashion and numerical results for various cases are presented.     

实测数据驱动的挖掘机工作装置疲劳寿命预测

以某型挖掘机为研究对象,建立其工作装置刚柔耦合动力学模型,基于实测油缸位移数据驱动该模型,得到其主要性能参数和典型工况危险部位应力.根据强度理论、动力学仿真结果和工程经验,分析挖掘机动臂和斗杆的易开裂部位,得到典型焊缝高危点,并通过实测应力应变数据进行验证.以刚柔耦合动力学仿真所得的铰点载荷作为输入,利用nCode疲劳分析软件仿真预测挖掘机动臂和斗杆的疲劳寿命.结果表明,实测数据驱动的刚柔耦合动力学仿真可以准确获取挖掘机实际挖掘过程的动力学特性,基于该仿真模型提取铰点载荷并用于预测疲劳寿命的方法切实可行.     

Approximating thermo-viscoelastic heating of largely strained solid rubber components

Mechanically induced viscoelastic dissipation is difficult to compute when the constitutive model is defined by history integrals. The computation of the viscous energy dissipated is in the form of a double convolution integral. In this study, we present a method to approximate the dissipation for constitutive models in history integral form that represent Maxwell-like materials. The dissipation is obtained without directly computing the double convolution integral. The approximation requires that the total stress can be separated into elastic and viscous components, and that the relaxation form of the constitutive law is defined with a Prony series. A numerical approach often taken to approximate a history integral involves interpolating the history integral’s kernel across a time step. Integration then yields finite difference equations for the evolution of the viscous stresses in time. In the case when the material is modeled with a Prony series, the form of these finite difference equations is similar to the form of the finite difference equations for a Maxwell solid. Since the dissipation rate in a Maxwell solid can be easily computed from knowledge of its viscous stress and the Prony series constants (spring-dashpot constants), we computationally investigated employing a Maxwell solid’s dissipation function to couple thermal and large strain history integral based finite element models of solid rubber components. Numerical data is provided to support this analogy and to help understand its limitations. A rubber cylinder with an imbedded steel disk is dynamically loaded, and the non-uniform heating within the cylinder is computed.     

A natural quadrature formula for the numerical evaluation of the Macgregor-Westergaard complex potentials es crack problems

The method of singular integral equations can be used for the numerical solution of crack problems in plane and antiplane elasticity. Here we consider the problem of the subsequent numerical evaluation of the stress components in the whole cracked medium by using the MacGregor-Westergaard complex potentials. To this end we use a modified quadrature formula for Cauchy type (but not principal value) integrals and their derivatives, where the poles of the integrands are properly taken into consideration. This is achieved by using a natural interpolation-extrapolation formula for singular integral equations and, for this reason, the new term ‘natural quadrature formula’ is proposed. Two simple applications to specific crack problems, based on the Gauss- and Lobatto-Chebyshev quadrature formulas, show the efficiency of the suggested quadrature formula.     

On the evaluation of stress intensity factors for a simple crack under parametric loading

Two analytical approaches for the evaluation of stress intensity factors at the tips of a single straight crack in plane isotropic elasticity under symmetric tensile loading along the crack edges including a parameter are considered. The first method leads to an ordinary differential equation for the stress intensity factor (or to a system of such equations) with respect to the loading parameter, whereas the second method leads to closed-form results for the related integral by using Laplace transform techniques. Several elementary transcendental functions, such as the exponential function, were used in the loading distribution for an illustration of the present approaches and related results are presented. The computer algebra system Maple V was also used together with Gröbner bases (for the derivation of the differential equations) and with definite integration (for the derivation of the closed-form formulae).     

Boundary element analysis of three-dimensional mixed-mode cracks via the interaction integral

A three-dimensional boundary element method (BEM) implementation of the interaction integral methodology for the numerical analysis of mixed-mode three-dimensional cracks is presented in this paper. The interaction integral is evaluated from a domain representation naturally compatible with the BEM, since stresses, strains and derivatives of displacements at internal points can be evaluated using their appropriate boundary integral equations. Special emphasis is put in the selection of the auxiliary function that represents the virtual crack advance in the domain integral. This is found to be a key feature to obtain reliable results at the intersection of crack fronts with free surfaces. Several examples are analysed to demonstrate the efficiency and accuracy of the implementation.     

Continuum shape sensitivity analysis of a mixed-mode fracture in functionally graded materials

This paper presents two new methods for conducting a continuum shape sensitivity analysis of a crack in an isotropic, linear-elastic functionally graded material. These methods involve the material derivative concept from continuum mechanics, domain integral representation of interaction integrals, known as the M-integral, and direct differentiation. Unlike virtual crack extension techniques, no mesh perturbation is needed to calculate the sensitivity of stress–intensity factors. Since the governing variational equation is differentiated prior to the process of discretization, the resulting sensitivity equations are independent of approximate numerical techniques, such as the meshless method, finite element method, boundary element method, or others. Three numerical examples are presented to calculate the first-order derivative of the stress–intensity factors. The results show that first-order sensitivities of stress intensity factors obtained using the proposed method are in excellent agreement with the reference solutions obtained using the finite-difference method for the structural and crack geometries considered in this study.     

Boundary element method for membrane and torsion crack problems

Here we present as an application of [12] an improved Galerkin method for the boundary integral equations governing a plane interface problem. Membrane and torsion crack problems can be treated by slight modifications.A tedious analysis incorporating the Mellin transform shows that the coupled system of integral equations—with some Fredholm equations of the second kind and some of the first kind—on the boundary curve Γ is strongly elliptic, i.e., there holds a Gårding inequality. This property implies convergence of almost optimal order of the Galerkin procedure. The use of singularity functions together with regular finite elements on Γ provides convergence results in a scale of Sobolev spaces and even quasi-optimal asymptotic error estimates for the stress intensity factors. These factors are computed directly by our Galerkin scheme, i.e., no additional computations are needed.The Galerkin method is implemented by an appropriate numerical integration leading to a Galerkin collocation. The latter is a modified collocation method which can be easily implemented on computing machines.     

Planar crack occupying a finite doubly connected region inside an infinite elastic solid

A method is proposed for the approximate solution of the problem of an embedded pressurized planar crack occupying a finite doubly connected region inside an infinite elastic solid. The formulation of the problem produces a system of two integral equations for determining the unknown normal stresses on the plane of the crack outside the crack region, which can be solved using numerical procedures. The proposed method has been applied to obtain the opening mode stress intensity factors K_I, along the boundary lines of an annular crack subjected to a uniform internal pressure.     

Numerical simulation of multiple 3D fracture propagation using arbitrary meshes

This paper describes a mesh-independent finite element based method for propagating fractures in three dimensions. The iterative algorithm automatically grows fractures in a 3D brittle medium represented by an isotropic linear elastic matrix. Growth is controlled by an input failure and propagation criterion. The geometry and mesh are stored separately, and mesh refinement is topologically guided. Propagation results in the modification of crack geometry, as opposed to changes in the mesh, as the arbitrary tetrahedral mesh adapts to the evolving geometry. Stress intensity factors are computed using the volumetric J Integral on a virtual piecewise cylinder. Modal stress intensity factors are computed using the decomposition method. Mesh and cylinder size effects are studied, as is computational efficiency. A through-going crack embedded in a thick slab, and a horizontal and inclined penny-shape crack, are used to validate the accuracy of the method. The predicted stress intensity factors are in good agreement with analytical solutions. For six integration points per tip segment, integration local to single tips, and a cylinder radius that adapts to the local geometric conditions, results agree with analytical solutions with less than 5% deviation from experimental results.     

3D mode I crack analysis of piezoelectrics

The finite-part integral concept is first used to prove rigidly hypersingular integral equations for a mode I crack embedded an infinite transversely isotropic piezoelectric solid. With three-dimensional linear piezoelectricity theory, investigations on the singular electroelastic fields in the vicinity of the crack are thereafter made by the dominant-part analysis. Finally, numerical solutions of several typical planar cracks with hypersingular integral equation method are performed to give the electroelastic intensity factor K-fields and the energy release rate G. Accuracies of results are found to be very high.     

The laplace transform DBEM for mixed-mode dynamic crack analysis

A boundary element method (BEM) for the two-dimensional analysis of structures with stationary cracks subjected to dynamic loads is presented. The difficulties in modelling the structures with cracks by BEM are solved by using two different equations for coincident points on the crack surfaces. The equations are the displacement and the traction boundary integral equations. This method of analysis requires discretization of the boundary and the crack surfaces only. The time-dependent solutions are obtained by the Laplace transform method, which is used to solve several examples. The influence of the number of boundary elements and the number of Laplace parameters is investigated and a comparison with other reported solutions is shown.     

基于Abaqus柔度标定法的Q235材料断裂韧性仿真

为简便、准确地获得Q235材料的应力强度因子值和J积分值,用Abaqus对Q235材料进行有限元仿真,得到三点弯曲试样及其裂纹尖端区域的应力分布情况;针对裂纹尖端的奇异性,引入折叠单元进行裂纹尖端单元的奇异性建模.不同尺寸试件应力强度因子仿真值与试验值基本一致,表明该方法可以准确预测材料断裂参数.     

半椭圆表面裂纹前缘应力强度因子的计算

在断裂力学中,如何求取应力强度因子一直是一个重要的课题.该文通过MSC.Marc提供的断裂力学模块,采用三维J积分法计算含有半椭圆表面裂纹前缘应力强度因子.首先通过MSC.Marc.Mentat建立特定裂纹体有限元模型,假设裂纹前缘处在平面应变状态下.由MSC.Marc计算出裂纹前沿的J积分,再由J积分计算出裂纹前缘的应力强度因子值.最后将计算结果与经验公式得到的结果进行了比较.仿真结果表明,通过MSC.Marc采用三维J积分法计算的应力强度因子具有较高的准确性和可靠性.     

The axisymmetric problem for a thick-walled spherical shell with an external edge crack

This paper considers the elasto-static axisymmetric problem for a thick-walled spherical shell containing a circumferential edge crack on the outer surface. Using the standard integral transform technique, the problem is formulated in terms of a singular integral equation of the first kind which has a generalized Cauchy kernel as the dominant part. As an example the axisymmetric load problem has been solved. The integral equation is solved numerically and the influences of the geometrical configurations on the stress intensity factors and crack opening displacements are shown graphically in detail.