Computational modeling of strong and weak discontinuities using the extended finite element method

In this article, the extended finite element method is employed to solve problems, including weak and strong discontinuities. To this end, a level set framework is used to represent the discontinuities location, and the Heaviside and Branch function are included in the standard finite element method. The case of two arbitrary curved cracks is solved numerically and stress intensity factor (SIF) values at the crack tips are calculated based on the evaluation of the crack tip opening displacement. Afterwards, J-integral methodology is adopted to evaluate the SIFs for isotropic and anisotropic bi-material interface crack problems. Numerical results are verified with those presented in the literature.     

A Finite Element Analysis for Evaluation of J-Integral in Plates Made of Functionally Graded Materials with a Semicircular Notch

Journal of Failure Analysis and Prevention - This work introduces a numerical investigation using finite element method to evaluate the J-integral at crack tip in titanium boride...     

THE FRACTURE BEHAVIOUR OF A CENTRE CRACKED TENSILE SPECIMEN

Abstract— This paper reviews the stress intensity factor, limit load, compliance and J-integral functions for a centre cracked tensile (CCT) specimen available in the literature. Compliance and J-integral functions are derived from the optimum stress intensity factor and limit load solutions. The functions are compared with the results obtained from two-dimensional finite element analyses of the specimen.
The finite element results have confirmed the accuracy of the compliance and limit load functions available in the literature and suggest that the unloading compliance technique, based on crack mouth opening displacement, could be developed for a CCT specimen. Non-linear finite element analyses have shown that J can be estimated from the measured load versus load-point displacement behaviour providing a/W ≥ 0.5     

Uncertainty analysis of elastostatic problems incorporating a new hybrid stochastic-spectral finite element method

This article aims to present a combination of stochastic finite element and spectral finite element methods as a new numerical tool for uncertainty quantification. One of the well-established numerical methods for reliability analysis of engineering systems is the stochastic finite element method. In this article, a commonly used version of the stochastic finite element method is combined with the spectral finite element method. Furthermore, the spectral finite element method is a numerical method employing special orthogonal polynomials (e.g., Lobatto) and quadrature schemes (e.g., Gauss-Lobatto-Legendre), leading to suitable accuracy, and much less domain discretization with excellent convergence as well. The proposed method of this article is a hybrid method utilizing efficiencies of both methods for analysis of stochastically linear elastostatic problems. Moreover, a spectral finite element method is proposed for numerical solution of a Fredholm integral equation followed by the present method, to provide further efficiencies to accelerate stochastic computations. Numerical examples indicate the efficiency and accuracy of the proposed method.     

Coupled thermo-mechanical analysis of metal-forming processes through a combined finite element–boundary element approach

This paper presents a new approach for obtaining the distribution of temperature in the dies during thermo-mechanical numerical analysis of metal forming problems. The proposed approach is based on a solution resulting from the combination of the finite element method with the boundary element method. The finite element method is used to perform the numerical modelling of the thermo-mechanical deformation of the workpiece, taking into account the geometrical and material non-linearities as well as the influence of the temperature distribution on the mechanical behaviour of the material. The boundary element method is applied for computing the distribution of temperatures in the dies. The combination of the two numerical methods is made using the finite element solution of the heat flow exchanged across the die–workpiece interface to define the boundary conditions to be applied on the thermal analysis of the dies. A numerical example of compression under plane-strain conditions is included to show the applicability of the proposed approach. © 1998 John Wiley & Sons, Ltd.     

Study on numerical approaches for the evaluation of J-Integral Results in 3D problems

For numerical analyses of fracture mechanics problems often a combination of the finite element method with a post processor program for the evaluation of J-integral values is used. Instead of calculating a line integral as originally proposed by RICE it is reasonable to evaluate surface or volume integrals (for two or three dimensional calculations, respectively) in this case. In this paper 3D-formulations proposed by DE LORENZI and ATLURI are considered and several possibilities of the numerical realisation of these formulations are described. While the De Lorenzi proposal is contained as subroutines in the GRS-version of the standard finite element program ADINA, the Atluri formulation is used in separate post-processing programs developed by GRS. As a first application three-dimensional calculations of a compact-tension-shear specimen are considered.     

Hyper-singular boundary element method for elastoplastic fracture mechanics analysis with large deformation

In this paper a two-dimensional hyper-singular boundary element method for elastoplastic fracture mechanics analysis with large deformation is presented. The proposed approach incorporates displacement and the traction boundary integral equations as well as finite deformation stress measures, and general crack problems can be solved with single-region formulations. Efficient regularization techniques are applied to the corresponding singular terms in displacement, displacement derivatives and traction boundary integral equations, according to the degree of singularity of the kernel functions. Within the numerical implementation of the hyper-singular boundary element formulation, crack tip and corners are modelled with discontinuous elements. Fracture measures are evaluated at each load increment, using the J-integral. Several cases studies with different boundary and loading conditions have been analysed. It has been shown that the new singularity removal technique and the non-linear elastoplastic formulation lead to accurate solutions.     

Application of finite element methods to thermohydrodynamic lubrication

A finite element formulation is presented for the equations governing the steady thermohydrodynamic behaviour of liquid lubricated bearings. This formulation permits application of the iterative solution scheme to bearings of arbitrary geometry. A generalized Reynolds equation resulting from the combination of the mass and momentum conservation equations is cast into variational form and used to derive general finite element equations. The method of weighted residuals with Galerkin's criterion is used to generate finite element matrix equations for the thermal energy equation. In addition to the finite element formulation, a discussion of appropriate finite difference techniques is also given for problems without complex geometry. As an example, the formulations are applied to obtain numerical solutions for a three-dimensional sector thrust bearing operating in the thermohydrodynamic regime. Pressure, velocity and temperature distributions are give, and the thermohydrodynamic solutions are compared with the results of classical isothermal theory.     

Least squares element method for boundary eigenvalue problems

Linear and non-linear boundary eigenvalue problems are discretized by a new finite element like method. The reason for the new construction principle is the non-linear dependence of the dynamic stiffness element matrix on an eigenparameter. The dynamic stiffness element matrix is evaluated for a fixed number of parameters and is then elementwise replaced by a polynomial in the eigenparameter by solving least squares problems. A fast solver is introduced for the resulting non-linear matrix eigenvalue problem. It consists of a combination of bisection method and inverse iteration. The superiority of the newconstructionprinciple in comparison with the finite or dynamic element method is demonstrated finally for some numerical examples.     

压力管道含环向表面裂纹的J积分估算方法

本文详细讨论了含环向表面裂纹管道的SC.ENG1和SC.ENG2 J积分估算方法,建立了含环向表面裂纹管道的有限元模型,对上述方法的有效性进行了考察。采用三维弹塑性有限元方法分析和讨论了表面裂纹前缘的J积分的分布规律;及具有不同长度屈服平台的管道材料对J积分的影响,对该估算方法对于具有屈服平台的国内管道用钢的适用性和有效性进行了讨论。     

陀螺转子动力学系统的时间有限元内点法

将保辛的时间有限元法(FEM)应用于陀螺转子动力学系统,给出了陀螺转子动力学系统时间有限元法的时间单元刚度阵列式和非齐次外力的表达式,以及辛时间传递矩阵。在此基础上,提出了精度更高的时间有限元内点法(IDTFEA),该方法既继承了时间有限元保辛的优良特性,又大大提高了数值计算精度,具有非常明显的优越性。算例给出了该方法和Newmark方法的比较结果,表明该方法的优越性。     

Global-local finite element

Finite element procedures usually require more degrees of freedom for a specified accuracy than does a classical Ritz procedure if suitable coordinate functions are available. This paper develops a combined global and local dependent variable representation which couples the conventional and finite element Ritz methods. This hybrid method preserves much of the flexibility of the finite element method while increasing the solution accuracy for a specified system order. The method is illustrated by examination of a beam and a plate vibration problem.     

Element Analysis of Ceramic Coatings under Spherical Indentation with Metallic Interlayer：Part Ⅱ Ring Crack

Spherical indentation of ceramic coatings with metallic interlayer was performed by means of axisymmetric finite element analysis （FEA）. Two typical ceramic coatings with relatively high and low elastic modulus deposited on aluminum alloy and carbon steel were considered. The fracture mechanics of the ceramic coatings mechanisms due to occurrence of surface ring cracks extending traverse the coating thickness under spherical indentation are investigated within the framework of linear fracture mechanics. The J-integral associated to such cracks was computed. The evolution of J-integral vs the crack length and the indentation depth was studied. The effects of the interlayer, the coating and the substrate on the J-integral evolution were discussed. The results show that a suitable metallic interlayer can improve the fracture resistance of the coating systems under the same indentation conditions through reducing the J-integral.     

An efficient finite element solution using a large pre-solved regular element

In this paper a finite element algorithm is presented using a large pre-solved hyper element. Utilizing the largest rectangle/cuboid inside an arbitrary domain, a large hyper element is developed that is solved using graph product rules. This pre-solved hyper element is efficiently inserted into the finite element formulation of partial differential equations (PDE) and engineering problems to reduce the computational complexity and execution time of the solution. A general solution of the large pre-solved element for a uniform mesh of triangular and rectangular elements is formulated for second-order PDEs. The efficiency of the algorithm depends on the relative size of the large element and the domain; however, the method remains as efficient as a classic method for even relatively small sizes. The application of the method is demonstrated using different examples.     

A least‐squares coupling method between a finite element code and a discrete element code

This paper presents a coupling method between a discrete element code CeaMka3D and a finite element code Sem. The coupling is based on a least‐squares method, which adds terms of forces to finite element code and imposes the velocity at coupling particles. For each coupling face, a small linear system with a constant matrix is solved. This method remains conservative in energy and shows good results in applications. Copyright © 2014 John Wiley & Sons, Ltd.     

Recursive genetic algorithm-finite element method technique for the solution of transformer manufacturing cost minimisation problem

The transformer manufacturing cost minimisation (TMCM), also known as transformer design optimisation, is a complex constrained mixed-integer non-linear programming problem with discontinuous objective function. This paper proposes an innovative method combining genetic algorithm (GA) and finite element method (FEM) for the solution of TMCM problem. The main contributions of the proposed method are: (a) introduction of an innovative recursive GA with a novel external elitism strategy associated with variable crossover and mutation rates resulting in an improved GA, (b) adoption of two particular finite element models of increased accuracy and high computational speed for the validation of the optimal design by computing the no-load loss and impedance and (c) combination of the innovative recursive GA with the two particular finite element models resulting in a proposed GA-FEM model that finds the global optimum, as concluded after several tests on actual transformer designs, while other existing methods provided suboptimal solutions that are 3.1?5.8% more expensive than the optimal solution.     

Modelling crack growth by level sets in the extended finite element method

An algorithm which couples the level set method (LSM) with the extended finite element method (X‐FEM) to model crack growth is described. The level set method is used to represent the crack location, including the location of crack tips. The extended finite element method is used to compute the stress and displacement fields necessary for determining the rate of crack growth. This combined method requires no remeshing as the crack progresses, making the algorithm very efficient. The combination of these methods has a tremendous potential for a wide range of applications. Numerical examples are presented to demonstrate the accuracy of the combined methods. Copyright © 2001 John Wiley & Sons, Ltd.     

Element Analysis of Ceramic Coatings under Spherical Indentation with Metallic Interlayer:Part Ⅱ Ring Crack

Spherical indentation of ceramic coatings with metallic interlayer was performed by means of axisymmetric finite element analysis(FEA). Two typical ceramic coatings with relatively high and low elastic modulus deposited on aluminum alloy and carbon steel were considered. The fracture mechanics of the ceramic coatings mechanisms due to occurrence of surface ring cracks extending traverse the coating thickness under spherical indentation are investigated within the framework of linear fracture mechanics. The J-integral associated to such cracks was computed. The evolution of J-integral vs the crack length and the indentation depth was studied. The effects of the interlayer, the coating and the substrate on the J-integral evolution were discussed. The results show that a suitable metallic interlayer can improve the fracture resistance of the coating systems under the same indentation conditions through reducing the J-integral.     

Atomistic simulations of J-integral in 2D graphene nanosystems

The J-integral is investigated in discrete atomic systems using molecular mechanics simulations. A method of calculating J-integral in specified atomic domains is developed. Two cases, a semiinfinite crack in an infinite domain under the remote K-field deformation and a finite crack length in a finite geometry under the tensile and shear deformation prescribed on the boundary, are studied in the two-dimensional graphene sheets and the values of J-integral are obtained under small-strain deformation. The comparison with energy release rates in Mode I and Mode II based on continuum theory of linear elastic fracture mechanics show good agreements. Meanwhile, the nonlinear strain and stress relation of a 2D graphene sheet is evaluated and is fitted with a power law curve. With necessary modifications on the Tersoff-Brenner potential, the critical values of J-integral of 2D graphene systems, which denoted as Jc, are eventually obtained. The results are then compared with those from the relevant references.