Extended finite element-based cohesive zone method for modeling simultaneous hydraulic fracture height growth in layered reservoirs

In this study,a fully coupled hydromechanical model within the extended finite element method(XFEM)-based cohesive zone method(CZM)is employed to investigate the simultaneous height growth behavior of multi-cluster hydraulic fractures in layered porous reservoirs with modulus contrast.The coupled hydromechanical model is first verified against an analytical solution and a laboratory experiment.Then,the fracture geometry(e.g.height,aperture,and area)and fluid pressure evolutions of multiple hydraulic fractures placed in a porous reservoir interbedded with alternating stiff and soft layers are investigated using the model.The stress and pore pressure distributions within the layered reservoir during fluid injection are also presented.The simulation results reveal that stress umbrellas are easily to form among multiple hydraulic fractures’tips when propagating in soft layers,which impedes the simultaneous height growth.It is also observed that the impediment effect of soft layer is much more significant in the fractures suppressed by the preferential growth of adjoining fractures.After that,the combined effect of in situ stress ratio and fracturing spacing on the multi-fracture height growth is presented,and the results elucidate the influence of in situ stress ratio on the height growth behavior depending on the fracture spacing.Finally,it is found that the inclusion of soft layers changes the aperture distribution of outmost and interior hydraulic fractures.The results obtained from this study may provide some insights on the understanding of hydraulic fracture height containment observed in filed.

STRESS FIELD ANALYSIS OF EXTRA-HEIGHT FORGING DIE USING FINITE ELEMENT METHOD

ＴｈｅｅｘｔｒａｈｅｉｇｈｔｆｏｒｇｉｎｇｄｉｅｉｎＳｏｕｔｈｅｗｅｓｔＡｌｕｍｉｎｉｕｍＦａｂｒｉｃａｔｉｏｎＰｌａｎｔｉｓａｓｐｅｃｉａｌｄｉｅｆｏｒｍａｋｉｎｇａｒｍａｍｅｎｔａｎｄｓｐｅｃｉａｌｃｉｖｉｌｐｒｏｄｕｃｔｓｉｎＣｈｉｎａ．Ａ...

Evaluation of mixed-mode stress intensity factors by extended finite element method

Extended finite element method （XFEM） implementation of the interaction integral methodology for evaluating the stress intensity factors （SIF） of the mixed-mode crack problem is presented. A discontinuous function and the near-tip asymptotic function are added to the classic finite element approximation to model the crack behavior. Two-state integral by the superposition of actual and auxiliary fields is derived to calculate the SIFs. Applications of the proposed technique to the inclined centre crack plate with inclined angle from 0° to 90° and slant edge crack plate with slant angle 45°, 67.5° and 90° are presented, and comparisons are made with closed form solutions. The results show that the proposed method is convenient, accurate and computationallv efficient.

Three-Dimensional Thermo-Elastic-Plastic Finite Element Method Modeling for Predicting Weld-Induced Residual Stresses and Distortions in Steel Stiffened-Plate Structures

The objective of the present paper is to develop nonlinear finite element method models for predicting the weld-induced initial deflection and residual stress of plating in steel stiffened-plate structures. For this purpose, three-dimensional thermo-elastic-plastic finite element method computations are performed with varying plate thickness and weld bead length (leg length) in welded plate panels, the latter being associated with weld heat input. The finite element models are verified by a comparison with experimental database which was obtained by the authors in separate studies with full scale measurements. It is concluded that the nonlinear finite element method models developed in the present paper are very accurate in terms of predicting the weld-induced initial imperfections of steel stiffened plate structures. Details of the numerical computations together with test database are documented.

Three-dimensional analysis of elastic stress distribution of indented ceramic surface by finite element method

The three-dimensional stress distributions in the area surrounding indentation pattern for three different materials, Al2O3, Si3N4 and SiC were analyzed by finite element method(FEM). Those theoretical results were also compared with the experimental ones by Rockwell hardness test. The effect of loading stress on the plastic deformation in specimens, surface was investigated on the assumption of shear strain energy theory by Huber-Mises when the materials were indented. The distributions of nomal stress, shear stress, and Mises stress were analysed with variations of loading conditions. It is clear that the analytical results for the stress distributions, the crack length and its density of probability are in good agreement with the experimental results.

Genetic algorithm-finite element method inversion of the factors determining the recent tectonic stress field of part of East Asia area

Genetic algorithm finite element method (GA FEM) is applied to the study of tectonic stress field of part of East Asia area. From the observed stress distribution, 2 D elastic plane stress inversion is made to deduce the boundary forces and investigate controlling factors. It is suggested that the continent continent collision is the dominant factor controlling the Chinese tectonic stress field. The ocean continent convergence along the subduction zone is an important factor. There exists tensile boundary force along the marginal sea.

Study on the Stress of DLC/MCT Interface by Finite Element Method

Micro-indention and finite element method (FEM) are used to study the stress at the interface between diamond-like carbon (DLC) film and mercury cadmium telluride (MCT) substrate, with different coating thickness, deposition temperature and indention load. The FEM simulation results show that when Young's modulus ratio of the coating to the substrate Ec/Es<1, Whether a load was applied or not, the interfacial maximum shear stress decreased with the increase of coating thickness. The Von mises stress always concentrated at the interface. The maximum value of the stress locates at the edge of the interface for thin film (h1/h2<0. l), however, it will locate at the center of the interface while the film become thick (h1/h2>0. 1 ). The stress also increased with raising the film deposition temperature, and the temperature affected the strain obviously. When a load was applied, the stress would concentrate where the load was applied, and the stress value is much larger than that of unloading. When the film stress exceeds the film fracture strength, film cracking occurs at the location where load is applied.

COMPUTATION OF STRESS INTENSITY FACTORS BY THE SUB-REGION MIXED FINITE ELEMENT METHOD OF LINES

Based on the sub-region generalized variationM principle, a sub-region mixed version of the newly-developed semi-analytical ＇finite element method of lines＇ （FEMOL） is proposed in this paper for accurate and efficient computation of stress intensity factors （SIFs） of two-dimensional notches/cracks. The circular regions surrounding notch/crack tips are taken as the complementary energy region in which a number of leading terms of singular solutions for stresses are used, with the sought SIFs being among the unknown coefficients. The rest of the arbitrary domain is taken as the potential energy region in which FEMOL is applied to obtain approximate displacements. A mixed system of ordinary differential equations （ODEs） and algebraic equations is derived via the sub-region generalized variational principle. A singularity removal technique that eliminates the stress parameters from the mixed equation system eventually yields a standard FEMOL ODE system, the solution of which is no longer singular and is simply and efficiently obtained using a standard general-purpose ODE solver. A number of numerical examples, including bi-material notches/cracks in anti-plane and plane elasticity, are given to show the generally excellent performance of the proposed method.

Stress and Displacement Distribution of Soft Clay Slope with 2D and 3D Elastoplastic Finite Element Method

Based on elastoplastic model, 2D and 3D finite element method （FEM） are used to calculate the stress and displacement distribution in the soft clay slope under gravity and uniform load at the slope top. Stability analyses indicate that 3D boundary effect varies with the stress level of the slope. When the slope is stable, end effect of 3D space is not remarkable. When the stability decreases, end effect occurs; when the slope is at limit state, end effect reaches maximum. The energy causing slope failure spreads preferentially along y-z section, and when the failure resistance capability reaches the limit state, the energy can extend along x-axis direction. The 3D effect of the slope under uniform load on the top is related to the ratio of load influence width to slope height, and the effect is remarkable with the decrease of the ratio.

A FINITE ELEMENT METHOD FOR STRESS ANALYSIS OR ELASTOPLASTIC BODY WITH POLYGONAL LINE STRAIN——HARDENING

In this paper, the stress-strain curve of material is fitted by polygonal line composed of three lines. According to the theory of proportional loading in elastoplasticity, we simplify the complete stress-strain relations, which are given by the increment theory of elastoplasticity. Thus, the finite element equation with the solution of displacement is derived. The assemblage elastoplastic stiffness matrix can be obtained by adding something to the elastic matrix, hence it will shorten the computing time. The determination of every loading increment follows the von Mises yield criteria. The iterative method is used in computation. It omits the redecomposition of the assemblage stiffness matrix and it will step further to shorten the computing time. Illustrations are given to the high-order element application departure from proportional loading, the computation of unloading fitting to the curve and the problem of load estimation.

Using Extended Finite Element Method for Computation of the Stress Intensity Factor, Crack Growth Simulation and Predicting Fatigue Crack Growth in a Slant-Cracked Plate of 6061-T651 Aluminum

The 6061-T651 aluminium alloy is one of the most common aluminium alloys for marine components and general structures. The stress intensity factor (SIF) is an important parameter for estimating the life of the cracked structure. In this paper, the stress intensity factors of a slant-cracked plate, which is made of 6061-T651 aluminum, have been calculated using extended finite element method (XFEM) and finite element method (FEM) in ABAQUS software and the results were compared with theoretical values. Numerical values obtained from these two methods were close to the theoretical values. In simulations of crack growth at different crack angles, the crack propagation angle values were closer to the theoretical values in XFEM method. Also, the accuracy and validity of fatigue crack growth curve were much closer to the theoretical graph in XFEM than the FEM. Therefore, in this paper the capabilities of XFEM were realized in analyzing issues such as cracks.

THE APPLICATION OF COMPATIBLE STRESS ITERATIVE METHOD IN DYNAMIC FINITE ELEMENT ANALYSIS OF HIGH VELOCITY IMPACT

There is a common difficulty in elastic-plastic impact codes such as EPIC[2,3] NONSAP[4], etc.. Most of these codes use the simple linear functions usually taken from static problem to represent the displacement components. In such finite element formulation, the stress components are constant in each element and they are discontinuous in any two neighboring elements. Therefore, the bases of using the virtual work principle in such elements are unreliable. In this paper, we introduce a new method, namely, the compatible stress iterative method, to eliminate the above-said difficulty. The calculated examples show that the calculation using the new method in dynamic finite element analysis of high velocity impact is valid and stable, and the element stiffness can be somewhat reduced.

Galerkin-based quasi-smooth manifold element(QSME)method for anisotropic heat conduction problems in composites with complex geometry

The accurate and efficient analysis of anisotropic heat conduction problems in complex composites is crucial for structural design and performance evaluation. Traditional numerical methods, such as the finite element method(FEM), often face a trade-off between calculation accuracy and efficiency. In this paper, we propose a quasi-smooth manifold element(QSME) method to address this challenge, and provide the accurate and efficient analysis of two-dimensional(2D) anisotropic heat conduction problems in composites with complex geometry. The QSME approach achieves high calculation precision by a high-order local approximation that ensures the first-order derivative continuity.The results demonstrate that the QSME method is robust and stable, offering both high accuracy and efficiency in the heat conduction analysis. With the same degrees of freedom(DOFs), the QSME method can achieve at least an order of magnitude higher calculation accuracy than the traditional FEM. Additionally, under the same level of calculation error, the QSME method requires 10 times fewer DOFs than the traditional FEM. The versatility of the proposed QSME method extends beyond anisotropic heat conduction problems in complex composites. The proposed QSME method can also be applied to other problems, including fluid flows, mechanical analyses, and other multi-field coupled problems, providing accurate and efficient numerical simulations.

Finite Element Analysis on Plane Stress Crack Growth in a Power-Law Hardening Material

Aim To determine numerically the field characteristics in the vied at the tip of a place crack growing steadily in a power-law hardening material. Meteods. Methods on the Euler mode and small-scale yield assumption, the numerical results were given by nonlinear finite element analysis. Results The numerical results of the shape of the active plastic sone, the angular distribution of stresseses and Clack tip opening displacement (CTOD) in the vicinity at the hp of the steadily groWing CraCk are determined. Conclusion The comparison between the numerical results given by the present wort and those given by analytic asymptotic analysis shows that the present work reached a very high accuracy.

Self-adaptive one-dimensional nonlinear finite element method based on element energy projection method

The element energy projection （EEP） method for computation of super- convergent resulting in a one-dimensional finite element method （FEM） is successfully used to self-adaptive FEM analysis of various linear problems, based on which this paper presents a substantial extension of the whole set of technology to nonlinear problems. The main idea behind the technology transfer from linear analysis to nonlinear analysis is to use Newton＇s method to linearize nonlinear problems into a series of linear problems so that the EEP formulation and the corresponding adaptive strategy can be directly used without the need for specific super-convergence formulation for nonlinear FEM. As a re- sult, a unified and general self-adaptive algorithm for nonlinear FEM analysis is formed. The proposed algorithm is found to be able to produce satisfactory finite element results with accuracy satisfying the user-preset error tolerances by maximum norm anywhere on the mesh. Taking the nonlinear ordinary differential equation （ODE） of second-order as the model problem, this paper describes the related fundamental idea, the imple- mentation strategy, and the computational algorithm. Representative numerical exam- ples are given to show the efficiency, stability, versatility, and reliability of the proposed approach.

Finite Element Analysis of the Base

This paper describes the structure of the base,on which two working arms are installed simultaneously.To ensure structura safety,the fatigue failure analysis and statics analysis are finished using the finite element method.The calculation can make sure that the structure of the base meets the design standard,and the material can be reduced one grade.

Stability assessment of landslide-prone road cut rock slopes in Himalayan terrain:A finite element method based approach

Large-scale slope destabilization could be aggravated due to swift urbanization and ever-rising demands of geoengineering projects such as dams,tunnels,bridges and widening roads.National Highway-58 connects Delhi to Badrinath in India,which passes through complex geomorphological and geological terrain and often encounters cut slopes susceptible to slope failures.In the present investigation,a detailed geotechnical appraisal is conducted along the road cut slopes from Rishikesh to Devprayag in the Himalayas.Twenty vulnerable road cut slopes were demarcated for detailed slope stability analysis using Phase2D finite element modeling simulator.Nonlinear generalized Hoek-Brown(GHB)criterion was adopted for stability analyses.Out of 20 slopes,five slopes(S6,S7,S18,S19 and S20)are unstable with factor of safety(FoS)less than or equal to 1,and thus needs immediate attention.The FoS values of four slopes(S2,S9,S13 and S17)lie between 1 and 1.3,i.e.marginally stable,and slopes S1,S3,S4,S5,S8,S10,Sll,S12,S14,S15 and S16 are stable.Mohr-Coulomb(MC)criterion was also adopted to compare the slope stability analysis with GHB criterion.The FoS calculated from GHB criterion is close to that using MC criterion for lower values of FoS whereas for higher values,the difference is marked.For the jointed rock in the Himalayan region,the nonlinear GHB criterion gives better results as compared to MC criterion and matches with the prevailing field conditions.Accordingly,some suggestions are proposed to strengthen the stability of cut slopes.

COMBINED DELAUNAY TRIANGULATION AND ADAPTIVE FINITE ELEMENT METHOD FOR CRACK GROWTH ANALYSIS

The paper presents the utilization of the adaptive Delaunay triangulation in the finite element modeling of two dimensional crack propagation problems, including detailed description of the proposed procedure which consists of the Delaunay triangulation algorithm and an adaptive remeshing technique. The adaptive remeshing technique generates small elements around crack tips and large elements in the other regions. The resulting stress intensity factors and simulated crack propagation behavior are used to evaluate the effectiveness of the procedure. Three sample problems of a center cracked plate, a single edge cracked plate and a compact tension specimen, are simulated and their results assessed.

Mixed finite element and differential quadrature method for free and forced vibration and buckling analysis of rectangular plates

This paper presents a combined application of the finite element method （FEM） and the differential quadrature method （DQM） to vibration and buckling problems of rectangular plates. The proposed scheme combines the geometry flexibility of the FEM and the high accuracy and efficiency of the DQM. The accuracy of the present method is demonstrated by comparing the obtained results with those available in the literature. It is shown that highly accurate results can be obtained by using a small number of finite elements and DQM sample points. The proposed method is suitable for the problems considered due to its simplicity and potential for further development.

3D Finite Element Numerical Simulation of Residual Stresses on Electron Beam Welded BT20 Plates

A three-dimensional finite-element model (FEM) used for calculating electron beam (EB) welding temperature and stresses fields of thin plates of BT20 titanium has been developed in which the nonlinear thermophysical and thermo-mechanical properties of the material has been considered. The welding temperature field, the distributions of residual stresses in as-welded (AW) and electron beam local post-weld heat treatment (EBLPWHT) conditions have been successfully simulated. The results show that: (1) In the weld center, the maximum magnitude of residual tensile stresses of BT20 thin plates of Ti alloy is equal to 60%- 70% of its yield strength σs. (2) The residual tensile stresses in weld center can be even decreased after EBLPWHT and the longitudinal tensile stresses are decreased about 50% compared to joints in AW conditions. (3) The numerical calculating results of residual stresses by using FEM are basically in agreement with the experimental results. Combined with numerical calculating results, the effects of electron beam welding and EBLPWHT on the distribution of welding residual stresses in thin plates of BT20 have been analyzed in detail.