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.

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.

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.

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.

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.

Thermoelastic analysis of multiple defects with the extended finite element method

In this paper, the extended finite element method (XFEM) is adopted to analyze the interaction between a single macroscopic inclusion and a single macroscopic crack as well as that between multiple macroscopic or microscopic defects under thermal/mechanical load. The effects of different shapes of multiple inclusions on the material thermomechanical response are investigated, and the level set method is coupled with XFEM to analyze the interaction of multiple defects. Further, the discretized extended finite element approximations in relation to thermoelastic problems of multiple defects under displacement or temperature field are given. Also, the interfaces of cracks or materials are represented by level set functions, which allow the mesh assignment not to conform to crack or material interfaces. Moreover, stress intensity factors of cracks are obtained by the interaction integral method or the M-integral method, and the stress/strain/stiffness fields are simulated in the case of multiple cracks or multiple inclusions. Finally, some numerical examples are provided to demonstrate the accuracy of our proposed method.

A novel twice-interpolation finite element method for solid mechanics problems

Formulation and numerical evaluation of a novel twice-interpolation finite element method （TFEM） is presented for solid mechanics problems. In this method, the trial function for Galerkin weak form is constructed through two stages of consecutive interpolation. The primary interpolation follows exactly the same procedure of standard FEM and is further reproduced according to both nodal values and averaged nodal gradients obtained from primary interpolation. The trial functions thus constructed have continuous nodal gradients and contain higher order polynomial without increasing total freedoms. Several benchmark examples and a real dam problem are used to examine the TFEM in terms of accuracy and convergence. Compared with standard FEM, TFEM can achieve significantly better accuracy and higher convergence rate, and the continuous nodal stress can be obtained without any smoothing operation. It is also found that TFEM is insensitive to the quality of the elemental mesh. In addition, the present TFEM can treat the incompressible material without any modification.

Improved methods for decreasing stresses of concrete slab of large-span through tied-arch composite bridge

Mechanical behavior of concrete slab of large-span through tied-arch composite bridge was investigated by finite element analysis (FEA). Improved methods to decrease concrete stresses were discussed based on comparisons of different deck schemes, construction sequences and measures, and ratios of reinforcement. The results show that the mechanical behavior of concrete slab gets worse with the increase of composite regions between steel beams and concrete slab. The deck scheme with the minimum composite region is recommended on condition that both strength and stiffness of the bridge meet design demands under service loads. Adopting in-situ-place construction method, concrete is suggested to be cast after removing the full-supported frameworks under the bridge. Thus, the axial tensile force of concrete slab caused by the first stage dead load is eliminated. Preloading the bridge before concrete casting and removing the load after the concrete reaching its design strength, the stresses of concrete slab caused by the second stage dead load and live load are further reduced or even eliminated. At last, with a high ratio of reinforcement more than 3%, the concrete stresses decrease obviously.

Application of scaled boundary finite element method in static and dynamic fracture problems

The scaled boundary finite element method （SBFEM） is a recently developed numerical method combining advantages of both finite element methods （FEM） and boundary element methods （BEM） and with its own special features as well. One of the most prominent advantages is its capability of calculating stress intensity factors （SIFs） directly from the stress solutions whose singularities at crack tips are analytically represented. This advantage is taken in this study to model static and dynamic fracture problems. For static problems, a remeshing algorithm as simple as used in the BEM is developed while retaining the generality and flexibility of the FEM. Fully-automatic modelling of the mixed-mode crack propagation is then realised by combining the remeshing algorithm with a propagation criterion. For dynamic fracture problems, a newly developed series-increasing solution to the SBFEM governing equations in the frequency domain is applied to calculate dynamic SIFs. Three plane problems are modelled. The numerical results show that the SBFEM can accurately predict static and dynamic SIFs, cracking paths and load-displacement curves, using only a fraction of degrees of freedom generally needed by the traditional finite element methods.

STUDY ON THREE-DIMENSIONAL FINITE BODIES CONTAINING CRACKS USING THE FINITE ELEMENT METHOD OF LINES

The three-dimensional finite element method of lines is presented, and the basic processing description of 3D FEMOL in cracking questions is given in detail. Applications to 3D bodies with cracks indicate that good accuracy can be obtained with relatively coarse girds. In particular, application to the tension specimen shows very good agreement with the evaluation of stress intensity factors, which is better than the results of other methods. This implies a considerable potential for using this method in the 3D analysis of finite geometry solids and suggests a possible extension of this technique to nonlinear material behavior.

Dynamic Crack Propagation Analysis Using Scaled Boundary Finite Element Method

The prediction of dynamic crack propagation in brittle materials is still an important issue in many engineering fields. The remeshing technique based on scaled boundary finite element method(SBFEM) is extended to predict the dynamic crack propagation in brittle materials. The structure is firstly divided into a number of superelements, only the boundaries of which need to be discretized with line elements. In the SBFEM formulation, the stiffness and mass matrices of the super-elements can be coupled seamlessly with standard finite elements, thus the advantages of versatility and flexibility of the FEM are well maintained. The transient response of the structure can be calculated directly in the time domain using a standard time-integration scheme. Then the dynamic stress intensity factor(DSIF) during crack propagation can be solved analytically due to the semi-analytical nature of SBFEM. Only the fine mesh discretization for the crack-tip super-element is needed to ensure the required accuracy for the determination of stress intensity factor(SIF). According to the predicted crack-tip position, a simple remeshing algorithm with the minimum mesh changes is suggested to simulate the dynamic crack propagation. Numerical examples indicate that the proposed method can be effectively used to deal with the dynamic crack propagation in a finite sized rectangular plate including a central crack. Comparison is made with the results available in the literature, which shows good agreement between each other.

Nonlinear simulation of arch dam cracking with mixed finite element method

This paper proposes a new, simple and efficient method for nonlinear simulation of arch dam cracking from the construction period to the operation period, which takes into account the arch dam construction process and temperature loads. In the calculation mesh, the contact surface of pair nodes is located at places on the arch dam where cracking is possible. A new effective iterative method, the mixed finite element method for friction-contact problems, is improved and used for nonlinear simulation of the cracking process. The forces acting on the structure are divided into two parts： external forces and contact forces. The displacement of the structure is chosen as the basic variable and the nodal contact force in the possible contact region of the local coordinate system is chosen as the iterative variable, so that the nonlinear iterative process is only limited within the possible contact surface and is much more economical. This method was used to simulate the cracking process of the Shuanghe Arch Dam in Southwest China. In order to prove the validity and accuracy of this method and to study the effect of thermal stress on arch dam cracking, three schemes were designed for calculation. Numerical results agree with actual measured data, proving that it is feasible to use this method to simulate the entire process of nonlinear arch dam cracking.

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.

Simulation of Lumbar Spinal Stenosis Using the Finite Element Method

Lumbar spine stenosis(LSS)is a narrowing of the spinal canal that results in pressure on the spinal nerves.This orthopedic disorder can cause severe pain and dysfunction.LSS is a common disabling problem amongst elderly people.In this paper,we developed a finite element model(FEM)to study the forces and the von Mises stress acting on the spine when people bend down.An artificial lumbar spine(L3)was generated from CT data by using the FEM,which is a powerful tool to study biomechanics.The proposed model is able to predict the effect of forces which apply to the lumbar spine.In addition,FEM allows us to investigate the tests into the lumbar spine instead of applying the tests to the real spine in humans.The proposed model is highly accurate and provides precise information about the lumbar spine(L3).We investigate the behavior of humans in daily life which effects to the lumbar spine in a normal person and a patient with LSS.The computational results revealed high displacement levels around the spinal canal and lower displacement levels in the spinal body when bending down.The total displacement of the axial load in a normal person was higher when compared with patients with LSS.Higher degree bends resulted in a lower total displacement when compared with lower degree bends,while the von Mises stress decreased as the bending degree increased.

FORMING MICHELL TRUSS IN THREE-DIMENSIONS BY FINITE ELEMENT METHOD

The finite element method to form Michell truss in three_dimensions is presented.The orthotropic composite with fiber_reinforcement is employed as the material model to simulate Michell truss.The orientation and densities of fibers at nodes are taken as basic design variables.The stresses and strains at nodes are calculated by finite element method.An iteration scheme is suggested to adjust the orientations of fibers to be along the orientations of principal stresses, and the densities of fibers according to the strains in the orientations of fibers.The strain field satisfying Michell criteria and truss_like continuum are achieved after several iterations. Lastly, the Michell truss is showed by continuous lines, which are formed according to the orientations of fibers at nodes. Several examples are used to demonstrate the efficiency of the presented approach.

Numerical investigation of temperature gradient-induced thermal stress for steel–concrete composite bridge deck in suspension bridges

A3D finite element model(FEM)with realistic field measurements of temperature distributions is proposed to investigate the thermal stress variation in the steel–concrete composite bridge deck system.First,a brief literaturereview indicates that traditional thermal stress calculation in suspension bridges is based on the2D plane structure with simplified temperature profiles on bridges.Thus,a3D FEM is proposed for accurate stress analysis.The focus is on the incorporation of full field arbitrary temperature profile for the stress analysis.Following this,the effect of realistic temperature distribution on the structure is investigated in detail and an example using field measurements of Aizhai Bridge is integrated with the proposed3D FEM model.Parametric studies are used to illustrate the effect of different parameters on the thermal stress distribution in the bridge structure.Next,the discussion and comparison of the proposed methodology and simplified calculation method in the standard is given.The calculation difference and their potential impact on the structure are shown in detail.Finally,some conclusions and recommendations for future bridge analysis and design are given based on the proposed study.

APPLICATION OF STOCHASTIC FINITE ELEMENT METHOD TO STRENGTH AND STABILITY ANALYSIS OF EARTH DAMS

This paper applies the stochastic finite element method to analyse the statistics of stresses in earth dams and assess the safety and reliability of the dams. Formulations of the stochastic finite element method are briefly reviewed and the procedure for assessing dam's strength and stability is described. As an example, a detailed analysis for an actual dam Nululin dam is performed. A practical method for studying built-dams based on the prototype observation data is described.