Finite element simulation of elastoplastic fieldnear crack tips and results for a central crackedplate of le-lhp material under tension

The elastoplastic field near crack tips is investigated through finite element simulation.A refined mesh model near the crack tip is proposed. In the mesh refining area, element size continuously varies from the nanometer scale to themicrometer scale and the millimeter scale. Graphics of the plastic zone, the crack tip blunting, and the deformed crack tip elements are given in the paper.Based on the curves of stress and plastic strain, closely near the crack tip, the stresssingularity index and the stress intensity factor,as well as the plastic strain singularity index and the plastic strain intensity factor are determined.Thestress and plastic strainsingular index vary with the load, while the dimensions of the stress and the plastic strain intensity factorsdependon the stress and the plastic strain singularity index, respectively. The singular field near the elastoplastic crack tip is characterized by the stress singularity index and the stress intensity factor, or alternativelythe plastic strain singularity index and the plastic strain intensityfactor.At the end of the paper, following Irwin’s concept of fracture mechanics,σδKσδKcriterion andεδQεδQcriterion are proposed.Besides, crack tip angle criterion is also presented.

Analysis of elastoplasticity problems using an improved complex variable element-free Galerkin method

In this paper, based on the conjugate of the complex basis function, a new complex variable moving least-squares approximation is discussed. Then using the new approximation to obtain the shape function, an improved complex variable element-free Galerkin（ICVEFG） method is presented for two-dimensional（2D） elastoplasticity problems. Compared with the previous complex variable moving least-squares approximation, the new approximation has greater computational precision and efficiency. Using the penalty method to apply the essential boundary conditions, and using the constrained Galerkin weak form of 2D elastoplasticity to obtain the system equations, we obtain the corresponding formulae of the ICVEFG method for 2D elastoplasticity. Three selected numerical examples are presented using the ICVEFG method to show that the ICVEFG method has the advantages such as greater precision and computational efficiency over the conventional meshless methods.

Hybrid natural element method for large deformation elastoplasticity problems

We present the hybrid natural element method（HNEM） for two-dimensional elastoplastic large deformation problems. Sibson interpolation is adopted to construct the shape functions of nodal incremental displacements and incremental stresses. The incremental form of Hellinger–Reissner variational principle for elastoplastic large deformation problems is deduced to obtain the equation system. The total Lagrangian formulation is used to describe the discrete equation system.Compared with the natural element method（NEM）, the HNEM has higher computational precision and efficiency in solving elastoplastic large deformation problems. Some numerical examples are selected to demonstrate the advantage of the HNEM for large deformation elastoplasticity problems.

Structural Optimization of Lap Link Based on Elastoplastic Finite Element Analysis

Based on finite-deformation elastoplastic theory, a scheme to solve the structural problems of the lap link by using ANSYS is proposed. The analysis results show that the maximum deformation exists at the loading spot of the lateral pin and the stiffness of this area needs to be enhanced; the maximum stresses occur at the two sides adjacent to the loading spot and the intensity around this region should be strengthened;the materials at the pole and pinhole with relatively low stress are redundant and removing excessive weight is possible. Based on the analysis, corresponding improvements are tentatively made, and the simulation results prove that, the stiffness and intensity of the new structure are improved. Furthermore, the reliability and validity of this design are verified by tensile tests of two types of structure.

Neural network method for solving elastoplastic finite element problems

A basic optimization principle of Artificial Neural Network—the Lagrange Programming Neural Network (LPNN) model for solving elastoplastic finite element problems is presented. The nonlinear problems of mechanics are represented as a neural network based optimization problem by adopting the nonlinear function as nerve cell transfer function. Finally, two simple elastoplastic problems are numerically simulated. LPNN optimization results for elastoplastic problem are found to be comparable to traditional Hopfield neural network optimization model.

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.

FINITE ELEMENT ANALYSIS OF CONCRETE BASED ON TWO SURFACE ELASTOPLASTIC MODEL

This paper presents finite element formulas based on two Surface elastoplastic yielding model. The study also discusses the numerical procedures and develops the corresponding software. These formulas have provided accurate elastoplastic method for analysing concrete, rock and soil like materials.

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.

Boundary element analysis for elastic and elastoplastic problems of 2D orthotropic media with stress concentration

Both the orthotropy and the stress concentration are common issues in modem structural engineering. This paper introduces the boundary element method （BEM） into the elastic and elastoplastic analyses for 2D orthotropic media with stress concentration. The discretized boundary element formulations are established, and the stress formulae as well as the fundamental solutions are derived in matrix notations. The numerical procedures are proposed to analyze both elastic and elastoplastic problems of 2D orthotropic me- dia with stress concentration. To obtain more precise stress values with fewer elements, the quadratic isoparametric element formulation is adopted in the boundary discretization and numerical procedures. Numerical examples show that there are significant stress concentrations and different elastoplastic behaviors in some orthotropic media, and some of the computational results are compared with other solutions. Good agreements are also observed, which demonstrates the efficiency and reliability of the present BEM in the stress concentration analysis for orthotropic media.

Elastoplastic response of functionally graded cemented carbides due to thermal loading

Finite dement formulations are used to simulate the evolution of the elastoplastic response of functionally graded cemented carbides （FGCC） due to thermal loading. The geometry of specimens is an axisymmetric solid cylinder with a two-dimensional gradient. The elastoplastic constitutive relationship is developed by constraint factors. Numerical results show that compressive stresses occur in the surface zone and tensile stresses in the cobalt rich zone when the temperature drops from the initial stress-free temperature of 800 to 0℃. The maximum value of the surface compressive stress is 254 MPa and the maximum value of the tensile stress is 252 MPa in the cobalt rich zones. When the cobalt concentration difference in the specimens is equal to or greater than 0.3, there is pronounced plastic flow in cobalt rich zone. When the temperature heats up from 0 to 800 ℃, the total plastic strain reaches 0.001 4. Plastic flow has a significant effect on the reduction of thermal stress concentration.

A review of flexibility-based finite element method for beam-column elements

For material nonlinear problem,elements derived with the flexibility-based method are more accurate than classical elements derived with the stiffness-based method. A review of the current state of the art of the flexibility-based finite element method is provided to enhance the robustness of structure analysis. The research on beam-column elements is the mainstream in the research on flexibility-based finite element method at present. The original development of flexibility-based finite element method is reviewed, and the further development of this method is then presented in several specific aspects, such as geometrically nonlinear analysis and dynamic analysis. The further research needed to be carried out in the future is finally discussed.

Elastoplastic analysis of thin-walled structures in reservoir area

In the structural design of the high pier,in order to analyze the strength and structure stability,the pier was often considered a thin-walled structure.Elastoplastic incremental theory was used to establish the model of elastoplastic stability of high pier.By considering the combined action of pile,soil and pier together,the destabilization bearing capacity was calculated by using 3-D finite element method(3-D FEM) for piers with different pile and section height.Meanwhile,the equivalent stress in different sections of pier was computed and the processor of destabilization was discussed.When the pier is lower,the bearing capacity under mutual effect of pile,soil and pier is less than the situation when mutual effect is not considered;when the pier is higher,their differences are not conspicuous.Along with the increase of the cross-sectional height,the direction of destabilization bearing capacity is varied and the ultimate capacity is buildup.The results of a stability analysis example are almost identical with the practice.

ANALYSIS OF ELASTOPLASTIC DEFORMATION IN METAL-MATRIX COMPOSITES WITH PARTICULATE REINFORCEMENTS

In this paper, elastoplastic stress-strain behavior during tensile deformation of an aluminum alloy matrix composite containing alumina circular and non-circular particles is analyzed. In terms of cell models in conjunction with continuum plasticity theory, various periodic arrays of particles are assumed in a three-dimensional finite element simulation. The geometrical effects of particle volume fraction, shape, aspect ratio, array and distribution, as well as non-circular particle orientation on the overall elastoplastic stress-strain behavior are examined in view to design optimum microstructures of the composites.

APPLICATION OF ARTIFICIAL NEURAL NETWORK TO INVERSE PROBLEMS OF ESTIMATING INNER ETCH OF ELASTOPLASTIC PIPE UNDER PRESSURE

To determine a variation of pipe's inner geometric shape as due to etch, the three-layered feedforward artificial neural network is used in the inverse analysis through observing the elastoplastic strains of the outer wall under the working inner pressure. Because of different kinds of inner wail radii and eccentricity. several groups of strains calculated with computational mechanics are used for the network to do learning. Numerical calculation demonstrates that this method is effective and the estimated inner wall geometric parameters have high precision.

AN EFFECTIVE BOUNDARY METHOD FOR THE ANALYSIS OF ELASTOPLASTIC PROBLEMS

In this paper, a series of effective formulae of the boundary element method is presented. In these formulae, by using a new variable, two kernels are only of the weaker singularity of Lnr (where r is the distance between a source point and a field point). Hence, the singularities in the conventional displacement formulation and stress formulation at internal points are reduced respectively so that the 'boundary-layer'' effect which strongly degenerates the accuracy of stress calculation by using original formulae is eliminated. Also the direct evaluation of coefficients C (boundary tensor), which are difficult to calculate, is avoided. This method is used in elastoplastic analysis. The results of the numerical investigation demonstrate the potential advantages of this method.

Design on the Prestressed Concrete Frame Beam-column

A bidirectional ribbed concrete beam slab structure was widly adopted for the upper space of industrial buildings.To maintain ample space and minimize the presence of conventional columns,a bidirectional prestressed concrete beam is often employed.The intersection node of the prestressed concrete frame beam column was characterized by a high density of steel reinforcement,significant structural loads,and complex construction requirements.To ensure the quality,safety,and progress of prestressed frame beamcolumn intersection nodes during construction,this article proposed a new technology for constructing such nodes,which includes setting the tensioning and haunching ends of nodes at different positions,using ABAQUS finite element software to optimize the design of cross-sectional dimensions,conducting stress analysis simulations.

螺栓联接结合面三维分形刚度模型与实验研究

为更准确地分析螺栓联接体的静动态特性,根据三维分形理论,考虑微凸体弹塑性接触在内的4种变形阶段,分别得到螺栓联接结合面的法向载荷与切向载荷,进而建立了螺栓联接结合面法向刚度与切向刚度模型,并分析了各参数对螺栓联接结合面刚度模型的影响关系。开展了有限元分析与实验研究,应用所建立的法向刚度与切向刚度模型,将考虑结合面影响的螺栓联接体有限元分析结果分别与忽略结合面影响的螺栓联接体有限元分析结果以及实验结果对比。研究结果显示,增大预紧力、工作载荷、分形维数、材料特性参数,或是减小分形尺度参数,可增大螺栓联接结合面的刚度;应用所建立结合面刚度模型的螺栓联接体有限元分析结果与实验结果误差在8%以内,远小于忽略结合面影响的有限元分析误差。

考虑结合面特性影响的机床整机有限元静力学分析模型

针对机床数字化设计中典型结合面建模精度误差较大的问题,提出了一种采用虚拟材料等效结合面静力学特性的方法,建立了考虑结合面特性影响的机床整机有限元静力学分析模型,并完成了相应的静刚度测试实验。首先,综合考虑了弹塑性变形机制和摩擦力的影响,提出了一种新的结合面法向和切向刚度的分析模型;其次,根据不同类型结合面的特点,采用虚拟材料模拟结合面的刚度特性,建立了刚度特性与虚拟材料弹性模量和泊松比的关系,并将其应用于精密数控机床整机的静刚度分析;最后,开展了整机工艺系统的静刚度测试实验,得到了主轴末端X、Y、Z三个方向的刚度分别为26.60 N/μm、41.87 N/μm和40.17 N/μm,并将其与仿真数据进行了对比。研究结果表明:不考虑结合面影响的模型相对误差将近17%,而考虑结合面影响的模型相对误差在5%以内,验证了考虑结合面特性影响的机床整机有限元静力学分析模型的有效性;采用虚拟材料等效结合面静力学特性的方法可作为机床数字化设计的一种可行的方法。

基于有限元修正法的薄膜温度本构构建及验证

目的由于薄膜在受力过程中易产生颈缩现象,且具有强烈的温度依赖性,现有工程应力-应变与本构模型均不能准确描述温度变化下的薄膜材料的载荷位移曲线,造成预测结果与实际严重不符,该问题亟待解决。方法在准静态拉伸(10 mm/min)与不同温度(-20、0、20、40、60℃)条件下,利用万能材料试验机对PE/PA/PE薄膜试样进行单轴拉伸试验,基于有限元修正法对材料的塑性应力进行修正,采用指数函数对PE/PA/PE薄膜的弹性模量、屈服强度进行描述,针对Johnson-Cook本构模型中的形函数进行修正,结合应变-温度耦合的温度项构建PE/PA/PE薄膜100%应变下的塑性应力-应变模型,在单层PE与五层PE/PA/PE/PA/PE薄膜中进行仿真验证。结果在-20~60℃下100%应变范围内薄膜颈缩从7.86 mm增加到8.12 mm;弹性模量、屈服强度与塑性应力随着温度的升高呈非线性降低;基于有限元修正法对真实应力应变进行修正并进行对比,发现相对误差由83.94%降低到4.73%;采用指数函数对弹性模量、屈服强度进行拟合,R2值分别为0.936和0.947;改进后的形函数与原模型对比,相对误差从42.5%降到6.49%;温度项与修正后的应力-应变最大相对误差为7.21%。将新构建的模型应用于PE与PE/PA/PE/PA/PE薄膜,最大相对误差为4.91%。结论在温度-20~60℃内,基于有限元修正法和修正后的本构模型能够很好地描述应变在100%以内的屈服强度、弹性模量和塑性应力随温度变化的规律,研究结果为薄膜的应用奠定了理论基础。

无额外自由度广义有限元扭曲网格仿真研究

研究了无额外自由度广义有限元方法在扭曲网格中仿真的健壮性。使用选择插值最小二乘方法构造的强化函数与额外自由度和网格无关。这使得此方法在避免了刚度阵奇异的同时,还拥有了对网格扭曲的鲁棒性。推导证明并展示了,无额外自由度广义有限元近似函数在扭曲网格中仍具有完美再生性。分别采用了规整和扭曲的网格对超弹性和亚弹-塑性两种材料进行了大变形仿真,在仿真中同时考虑了几何和材料的非线性,并将此方法同传统的线性有限元方法做了对比。三个典型仿真结果表明,所采用方法在扭曲网格中仍具有良好的准确性和收敛稳定性。