基于扩展有限元法的黏聚性裂缝模型的混凝土梁断裂过程模拟

为研究混凝土梁的断裂过程,提出用基于二维扩展有限元法（eXtended Finite ElementMethod,XFEM）的黏聚性裂缝模型模拟混凝土简支梁在集中载荷作用下的断裂过程.推导考虑近裂尖奇异性的基于XFEM的黏聚性裂缝模型,得出裂缝开度随裂缝长度的变化曲线;对上述模型与相关文献用有限元结合节点释放技术对相同时间的裂缝扩展的计算结果进行比较,二者结果吻合良好,并与实际裂缝扩展过程相符.计算结果证实基于XFEM的黏聚性裂缝模型能有效进行混凝土梁的断裂过程模拟.     

Topology optimization considering fracture mechanics behaviors at specified locations

As a typical form of material imperfection, cracks generally cannot be avoided and are critical for load bearing capability and integrity of engineering structures. This paper presents a topology optimization method for generating structural layouts that are insensitive/sensitive as required to initial cracks at specified locations. Based on the linear elastic fracture mechanics model (LEFM), the stress intensity of initial cracks in the structure is analyzed by using singularity finite elements positioned at the crack tip to describe the near-tip stress field. In the topology optimization formulation, the J integral, as a criterion for predicting crack opening under certain loading and boundary conditions, is introduced into the objective function to be minimized or maximized. In this context, the adjoint variable sensitivity analysis scheme is derived, which enables the optimization problem to be solved with a gradient-based algorithm. Numerical examples are given to demonstrate effectiveness of the proposed method on generating structures with desired overall stiffness and fracture strength property. This method provides an applicable framework incorporating linear fracture mechanics criteria into topology optimization for conceptual design of crack insensitive or easily detachable structures for particular applications.     

ALOF——新一代三维疲劳裂纹扩展分析软件

针对当前亟需开发能分析和评估含缺陷工程结构及装备的专业商业软件的现况,基于成熟的扩展有限元法(eXtended Finite Element Method,XFEM)和自主研发的虚节点法(Virtual Node Method,VNM),推出具有完全自主知识产权的三维疲劳裂纹扩展分析软件ALOF(Analyses Laboratory of Fracture).介绍ALOF求解断裂问题的流程及其特点:可以方便地导入完整的CAD模型及多种形式的裂纹模型,可以自动生成疏密合理的二维和三维裂纹扩展分析网格;具有丰富的失效准则库;能自动分层加密裂尖区域网格;能全自动地进行裂纹扩展计算等.与同类软件相比,ALOF更简单、更精准、更高效和更专业.利用ALOF进行的3个实际工程案例表明,ALOF能准确、高效评估任意复杂缺陷体的剩余强度和疲劳寿命.     

基于XFEM和正交实验法的裂纹参数对扭杆强度影响的分析

为研究裂纹对扭杆安全运行的影响,采用扩展有限元法（eXtended Finite Element Method, XFEM）对其进行裂纹扩展分析,并结合正交实验法研究裂纹参数对扭杆强度的影响.结果表明：裂纹的长度对扭杆强度影响最大,裂纹的形状对扭杆强度影响最小.该数值分析方法可应用于扭杆的设计和检修中.     

Study of TBM cutterhead fatigue crack propagation life based on multi-degree of freedom coupling system dynamics

Cutterhead is the core component of TBM tunneling equipment, which endures strong, multi-point distributed impact loads when the TBM tunnels, owing to the extreme surrounding rock environment of high hardness, high temperature and high quartz content. For this reason, the cutterhead works in an extremely severe vibration environment, which leads to engineering fault by a large area crack damage before the service life. Hence, the study on life prediction of TBM cutterhead under the impact loads is a core part of cutterhead design. This paper combines with the technology of system dynamics, linear elastic fracture mechanics and cumulative theory of fatigue damage, for the first time, proposes a method of fatigue crack propagation life prediction for the large and complex structures. In this paper, the TBM cutterhead of an actual project is taken as an example, to predict the fatigue crack propagation life of cutterhead piece and analyze the influences of plate thicknesses on fatigue life, then a new improved scheme of cutterhead structure is presented. The results show that the fatigue crack propagation life of actual cutterhead is 26.6 km, which is able to meet the requirement of 20 km service life. Moreover, the upper cover plate thickness has the greatest influence on cutterhead fatigue crack propagation life, with the thickness increasing 10%, the life increases nearly by 1.24 times. Then, the other influencing factors are as follows: thickness of the main support plate, thickness of the annular support plate and thickness of the support plate, whereas the influence of the lower cover plate thickness on fatigue life is minimal. Furthermore, the plate thickness limit sizes meeting the life requirement are obtained, and a new structure modified scheme of cutterhead is proposed. Compared with the original scheme, the new cutterhead scheme meets the requirements of structural strength and service life with 8.08% weight decrease, which achieves life determination design and lightweight design. The proposed method of fatigue crack propagation life prediction is feasible in the design and application stage of TBM cutterhead, besides, it is flexible enough and can also be applied in damage strength assessment, dynamic parameters optimization and establishment of nondestructive inspection cycle for the other large and complex structure, and takes on stronger project value and generality.     

A level-set-based topology and shape optimization method for continuum structure under geometric constraints

Recent advances in level-set-based shape and topology optimization rely on free-form implicit representations to support boundary deformations and topological changes. In practice, a continuum structure is usually designed to meet parametric shape optimization, which is formulated directly in terms of meaningful geometric design variables, but usually does not support free-form boundary and topological changes. In order to solve the disadvantage of traditional step-type structural optimization, a unified optimization method which can fulfill the structural topology, shape, and sizing optimization at the same time is presented. The unified structural optimization model is described by a parameterized level set function that applies compactly supported radial basis functions (CS-RBFs) with favorable smoothness and accuracy for interpolation. The expansion coefficients of the interpolation function are treated as the design variables, which reflect the structural performance impacts of the topology, shape, and geometric constraints. Accordingly, the original topological shape optimization problem under geometric constraint is fully transformed into a simple parameter optimization problem; in other words, the optimization contains the expansion coefficients of the interpolation function in terms of limited design variables. This parameterization transforms the difficult shape and topology optimization problems with geometric constraints into a relatively straightforward parameterized problem to which many gradient-based optimization techniques can be applied. More specifically, the extended finite element method (XFEM) is adopted to improve the accuracy of boundary resolution. At last, combined with the optimality criteria method, several numerical examples are presented to demonstrate the applicability and potential of the presented method.     

Design study of hole positions and hole shapes for crack tip stress releasing

The method of hole drilling near or at the crack tip is often used in fatigue damage repair. From a design optimization point of view, two questions are posed: Where should the hole(s) be drilled? And is there a better shape of the hole than a circular one? For the first question, we extend earlier results for isotropic material and in general study the influence of having orthotropic material. Optimal shapes are by no means circular, and we focus on the shape of a single hole centered at (or in front of) the crack tip. It is shown that the stress field at the crack boundary can be significantly improved by noncircular shapes. As a byproduct, an alternative method for extracting the stress intensity factor from a finite element analysis is presented.     

XFEM在高压管道裂纹扩展计算中的应用

介绍XFEM的基本理论,针对常规有限元计算困难的三维裂纹,运用XFEM完成三维高压管道中的裂纹扩展计算.根据管道裂纹扩展的计算结果,总结得到管道裂纹扩展的规律,得到径向裂纹比轴向裂纹更严重的结论.     

基于XFEM的折弯片断裂仿真

采用Abaqus的XFEM功能对折弯片的断裂问题进行仿真,断裂区为转角处的过渡区域.转角处圆弧的半径影响裂纹的开裂时间.裂纹的扩展路径具有任意性,细化网格下裂纹扩展方向不稳定,会超出断裂区.1阶单元和1阶减缩积分单元的分析结果比较接近.通用静态分析比动态隐式分析效率更高一些.在端部压力的作用下,折弯片约在1 ms内开裂,8 ms完全断开.Cohesive element算法的裂纹路径较LEFM方法更平滑一些.     

Automatic LEFM crack propagation method based on local Lepp–Delaunay mesh refinement

A numerical method for 2D LEFM crack propagation simulation is presented. This uses a Lepp–Delaunay based mesh refinement algorithm for triangular meshes which allows both the generation of the initial mesh and the local modification of the current mesh as the crack propagates. For any triangle t, Lepp(t) (Longest Edge Propagation Path of t) is a finite, ordered list of increasing longest edge neighbor triangles, that allows to find a pair of triangles over which mesh refinement operations are easily and locally performed. This is particularly useful for fracture mechanics analysis, where high gradients of element size are needed. The crack propagation is simulated by using a finite element model for each crack propagation step, then the mesh near the crack tip is modified to take into account the crack advance. Stress intensify factors are calculated using the displacement extrapolation technique while the crack propagation angle is calculated using the maximum circumferential stress method. Empirical testing shows that the behavior of the method is in complete agreement with experimental results reported in the literature. Good results are obtained in terms of accuracy and mesh element size across the geometry during the process.     

An evolutionary shape optimization for elastic contact problems subject to multiple load cases

Most structures in the real life are subject to multiple load cases. This paper aims at extending the evolutionary structural optimization (ESO) algorithm to optimal contact shape design for elastic bodies under the multiple load cases. To evaluate the reference stresses of each contact node in a finite element framework, an extreme stress criterion (the worst case design) and a weighted average criterion (Pareto design) are presented. In the extreme stress method, the highest nodal contact stress under all load cases is adopted as the reference level. In the weighted average method, the weighted sum of nodal contact stresses over all the load cases is regarded as the reference. It is found that these two criteria can produce different results. In this paper, the examples are presented to demonstrate some new features of contact shape optimization in the presence of the multiple load cases.     

Explicit level set and density methods for topology optimization with equivalent minimum length scale constraints

The goal of this paper is to introduce local length scale control in an explicit level set method for topology optimization. The level set function is parametrized explicitly by filtering a set of nodal optimization variables. The extended finite element method (XFEM) is used to represent the non-conforming material interface on a fixed mesh of the design domain. In this framework, a minimum length scale is imposed by adopting geometric constraints that have been recently proposed for density-based topology optimization with projections filters. Besides providing local length scale control, the advantages of the modified constraints are twofold. First, the constraints provide a computationally inexpensive solution for the instabilities which often appear in level set XFEM topology optimization. Second, utilizing the same geometric constraints in both the density-based topology optimization and the level set optimization enables to perform a more unbiased comparison between both methods. These different features are illustrated in a number of well-known benchmark problems for topology optimization.

     

Identification of multiple flaws in 2D structures using dynamic extended spectral finite element method with a universally enhanced meta-heuristic optimizer

In this paper, flaw detection of two-dimensional structures is carried out using the extended spectral finite element method (XSFEM) associated with particle swarm optimization (PSO) algorithm enhanced by a new so-called active/inactive flaw (AIF) strategy. The AIF strategy, which is inspired from earthquake engineering concepts, is proposed for the first time in this paper. The XSFEM is employed to model the cracked and holed structures, while the PSO, which is a suitable non-gradient method for solving such problems, is employed to find crack location as an optimizer. The XSFEM consists of remarkable capabilities with the main features of spectral finite element method (SFEM) and extended finite element method (XFEM) to analyze the damaged structures without remeshing, leading it to be a proper approach in iterative processes. Moreover, the XSFEM enhances the accuracy of wave propagation analysis, and decreases computational cost as well in comparison with the XFEM. The application of XSFEM in damage detection of structures is studied for the first time in this paper. Furthermore, the AIF strategy is proposed in order to handle a simultaneously discrete and continuous optimization in an efficient way reducing computational effort. Considering the AIF as a universal strategy, it can be used in any meta-heuristic optimizer. In this research, the PSO is seeking for geometrical properties and the number of flaws in order to detect them by minimizing an error function based on sensor measurements. To overcome the challenge of unknown number of flaws, the proposed AIF strategy is employed in the PSO. Several benchmark examples are examined to evaluate capability and accuracy of the proposed algorithm for detection of cracks and holes.     

Axisymmetric shell optimization under fracture mechanics and geometric constraint

This paper describes a problem of axisymmetric shell optimization under fracture mechanics and geometric constraints. The shell is made from quasi-brittle materials, and through crack arising is admitted. It is supposed that the shell is loaded by cyclic forces. A crack propagation process related to the stress intensity factor is described by Paris fatigue law. The problem of finding the meridian shape and the thickness distribution (geometric design variables) of the shell having the smallest mass subject to constraints on the cyclic number for fatigue cracks and geometrical constraint on the shell volume is investigated. Special attention is devoted to different possibilities of problem transformation and analytical methods of their solution. Using minimax approach, optimal shapes of the shells and their thickness distributions have been found analytically.     

Shape optimization of heavy load carrying components for structural performance and manufacturing cost

This paper addresses the trade-off between structural performance and manufacturing cost of heavy load carrying components by incorporating virtual machining (VM) technique in computer-aided design (CAD)-based shape optimization problem. A structural shape optimization problem is set up to minimize total cost, subject to the limits on structural performance measures. For every design iteration, finite element analysis (FEA) is conducted to evaluate structural performance, and VM is employed to ascertain machinability and estimate machining time. Design sensitivity coefficients of objective function and constraints are computed and supplied to the optimization algorithm. Based on the gradients, the algorithm determines design changes, which are used to update FEA and VM models. The process is repeated until specified convergence criterion is satisfied. Application programs developed to integrate commercially available CAD/CAM/FEA/Design optimization tools enable implementation in virtual environment and facilitate automation. The application programs can be reused for similar design problems provided that the same set of tools is used.     

A CAD-based design parameterization for shape optimization of elastic solids

In this paper a CAD-based design sensitivity analysis (DSA) and optimization method using Pro/ENGINEER for shape design of structural components is presented. The CAD-based design model is critically important for multidisciplinary shape design optimization. Only when each discipline can compute the design sensitivity coefficients of the CAD-based design model, can a true multidisciplinary what-if study, trade-off analysis, and design optimization be carried out. The proposed method will allow the design engineer to compute design sensitivity coefficients of structural performance measures such. as stress and displacement, evaluated using existing finite element analysis (FEA) tools, both h- and p-versions, with respect to design variables defined in the parameterized CAD model. The proposed method consists of (i) a CAD-based design parameterization technique that ties the structural DSA and optimization to a CAD tool; (ii) a design velocity field computation that defines material point movement due to design change in CAD geometry, satisfies linearity and regularity requirements, and supports both hand p-version FEA meshed using existing mesh generators; and (iii) a design optimization method that supports structural geometric and finite element model updates in Pro/ENGINEER during the optimization process.     

Accuracy test of sensitivity analysis in the semi-analytic method with respect to configuration variables

Configuration optimization is a structural optimization method where the geometrical shape of the structures can be changed during the optimization process. Sensitivity informations are required in the general optimization and quite costly. Especially, they are extemely expensive in the structural optimization where the finite element analysis is utilized. Since the nodal coordinates are regarded as design variables in the configuration optimization, the sensitivities according to the nodal coordinates must be calculated. The characteristics of the configuration optimization is that the transformation matrix in the finite element analysis is a function of design variables. Thus the sensitivity calculation in the configuration optimization is even more complicated. For the efficient sensitivity calculations, various methods have been proposed. They are the analytic method (AM), overall finite difference method (OFD), and semi-analytic method (SM). The semi-analytic method consists of the forward and central difference approximation. This study has been conducted to choose an appropriate method by comparison based on the mathematical and numerical aspects. Some standard structural problems are selected for the evaluations.