Fracture mechanics in timber engineering – Strength analyses of components and joints

Traditional timber engineering design approaches use for simple geometries stress- or strain-based criteria for strength analyses. For more complex cases purely empirical methods are also used. Although practical, purely empirical methods are not general, and could lead to estimations on the unsafe side, if extrapolated outside their original scope. It is furthermore known that stress- or strain-based methods are not useful in situations where large stress or strain concentrations arise, such as close to holes or notches, in dowel joints or in glued joints. Furthermore, such phenomena like size effects cannot be predicted, unless stochastic methods are introduced. The paper discusses some fracture mechanics strength analysis methods that in recent years have been proposed in relation to timber engineering strength design. The methods discussed range from simple hand calculations based on linear elastic fracture mechanics and useful for simple geometries to finite element analyses for general cases taking into account non-linear performance of the material during fracture. Fracture mechanics results in rational strength design, which is based on mechanics, as opposed to purely empirical methods, and with parameters with a clear physical meaning. In order to obtain material characteristics needed for this approach examples of test methods are discussed. Application examples include structural components, dowel joints and adhesive joints. Design formulae for beams with notches at the support and for the pull out strength of glued-in rods are presented.     

Finite-volume micromechanics of periodic materials: Past,present and future

The finite-volume method is now a well-established tool in the numerical engineering community for simulation of a wide range of problems in fluid and solid mechanics. Its acceptance by the mechanics of heterogeneous media community, however, continues to be slow, often characterized by confusion with the finite-element method or so-called higher-order theories. Herein, we provide a brief historical perspective on the evolution of this important technique in the fluid mechanics community, its transition to the solution of solid mechanics boundary-value problems initiated in Europe in 1988, and the recent developments aimed at the solution of unit cell problems of periodic heterogeneous media. The differences and similarities with the finite-element method are highlighted, and the resulting tangible advantages of the finite-volume technique discussed and illustrated. Finally, our most recent results in this area are presented which demonstrate the method’s capability of solving unit cell problems with complex architectures in a variety of settings and applications, while revealing undocumented effects of interest in the development of new material microstructures with targeted response. Recent attempts to develop alternative versions of this technique are also discussed, together with our ongoing work to generalize the finite-volume micromechanics approach in order to further enhance its predictive capabilities and efficiency.     

Approaches of fracture mechanics to the concept of engineering safety

We present basic principles of the concept of safety of complex engineering systems and discuss general problems of the mechanics of catastrophes. We generalize approaches of fracture mechanics to the analysis of safety and survivability of engineering systems. To estimate the admissibility of states of cracked engineering structures, one may introduce safety factors in the unified equations of fracture mechanics. We consider some methods for the calculation of safety factors within the framework of different criterional approaches of fracture mechanics. It should be emphasized that, in analyzing safety and survivability, one should, first of all, take into account the transition of a crack from the region of admissible states to the region of catastrophic fracture of engineering structures. Blagonravov Institute of Mechanical Engineering, Russian Academy of Sciences, Moscow. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 32, No. 2, pp. 35–42, March–April, 1996.     

Computational fracture mechanics: Research and application

This paper focuses on the impact of computational methodology on furthering the understanding of fundamental fracture phenomena. The current numerical approaches to the solution of fracture mechanics problems, e.g. finite element (FE) methods, finite difference methods and boundary element methods, are reviewed. The application of FE methods to the problems of linear elastic fracture problems is discussed. Particular emphases are placed on the stress intensity factors, energy release rate in mixed mode fracture and dynamic crack propagation. Numerical solutions of ductile fracture problems are surveyed. A special focus is placed on stable crack growth problems. The need for further research in this area is emphasized. The importance of large strain phenomena and accurate modeling of non-linearities is highlighted. An expanded version of fracture mechanics methodology is given by Liebowitz [Advances in Fracture Research 3. Pergamon Press, Oxford (1989)]; additional treatment is given in this paper to numerical results incorporating error estimates and algorithms for mesh design into the FE code. The adaptive method involves various stages which includes FE analysis, error estimation/indication, mesh refinement and fracture/failure analysis iteratively. Reference is made to integrate expert knowledge and a hierarchical, rule-based, decision process to fracture mechanics for the purpose of designing practical fracture-proof engineering products. Some further areas of research in adaptive finite element analysis are discussed.     

Fracture toughness measurement by cylindrical specimen with ring-shaped crack

A method for measuring the plane strain fracture toughness of metals by means of cylindrical specimen in tension with axi-symmetrical ring-shaped crack is discussed. Owing to the fact that the crack tip of such a specimen is closer to ideal plane strain state, the K_1c value measured is effective and reliable. This investigation has fairly satisfactorily solved the problems of crack prefabrication, experimental technique, data processing and requirements for specimen dimensions.In both safety evaluation and life estimation of engineering components by linear elastic fracture mechanics, it is necessary to measure the fracture resisting parameter—fracture toughness under plane strain. According to the ASTM-E399-74 standard[1], when measuring the fracture toughness K_1c values of medium and low strength steels with a standard compact tension specimen or three-point bending specimen, it is necessary to use specimens of large dimensions, great tonnage fatigue testing machine and universal testing mechine. Naturally, this presents great difficulties to the investigation and application of fracture mechanics and it is precisely for the purpose of overcoming these difficulties that we have studied the method of measuring the plane strain fracture toughness by a cylindrical specimen in tension with axi-symmetrical ring-shaped crack. This method has fairly satisfactorily solved the problems of crack prefabrication, experimental technique, data processing and requirements for specimen size. Owing to the fact that the field around the crack tip of such a specimen is closer to ideal plane strain state, the results obtained are values smaller than those by using compact tension and three-point bending specimens and are more reliable fracture resisting constants for materials in linear elastic fracture mechanics analysis. Moreover, this method is more practical and economical because no expensive large fatigue testing machine is needed and the specimen size is small.     

世界铁路发展状况及其关键力学问题 全国结构工程学术会议特邀报告

论述了世界部分发达国家和我国铁路发展情况、铁路运输的优点及其在经济建设中所发挥的作用。介绍了世界发达国家和我国铁路发展历史和未来轨道交通发展方向。详细讨论了现有铁路运输存在的问题和未来高速铁路亟待解决的关键力学问题。它们主要是:(1)弓网/列车/轨道(桥梁)大系统耦合动力学; (2)车辆结构强度和可靠度问题;(3)轮轨关系(脱轨、粘着、滚动接触疲劳和波浪形磨损、轮轨噪声);(4)高速列车弓网动力学和高速受流条件下摩擦磨损;(5)轨道结构关键力学和严酷环境下轨道工程破坏问题。这些问题直接危及到行车的安全和运行品质.并提出今后解决这些问题的主要方向。     

Finite fracture mechanics analysis of crack onset at a stress concentration in a UD glass/epoxy composite in off-axis tension

The presence of stress concentrations at holes and notches is known to reduce the strength of composite materials. Due to complexity of the damage processes at a stress raiser in a composite, different modeling approaches have been developed, ranging from empirical point and average stress criteria to involved damage mechanics or cohesive zone-based models of failure. Finite fracture mechanics approach with a coupled stress and energy failure criterion, recently developed and applied mainly to cracking in homogeneous isotropic materials, allows predicting the appearance and propagation of a crack using material strength and toughness characteristics obtained from independent tests. The present study concerns application of the finite fracture mechanics to the analysis of cracking at a notch in a UD glass/epoxy composite subjected to tensile off-axis loading. Based on UD composite strength and intralaminar toughness characterized by separate tests, finite fracture mechanics analysis provided conservative estimates of crack onset stress at the notch.     

Softening,localisation and adaptive remeshing. Capture of discontinuous solutions

Two approaches have been used in finite element studies of discontinuities (shocks) in fluid mechanics. These are discontinuity capture using suitable mesh adaptivity and discontinuity fitting by introduction of discontinuous shape functions in the formulation. Both procedures have been now used successfully in solid mechanics, but the paper discusses the particular advantages of the adaptive process.The causes of discontinuity in plastic failure are reviewed and differences from the analogous fluid mechanics problems are discussed.Dedicated to J. C. Simo     

Aspects of ductile fracture and adaptive mesh refinement in damaged elasto‐plastic materials

Numerical simulation of elasto‐plastic problems involving multi‐fracturing materials requires a reliable failure prediction technique and a robust solution algorithm. This work approaches ductile fracture by means of continuum damage mechanics, from which two new failure criteria based on coupled and uncoupled damage analysis are derived. A two‐parameter stress update algorithm for damaged materials based on a Newton–Raphson iterative procedure is presented. A posteriori error estimators using ductile failure concepts are also discussed. Copyright © 2001 John Wiley & Sons, Ltd.     

Comparative study of simulated annealing,genetic algorithms and tabu search for solving binary and comprehensive machine-grouping problems

Machine/part grouping problems have proven to be NP-complete and cannot be solved in polynomial time. Solving such problems of reasonable size often relies on heuristic approaches. Recently, several metaheuristic approaches have emerged as efficient tools for solving such problems. However, the development and implementation of such meta-heuristics have not been a trivial issue. The merits of each method and the problems involved in implementation may not be easily apprehended by practitioners, thereby posing difficulties in the selection of an efficient heuristic for industrial applications. For this reason, a comparative study of three important metaheuristic approaches--simulated annealing, genetic algorithms and tabu search for both binary (considering only machines and part types) and comprehensive (involving machine/part types, processing times, lot sizes, and machine capacities) machine grouping problems--was carried out. To test the performance of the three metaheuristics, two binary performance indices and two generalized performance indices were respectively used for binary and comprehensive machine/part grouping problems. The comparisons were made in terms of solution quality, search convergence behaviour and presearch effort. The results indicate that simulated annealing outperforms both genetic algorithm and tabu search particularly for large problems. The genetic algorithm seems slightly better than the tabu search method for the comprehensive grouping problems.     

Models and solution methodologies for the generalized grouping problem incellular manufacturing

In the present work, a generalized framework of machine-part grouping is considered where an operation can be performed on more than one machine. For group formation, both hierarchical and non-hierarchical approaches are proposed that use non-binary part-operation-machine incidence matrix. The grouping objective is to maximize the association of part operations with machines. For the non-hierarchical methods, heuristics based on Lagrangian relaxation are proposed to solve the resulting NP-complete problems. The relative suitability of the proposed approach for the various grouping scenarios is discussed. Numerical examples presented illustrate the issues related to the generalized grouping and various solution methodologies.     

Flow of a Polymer Solution between Two Rotating Rolls

A new model of calendering the film of a viscoelastic polymer solution based on the principles of mechanics of saturated porous media is suggested. The point of exit of the film from the gap is not prescribed as is done in traditional approaches but is determined from the condition of adhesion strength of the contact of the polymer with the rolls. An analytical solution of the stationary problem is obtained. Disturbances of this solution caused by periodic changes in the thickness of an incoming flow or a pulling rate are investigated.     

Analytical approaches to compression after impact (CAI) behavior of carbon fiber-reinforced composite materials

Analytical efforts to understand problems involving compression after impact (CAI) are reviewed. A theoretical solution of beam plate modeling is introduced to understand the buckling of multiple delaminated plates. Numerical efforts on CAI-related matters for rectangular plates are then briefly described to show the difficulties in evaluating the effects of the various factors on the compressive properties of impact-damaged laminates. Also, the reason for the simplification of the double-spiral damage to multiple circular delaminations is briefly explained from a mechanical viewpoint. Analytical schemes to evaluate the compressive strength of the impact-damaged laminates are introduced based on fracture mechanics. The accuracy and meaning of the solutions are discussed by comparing the present solutions with finite element analysis results.     

Computational fracture analysis of concrete gravity dams by crack-embedded elements––toward an engineering evaluation of seismic safety

From a point of view to utilize fracture mechanics of concrete for the solution of engineering problems, the problems in crack modeling, computational algorithm, and damping implementation are discussed in conjunction with safety assessment of concrete dam against large earthquakes. It is shown that the formulation for the crack-embedded element has an analogy with that of computational plasticity. This analogy enables us to utilize the return-mapping algorithm well established in computational plasticity for the dynamic analysis of crack growth in concrete. The ways of implementing damping to avoid diffused cracking are presented and simple examples of numerical analysis are shown to demonstrate the effect of damping and the performance of appropriate damping implementation for cracked elements.     

An integral equation approach to the computation of nonlinearfields in electrical machines

A numerical method based on an integral equation formulation, for the computation of nonlinear magnetostatic field, in two dimensions in cylindrical polar coordinates is given. The correctness of the method is illustrated by solving two linear two-dimensional magnetic field problems which have readily available analytical solutions. The dependence of the accuracy of the solution on the number and distribution of the meshes is studied on these examples. The method is then applied to the computation of the nonlinear field of a small salient pole synchronous machine. The technique used to accelerate the solution and other aspects of the solution are discussed. The program is used for the computation of magnetization characteristics, zero-power-factor characteristics, terminal voltages and their harmonics, and the field distribution in the air gap. Computed characteristics are compared with measurements. The results obtained illustrate that accurate and reasonably quick results are obtainable using this method     

Manufacturing cells' design in consideration of various production factors

A cell formation problem is introduced that incorporates various real-life production factors such as the alternative process routing, operation sequence, operation time, production volume of parts, machine capacity, machine investment cost, machine overload, multiple machines available for machine types and part process routing redesigning cost. None of the cell formation models in the literature has considered these factors simultaneously. A similarity coefficient is developed that incorporates alternative process routing, operation sequence, operation time and production volume factors. Although very few studies have considered the machine capacity violated issue under the alternative process routing environment, owing to the difficulties of the issue discussed here, these studies fail to deal with the issue because they depend on some unrealistic assumptions. Five solutions have been proposed here and are used to cope with this difficulty. A heuristic algorithm that consists of two stages is developed. The developed similarity coefficient is used in stage 1 to obtain basic machine cells. Stage 2 solves the machine-capacity violated issue, assigns parts to cells, selects process routing for each part and refines the final cell formation solution. Some numerical examples are used to compare with other related approaches in the literature and two large size problems are also solved to test the computational performance of the developed algorithm. The computational results suggest that the approach is reliable and efficient in either the quality or the speed for solving cell formation problems.     

Parallel eigenanalysis of multiaquifer systems

Finite element discretizations of flow problems involving multiaquifer systems deliver large, sparse, unstructured matrices, whose partial eigenanalysis is important for both solving the flow problem and analysing its main characteristics. We studied and implemented an effective preconditioning of the Jacobi–Davidson algorithm by FSAI‐type preconditioners. We developed efficient parallelization strategies in order to solve very large problems, which could not fit into the storage available to a single processor. We report our results about the solution of multiaquifer flow problems on an SP4 machine and a Linux Cluster. We analyse the sequential and parallel efficiency of our algorithm, also compared with standard packages. Questions regarding the parallel solution of finite element eigenproblems are addressed and discussed. Copyright © 2005 John Wiley & Sons, Ltd.     

Mixed Approximation Scheme of the Finite-Element Method for the Solution of Two-Dimensional Problems of the Elasticity Theory

For the solution of two-dimensional boundary-value problems of the elasticity theory, a triangular finite element, ensuring stability and convergence of mixed approximation, is proposed. The system of resolving equations of the mixed method is derived with account of strict satisfaction of static boundary conditions at the surface. To solve matrix equations of the mixed method, various algorithms of the conjugate-gradient method with the pre-conditional matrix have been considered. Numerical data on convergence and accuracy of the solution for a number of test problems of the elasticity theory and fracture mechanics are given. The results obtained by the conventional and mixed finite-element method approaches are compared.     

高温下张弦梁结构力学特征解析解

在实腹钢梁或钢桁架下部张拉预应力高强钢索形成预应力张弦梁结构,然而钢索的预应力对温度变化敏感,因此火灾是危及张弦梁结构安全性的重要灾害,求解高温下结构的力学特征解析解是进一步研究其火灾安全性能的理论基础。考虑高温下钢材材性的衰减、非线性热应变以及几何形变的耦合,建立张弦梁结构高温下梁单元与索单元建立基本平衡微分方程,分别推导出在均布荷载作用下张弦梁结构在均匀温度场及非均匀温度场中,结构跨中挠度、预应力索水平张力和撑杆轴力的解析解;并且基于张弦梁结构力学特征解析解,对比分析了张弦梁结构热力耦合数值分析模型的可靠性,可为后继设计张弦梁受火试验方案及研究其受火破坏机理提供参考。     

土工结构安全系数定义及相应计算方法讨论

以地基承载力、土坡稳定等常见土工结构问题为例,讨论土工结构安全系数的两种不同定义,一是极限 荷载与容许荷载之比,一是已有强度参数与保持稳定所需强度参数之比。分析表明,前一定义仅对某些结构适用, 而后一定义原则上可用于各种结构,具体选用要看结构及其所处环境的情况。当两种定义均适用时,允许安全系 数的取值可有较大差别,具体设计时应予注意。此外,还对两种安全系数的计算方法进行了讨论,包括滑移线法、极限平衡法、极限分析法等传统方法以及近年来应用日趋广泛的弹塑性有限元法、有限元极限分析法等,对各类 方法的优缺点及应用时需注意的问题给出自己的看法。