内压下破裂壳体结构的膨胀系数和几何非线性响应

基于裂缝边缘中心的横向或面外非线性动力响应,给出一种可行的方法以替代用于损伤容器设计的膨胀系数,并用以描述施加内压的破裂柱状壳体结构的特性。该法避免了膨胀系数的有限元分析中裂缝端网格选择的问题,还指出裂缝长度和裂缝宽度对响应的影响相同。发现裂缝宽度对响应的影响有重要的意义,但其在膨胀系数中是无用的。而且,目前单个膨胀系数仅适用于裂缝长度和壳半径比在某个范围的情况。研究表明:1)本文给出的方法不受裂缝长度与壳半径比值范围的限制;2)该法概念简单;3)从计算上看,由于目前的动力方法在粗网格处会快速收敛,通过使用基于壳体有限元的混合公式可以相对更加容易且准确有效地获得裂缝边缘中心的非线性响应。     

On the buckling of cylindrical shells with through cracks under axial load

Presence of cracks or similar imperfections can considerably reduce the buckling load of a shell structure. In this paper, the buckling of cylindrical shells with through cracks has been studied. A general finite element model has been proposed, verified and applied to some novel cracked shell buckling problems for which documented results are not available. A special purpose program has been developed for generating finite elements models of cylindrical shells with cracks of varying length and orientation. The buckling behavior of cracked cylinders in tension and compression has been studied. The results of the analysis are presented in parametric form when it seems to be appropriate. Sensitivity of the buckling load to the crack length and orientation has also been investigated.     

Buckling of cracked cylindrical thin shells under combined internal pressure and axial compression

Linear eigenvalue analysis of cracked cylindrical shells under combined internal pressure and axial compression is carried out to study the effect of crack type, size and orientation on the buckling behavior of cylindrical thin shells. Two types of crack are considered; through crack and thumbnail crack. Our calculations indicate that depending on the crack type, length, orientation and the internal pressure, local buckling may precede the global buckling of the cylindrical shell. The internal pressure, in general, increases the buckling load associated with the global buckling mode of the cylindrical shells. In contrast, the effect of internal pressure on buckling loads associated with the local buckling modes of the cylindrical shell depends mainly on the crack orientation. For cylindrical shells with relatively long axial crack, buckling loads associated with local buckling modes of the cylindrical shell reduce drastically on increasing the shell internal pressure. In contrast, the internal pressure has the stabilizing effect against the local buckling for circumferentially cracked cylindrical shells. A critical crack length for each crack orientation and loading condition is defined as the shortest crack causing the local buckling to precede the global buckling of the cylindrical shell. Some insight into the effect of internal pressure on this critical crack length is provided.     

Vibration, buckling and dynamic stability of cracked cylindrical shells

The presence of cracks in a structure can considerably affect its behaviour. This paper presents a finite element study on the vibration, buckling and dynamic stability behaviour of a cracked cylindrical shell with fixed supports and subject to an in plane compressive/tensile periodic edge load. The effects of crack length and orientation are analysed. Under tension load, the results show that the frequency of the shell initially increases with the load, but then decreases as the load further increases leading to buckling due to tension load. The size and the orientation of the crack and the loading parameter can all have a significant effect on the dynamic stability behaviour of the shell under both compressive and tensile loading. The effects of these parameters are discussed in detail.     

Fatigue Behavior Investigation and Stress Analysis for Rib-to-Deck Welded Joints in Orthotropic Steel Decks

The fatigue problems in orthotropic steel decks have raised widely concerns in recent years. This study focused on the root crack mechanism at rib-to-deck welded joints, based on the previous test results of sectional specimens and the matching FE analysis, the fatigue behaviors of structure detail were investigated by considering the effect of root gap shapes, weld penetrations, and plate thicknesses on crack initiation. Besides, various root crack depths were simulated in models to clarify the stress variations occurring during the propagation stage under cyclic loading. The results showed that the root gap shape and penetration rate have an impact on the root cracking direction and fatigue life at the initiation stage, but seem not directly related to the crack propagation mechanism; the higher penetration rate is advantageous for the prevention of root crack initiation. However, although the stiffness increased with the increase in plate thickness, the fatigue life of crack initiation might be reduced owing to the low fatigue strength of the thick deck plate, whereas the U-rib thickness has limited effect on the stress response of the root tip. Moreover, the significant difference between the 8 mm-crack model and other crack models is the high stress concentration around the crack tip. The stress conditions of root tip would be changed under loading cycles when a root crack propagated into half of deck plate thickness. Finally, the effect of structural dimensions on fatigue strength were also compared according to test results and FEA.     

Fracture toughness of high strength steel—using the notch stress intensity factor and volumetric approach

In the present paper, the crack initiation has been studied using notched circular ring specimens. A new criteria in brittle mode I fracture, based on normal stress at tip notch and the volumetric approach has been developed. The critical value of the notch intensity factor has been considered as fracture toughness.     

Instability of cracked CFRP composite cylindrical shells under combined loading

Numerical analysis of cracked composite cylindrical shells under combined loading is carried out to study the effect of crack size and orientation on the buckling behavior of laminated composite cylindrical shells. The interaction buckling curves of cracked laminated composite cylinders subject to different combinations of axial compression, torsion, internal pressure and external pressure are obtained, using the finite element method. In general, the internal pressure increases the critical buckling load of the CFRP cylindrical shells while torsion and external pressure decrease it. Numerical analyses show that axial crack has the most detrimental effect on the buckling load of a cylindrical shell while for cylindrical shells under combined external pressure and axial load, the global buckling shape is insensitive to the crack length and crack orientation.     

Buckling of cracked thin-plates under tension or compression

Plates are easily susceptible to buckling under compression, in particular when plate's thickness becomes sufficiently small with respect to others plate's sizes; such a mode of failure is often prevalent with respect to strength failure. The buckling phenomena under tension loading can also occur, especially in plates containing defects such as cracks or holes; when the buckling load is reached, complex wrinkling deflection patterns in compressed regions develops around such imperfections.In the present paper, the buckling analysis of variously cracked rectangular elastic thin-plates under tension and compression is considered. A short explanation of the buckling phenomena in plates is recalled and several numerical analyses, carried out by using the Finite Element Method (FEM), are performed in order to determine the critical load multiplier, both in compression and in tension, by varying some plates' parameters. In particular, the critical load multiplier is determined for different relative crack length, crack orientation and Poisson's coefficient of the plate's material which is made to range between 0.1 and 0.49.Moreover a simple approximate theoretical model to explain and predict the buckling phenomena in cracked plates under tension is proposed and some comparisons are made with FE numerical results in order to assess its reliability in predicting buckling load multipliers.Finally, the obtained results are graphically summarised (in dimensionless form) in several graphs and some interesting conclusions are drawn.     

氯氧镁水泥钢筋混凝土通电锈蚀的断裂性能分析

为了得到氯氧镁水泥钢筋混凝土开裂时的临界锈胀力,基于断裂力学研究了氯氧镁水泥钢筋混凝土在通电锈蚀试验下的断裂性能.根据Glinka-Shen权函数法,利用已知参考荷载下的裂纹尖端应力强度因子,得到孔边单裂纹方形板的权函数;然后推导出孔边单裂纹方形板的裂纹尖端应力强度因子计算公式;最后,由混凝土断裂准则给出通电锈蚀下混凝土开裂时临界锈胀力的计算公式及变化规律.结果表明:随着裂纹长度的增加,裂纹尖端应力强度因子增加,临界锈胀力减小;随着钢筋直径的增加,裂纹尖端应力强度因子减小.     

含裂纹三点弯曲试样裂纹尖端应力状态分析

裂纹尖端的应力状态与构件的断裂性能关系密切,尤其是厚度方向应力的影响更为显著。含裂纹三点弯曲试样是材料断裂行为研究的一种常用模型,本文以含裂纹三点弯曲试样为模型对裂纹尖端的应力状态进行了有限元分析。分析结果表明,平面内应力σx和σy最大值均出现在距离裂纹尖端一定距离处,并随着加载的进行而向外移动;厚度方向应力σz在裂纹顶端数值为零,在缺口尖端附近存在一个最大值,平面应变系数的最大值超过0.5,接近0.6。     

Fatigue performance of cracked rib-deck welded joint retrofitted by ICR technique

To evaluate the retrofit effect by ICR technique (a new technique developed in recent years), relative tests were carried out with two cracked rib-deck specimens. The fatigue performance, including crack propagation rate, remaining fatigue life, and stress variation was analyzed. An improvement was observed through the test results after the cracked specimen retrofitted. Crack propagation in the treated specimen was restrained by the closed surface and residual compressive stress, and the crack propagation rate was reduced significantly. Stress at the welded joint and the crack tip was redistributed after ICR treatment. An increasing has been found near the weld toe, and reduction is occurred at the crack tip, which matches FEM results. This stress variation might contribute to a delay in subsequent crack propagation.     

Finite element model updating on small-scale bridge model using the hybrid genetic algorithm

Finite element (FE) model-based dynamic analysis has been widely used to predict the dynamic characteristics of civil structures. FE model updating method based on the hybrid genetic algorithm, by combining genetic algorithm and the modified Nelder–Mead's simplex method, is presented to improve bridge structures' FE model. An objective function is formulated as a linear combination of fitness functions on natural frequencies, mode shapes and static deflections using measurements and analytical results to update both stiffness and mass simultaneously. A commercial FE analysis tool, which can utilise previously developed element library and solution algorithms, is adopted for applications on diversified and complex structures. The validity of the proposed method is verified by using a simply supported bridge model with three I-shaped girders. FE models such as grid, beam-shell and shell model are considered to modify initial FE models on the experimental structure. Experimental results suggest that the proposed method can be applied efficiently to various FE models and is feasible and effective when this method is applied to identify FE modelling errors.     

波浪腹板连接的双核防屈曲支撑承载力及滞回性能研究

提出一种用波浪腹板连接的双内核防屈曲支撑(简称CW-BRB)。CW-BRB由浪腹板连接两个内置一字板 内核的全钢约束矩形钢管组成,且两个一字板内核在伸出外围约束构件端头前后均通过肋板加强形成H形截面 ,整体外围约束的抗弯刚度及内核端部强度均获得极大改善,承载力设计效益显著提高。首先,简要介绍波 浪腹板剪切变形对CW-BRB弹性屈曲荷载的影响,为计算其约束比或正则化长细比提供依据。其次,重点研究 CW-BRB受力性能,通过建立CW-BRB的壳单元模型,分析其单调加载承载力与反复拉压荷载作用下的滞回性能 ,研究约束比变化对其受力性能与破坏机理的影响。最后,设计了1根单波浪腹板和1根双波浪腹板连接的 CW-BRB进行反复加载滞回性能试验研究,并采用壳单元及壳单元位移耦合技术建立CW-BRB试验试件的精细化 有限元模型,进行反复拉压荷载作用下的滞回性能数值模拟分析。试验结果与有限元计算结果吻合较好。     

Analysis of composite ENF specimen using higher order beam theories

Mathematical modelling, for the stress analysis of symmetric composite end notch flexure (ENF) specimen, has been presented using classical beam theory, first, second, and third order shear deformation beam theories to determine the strain energy release rate (SERR) for symmetric composites under mode II interlaminar fracture. In the present formulation, appropriate matching conditions have been applied at the crack tip and these matching conditions at the crack tip have been derived by enforcing the displacement continuity at the crack tip in conjunction with the variational equation. Compliance method has been used to calculate the SERR. Beam models under plane stress and plane strain conditions agree with each other with good performance to analyze the unidirectional and cross-ply composite ENF specimens, whereas for multidirectional composite ENF specimen, only the beam model under plane strain condition appears to be applicable with moderate performance. Third order shear deformation beam model of ENF specimen has been found to be better than other beam models in determining the SERR for unidirectional, cross-ply and multidirectional composites under mode II interlaminar fracture.     

Total strain FE model for reinforced concrete floors on piles

A finite element (FE) model using a total strain material model has been developed to predict the behavior of warehouse reinforced concrete floors on piles. The material model (not the FE model itself) was calibrated to material tests. The FE model for the floor structure was checked with full‐scale experiments. For a warehouse, punching load optimization and surface crack control are important design factors. It is concluded that if calibrated material models are used, total strain‐based FE models are able to indicate surface crack width and punching strength for several types of reinforcement. Furthermore, it is concluded that it is possible to develop a total strain material model from material tests. Copyright © 2007 John Wiley & Sons, Ltd.     

Experiments on conical shell reducers under uniform external pressure

In previous studies, a proliferation of research work has been undertaken on the buckling behavior of shell structures particularly conical shells. Nonetheless, no experimental studies are found in the literature on the buckling of a full and real configured model of a slender shell reducer with two cylindrical end boundaries. To this end, buckling behavior of three conical shell reducers under uniform peripheral pressure was investigated and evaluated experimentally in this paper. In addition, relevant FE simulations as well as theoretical predictions were taken into account to compare buckling load and modes of deformation. Derived results were aimed at generalizing the data for conical reducers in full scale within the range of this study.     

隧道周边不同位置径向裂纹对隧道围岩稳定性影响规律的研究

在爆炸载荷作用下,隧道周边会产生大量的径向裂隙,研究在双轴压缩荷载作用下不同位置处径向单裂纹直墙拱形隧道的破坏规律,分两种情况进行研究,一种是裂纹在隧道拱肩或拱顶部位,以拱顶半圆圆心为基点的径向裂纹;另一种是裂纹在隧道底板或边墙部位,其裂纹面与隧道底板、边墙成135°夹角。采用模型试验和数值模拟方法进行研究,模型试验采用水泥砂浆制作隧道模型,数值模拟计算隧道模型裂纹尖端应力强度因子和应力云图,模拟结果与试验结果对比较吻合。结果表明:1裂隙会降低隧道整体的稳定性以及抗压强度;2当裂纹在隧道拱肩或拱顶部位时,裂纹倾角θ=45°时,隧道的稳定性最差,最容易破坏;3当裂纹在隧道底板与边墙交界处时,隧道最容易破坏,整体稳定性最差。     

Fatigue Crack Tip Plasticity for Inclined Cracks

The evaluation of the crack tip deformation is essential to the estimation of crack growth under either static or cyclic loading. A 3-D elastic–plastic finite element analysis was developed to simulate the crack tip deformation along mixed mode inclined edge cracks in a steel plate subjected to either monotonic or cyclic loading at selected R-ratios. In this paper, two types of crack configurations were investigated: inclined cracks with equal inclined lengths (EICL) and inclined cracks with equal horizontal projection length (ECHP). The development of the monotonic (Δm) and cyclic (Δc) crack tip plastically zones and the monotonic (CTOD) and cyclic (ΔCTOD) crack tip opening displacements were traced to find the effect of the crack inclination angle, which significantly affected the size and shape of the crack tip plastic zone. The finite element results compared well with the analytical results based on modified Dugdale’s model. It was observed that Mode II has a significant effect on the plastic zone in the case of equal inclined crack length (EICL), i.e., Mode II increases as the crack angle decreases. Also, it is interesting to note that for the EICL case, the magnitude of Δc is delayed to appear with decreasing the inclination angle, for example, for θ?=?90° the cyclic plastic zone appeared at Δσ?=?103.32 MPa, while for θ?=?45° the cyclic plastic zone appeared at Δσ?=?132.84 MPa. Whereas, the variation of monotonic and cyclic plastic zone size in the equal crack horizontal projection (ECHP) case is not affected by the crack inclination angle. Furthermore, it was observed that the static crack tip opening displacement (CTOD) and the cyclic (ΔCTOD) are independent of the crack inclination angle in case of ECHP, due to such cracks take into consideration the effect of inclination angle through its length.     

Performance of orthogonal meshless finite volume method applied to elastodynamic crack problems

An orthogonal meshless finite volume method has been presented to solve some elastodynamic crack problems. An orthogonal weighted basis function is used to construct shape function so there is no problem of singularity in this new form. In this work, for three-dimensional dynamic fracture problems, a new displacement function is used at the tip of the crack to give a new OMFVM. When the new OMFVM is used, the singularity of the stresses at the tip of the crack can be shown better than that in the primal OMFVM. High computational efficiency and precision are other benefits of the method. Solving some sample crack problems of thin-walled structures show a good performance of this method.     

Accurate dynamic response of laminated composites and sandwich shells using higher order zigzag theory

Forced vibration response of laminated composite and sandwich shell is studied by using a 2D FE (finite element) model based on higher order zigzag theory (HOZT). This is the first finite element implementation of the HOZT to solve the forced vibration problem of shells incorporating all three radii of curvatures including the effect of cross curvature in the formulation using Sanders' approximations. The proposed finite element model satisfies the inter-laminar shear stress continuity at each layer interface in addition to higher order theory features, hence most suitable to model sandwich shells along with composite shells. The C₀ finite element formulation has been done to overcome the problem of C₁ continuity associated with the HOZT. The present model can also analyze shells with cross curvature like hypar shells besides normal curvature shells like cylindrical, spherical shells etc. The numerical studies show that the present 2D FE model is more accurate than existing FE models based on first and higher order theories for predicting results close to those obtained by 3D elasticity solutions for laminated composite and sandwich shallow shells. Many new results are presented by varying different parameters which should be useful for future research.