一维六方准晶层合简支梁自由振动与屈曲的精确解

伪Stroh型公式能够将多场耦合材料的控制方程转化为线性特征系统来求解,从而获得多层结构简支边界条件的精确解.本文利用伪Stroh型公式,研究一维六方准晶层合简支梁的自由振动和屈曲问题,通过传递矩阵法,获得准晶层合梁自由振动固有频率与临界屈曲载荷的精确解.通过与已有梁的剪切变形理论结果比较,验证了本文伪Stroh型公式的正确性和有效性.通过数值算例,分析由两种不同准晶材料组成的三明治层合梁的叠层方式、高跨比、层厚比及层数对梁的固有频率、临界屈曲载荷及其模态的影响规律.结果表明,叠层顺序和梁的高跨比、层厚比对准晶层合梁的自由振动固有频率和临界屈曲载荷有很大影响,可通过调整梁的几何尺寸和叠层顺序得到准晶层合梁的最佳固有频率和临界屈曲载荷.本文给出的精确解可为工程上研究准晶梁的各种数值解法和实验方法提供理论参考.     

冲击荷载与火灾联合作用下SFRC梁的力学行为

为了探究冲击荷载与火灾联合作用下钢纤维混凝土(steel fiber reinforced concrete, SFRC)梁的力学性能,联合应用高性能落锤试验系统、四点弯曲实验装置与装配式电炉开展了4根SFRC梁的冲击实验与高温恒载实验,观察了其破坏模式并记录了跨中位移和钢筋应变的时程曲线,探讨了冲击损伤SFRC梁的抗火性能。此外,在实验研究的基础上,考虑材料的应变率强化效应及温度软化效应,建立数值模型,首先对梁进行冲击加载模拟,并以冲击模拟结果为初始状态,采用热-力“顺序”耦合方法,对冲击加载与高温恒载联合作用下SFRC梁的力学行为进行了三维宏观有限元数值模拟。同时,考虑混凝土内部结构非均质性的影响,采用类似步骤,开展了细观模拟。宏/细观模拟结果与实验结果的良好吻合验证了本文数值方法的合理性与有效性,并体现了细观方法的优越性。研究发现,冲击能量较小时,SFRC梁在冲击荷载作用下,尽管局部混凝土开裂,梁整体残余变形较小,抗火性能有一定程度的下降;随着钢纤维掺量增大,混凝土基体抗剪强度增大,SFRC梁在冲击荷载作用下的开裂形态由弯剪裂缝并存向以弯曲裂缝为主转变;冲击损伤SFRC梁在高温恒载作用下裂缝分布较为集中,且发生脆性破坏。     

高层建筑结构边节点抗震性能研究

通过7根留有施工缝的高层建筑结构边节点的低周反复抗震性能试验,研究了轴压比、节点核心区的混凝土强度等级、柱中混凝土在梁中的延伸长度等对梁柱边节点抗震性能的影响,对构件的破坏特征、承载能力、延性性能、滞回曲线和骨架曲线进行了对比分析。试验结果表明:所有试验构件均为梁端受弯破坏;柱中混凝土在梁中的延伸长度对骨架曲线的形态、屈服荷载和最大荷载都没有显著影响;但是延伸长度对节点的延性性能是有影响的,延伸长度为0.5h(h为梁高)的边节点构件的位移延性系数小于延伸长度为1.0h和1.5h的构件。     

冻融和疲劳对预应力受弯构件损伤的影响

通过15根预应力及普通混凝土试验梁在经历不同冻融循环次数后的疲劳试验, 探索试验梁 相对动弹模衰减规律, 以相对动弹模为损伤变量, 通过方差分析方法定量分析冻融和疲劳两 种因素对构件损伤的影响. 研究表明试验梁在冻融和疲劳荷载双因素作用下, 初期以冻融损 伤为主, 之后很快发展为以疲劳损伤为主, 疲劳损伤是构件的主要损伤因素. 施加预应力或 提高预应力度对试验梁疲劳损伤有较明显的抑制作用, 将缩短试验梁全寿命中以疲劳损伤为 主的时间.     

THE FAILURE MODES OF CONCRETE BEAMS STRENGTHENED WITH NEAR SURFACE MOUNTED FRP BARS

为研究不同参数下表面内嵌纤维筋加固后T 形混凝土梁的破坏模式, 对5 根不同梁端锚固、FRP(fiber reinforced polymer) 筋表面特征和FRP 筋类型的T 形混凝土梁进行受弯性能试验. 结果表明, 无梁端锚固、光圆GFRP (glass fiber reinforced polymer) 筋和CFRP (carbon fiber reinforced polymer) 筋加固梁试件发生粘结破坏. 梁端锚固和FRP 筋表面特征影响加固梁试件的极限载荷, CFRP 筋加固梁试件的屈服载荷和极限载荷较大. 螺纹FRP 筋和有梁端锚固加固梁试件FRP 筋利用率较高. 因此, 有梁端锚固的表面内嵌螺纹GFRP 筋加固是最为有效的加固方式.     

复合材料层合梁在横向线载荷下的脱层扩展

基于可动边界变分原理对层合梁脱层扩展进行了分析;考虑了脱层间的接触效应,建立了层合梁在横向线载荷作用下的非线性控制微分方程及相应的定解条件;应用Griffith准则导出了脱层前缘各点处的能量释放率表达式;通过算例讨论了脱层长度、脱层深度、几何尺寸、材料性质等因素对脱层扩展的影响.研究表明:脱层越长、越深、横向载荷越大,脱层越容易扩展;梁的长高比L/h及材料的E_(11)/E_(22)越大,脱层越不易发生扩展.     

Elasticity solutions for plane anisotropic functionally graded beams

This paper considers the plane stress problem of generally anisotropic beams with elastic compliance parameters being arbitrary functions of the thickness coordinate. Firstly, the partial differential equation, which is satisfied by the Airy stress function for the plane problem of anisotropic functionally graded materials and involves the effect of body force, is derived. Secondly, a unified method is developed to obtain the stress function. The analytical expressions of axial force, bending moment, shear force and displacements are then deduced through integration. Thirdly, the stress function is employed to solve problems of anisotropic functionally graded plane beams, with the integral constants completely determined from boundary conditions. A series of elasticity solutions are thus obtained, including the solution for beams under tension and pure bending, the solution for cantilever beams subjected to shear force applied at the free end, the solution for cantilever beams or simply supported beams subjected to uniform load, the solution for fixed–fixed beams subjected to uniform load, and the one for beams subjected to body force, etc. These solutions can be easily degenerated into the elasticity solutions for homogeneous beams. Some of them are absolutely new to literature, and some coincide with the available solutions. It is also found that there are certain errors in several available solutions. A numerical example is finally presented to show the effect of material inhomogeneity on the elastic field in a functionally graded anisotropic cantilever beam.     

Flexural time-dependent cracking and post-cracking behaviour of FRP strengthened concrete beams

The time-dependent flexural cracking behaviour of reinforced concrete beams strengthened with externally bonded composite materials is investigated with a focus on the creep effects. A theoretical model is developed, which accounts for the creep of the different materials involved, and which also accounts for the time-dependent cracking and the tension-stiffening phenomenon. The deformability of the adhesive layer in shear and through its thickness, as well as its ability to transfer shear and vertical normal stresses, is considered in the model. The incremental governing equations are formulated via the variational principle of virtual work based on an incremental exponential algorithm for the creep modelling. The capabilities of the model are demonstrated through numerical examples including a comparison with test results available in the literature. The results show that creep causes a significant redistribution of the internal forces and the interfacial stresses at the adhesive interfaces with time, which should be carefully considered in the design of FRP strengthened members.     

四光束载波全息光弹性法的研究及应用

本文同时利用一台激光器的相干性和两台无位相联系的激光器间的非相干特性,提出了一种新的全息光弹性法,并用于等和线的测量上.该方法具有载波频率连续可调,一次曝光给出某一载荷下的等和载波条纹图的优点;通过滤波解调,能方便地给出模型受力过程中任意两个载荷下的差载等和线,为不能重复性实验(如裂纹扩展)提供了新的实验研究方法。     

模拟酸雨腐蚀下预应力混凝土梁的抗弯性能研究

为了探讨酸雨腐蚀环境对预应力混凝土梁抗弯性能的影响,制作了8根预应力混凝土梁,从混凝土强度等级、预应力度和钢绞线腐蚀率等方面,进行8根预应力混凝土梁的三分点静载试验。试验结果及分析表明,混凝土强度对屈服后试验梁的抗弯性能影响较大,对弹性阶段的刚度影响较小;随着预应力度的增加,试验梁的开裂荷载逐渐增大,进入裂缝阶段后,刚度下降速度逐渐加快;钢绞线腐蚀率越大,试验梁的极限抗弯承载力越低;腐蚀率在一定范围内（>3.22%）,随着腐蚀率的增大,预应力混凝土梁试件的开裂弯矩、屈服弯矩和极限弯矩明显降低。根据试验结果,提出了模拟酸雨环境下预应力混凝土梁试件抗弯承载力的计算方法,同时采用ANSYS软件对预应力混凝土梁进行非线性有限元分析,将试验梁的计算值和模拟值与试验值进行比较,均吻合较好。     

Analytic elasticity solution of bi-modulus beams under combined loads

A unified stress function for bi-modulus beams is proposed based on its mechanic sense on the boundary of beams. Elasticity solutions of stress and displacement for bi-modulus beams under combined loads are derived. The example analysis shows that the maximum tensile stress using the same elastic modulus theory is underestimated if the tensile elastic modulus is larger than the compressive elastic modulus. Otherwise, the maximum compressive stress is underestimated. The maximum tensile stress using the material mechanics solution is underestimated when the tensile elastic modulus is larger than the compressive elastic modulus to a certain extent. The error of stress using the material mechanics theory decreases as the span-to-height ratio of beams increases, which is apparent when L/h ≤5. The error also varies with the distributed load patterns.     

无腹筋RC悬臂梁抗剪强度及尺寸效应理论研究

不同于混凝土材料,钢筋混凝土(RC)构件的破坏模式与机制更为复杂,采用混凝土材料尺寸效应理论难以描述构件的尺寸效应行为。我国相关规范中并没有系统考虑构件尺寸及纵筋率对RC梁抗剪承载力的影响。为研究剪跨比及纵筋率对无腹筋RC梁剪切破坏及抗剪强度尺寸效应的影响,采用三维细观数值模拟方法,建立了RC梁剪切破坏力学分析模型,研究了剪跨比及纵筋率对RC梁剪切破坏及抗剪强度尺寸效应的影响机制与规律。研究结果表明,RC梁抗剪强度表现出极为显著的尺寸效应现象;RC梁抗剪强度随剪跨比的增大而减小,随纵筋率的增大而增大;剪跨比较小时,纵筋率对抗剪强度的影响尤为显著。此外,基于Ba■ant材料层次尺寸效应律,提出了考虑剪跨比及纵筋率影响的RC梁抗剪强度尺寸效应理论公式。对比试验结果,验证了所提公式的准确性与合理性。     

Experimental study and analysis of RC beams strengthened with CFRP laminates under sustaining load

Six reinforced concrete beams strengthened in flexure using carbon fiber reinforced polymer (CFRP) laminates subjected to different sustaining loads were tested. The main goal of the test is to examine the effects of initial load and load history on the ultimate strength of strengthened reinforced concrete beams by externally bonded CFRP laminates. The main experimental parameters include different levels of sustaining load at the time of strengthening and load history. To explain the experimental results in quantitative terms, a theoretical model for flexural behavior of the strengthened reinforced concrete beam is also developed. Test results in the current study show that sustaining load levels at the time of strengthening have important influence on the ultimate strength of strengthened reinforced concrete beams. If the initial load is basically same, the ultimate strength of reinforced concrete beams strengthened with CFRP laminates is almost same regardless of load history at the time of strengthening.     

弹性、弹塑性材料显式模拟计算中的准静态加载速度研究

摘 要：动力学显式算法采用时间积分原理,其较静力学隐式算法在强非线性问题中的适用性更广。为将此方法应用到岩土等非线性材料的计算中,考虑到显式算法中动能的影响会导致结果波动,分析动力学显式算法在模拟计算中的准静态加载速度的选取十分必要,如何在缩短模拟消耗时间与结果准确性之间寻求平衡是本文研究重点。研究中提出以加载-位移曲线的波动比来评价准静态计算效果,首先开展弹性材料的平面应变模拟试验以分析弹模、密度、泊松比、围压4个参数对准静态加载速度取值的影响,结果表明：弹模、泊松比、围压的增大会提高准静态加载速度;密度的增大则会减小准静态加载速度。通过对各影响因素与准静态加载速度的相关性分析给出了准静态加载速度取值的经验公式。最后,选取能够反映砂土复杂力学特性的弹塑性本构模型,开展其平面应变模拟试验,对比分析准静态加载速度经验公式在弹性材料与弹塑性材料中的适用性差异,并提出应用建议公式。     

Response and Damage Tolerance of Composite Sandwich Structures under Low Velocity Impact

The deformation and failure response of composite sandwich beams and panels under low velocity impact was reviewed and discussed. Sandwich facesheet materials discussed are unidirectional and woven carbon/epoxy, and woven glass/vinylester composite laminates; sandwich core materials investigated include four types of closed cell PVC foams of various densities, and balsa wood. Sandwich beams were tested in an instrumented drop tower system under various energy levels, where load and strain histories and failure modes were recorded for the various types of beams. Peak loads predicted by spring-mass and energy balance models were in satisfactory agreement with experimental measurements. Failure patterns depend strongly on the impact energy levels and core properties. Failure modes observed include core indentation/cracking, facesheet buckling, delamination within the facesheet, and debonding between the facesheet and core. In the case of sandwich panels, it was shown that static and impact loads of the same magnitude produce very similar far-field deformations. The induced damage is localized and is lower for impact loading than for an equivalent static loading. The load history, predicted by a model based on the sinusoidal shape of the impact load pulse, was in agreement with experimental results. A finite element model was implemented to capture the full response of the panel indentation. The investigation of post impact behavior of sandwich structures shows that, although impact damage may not be readily visible, its effects on the residual mechanical properties of the structure can be quite detrimental.     

Non-linear buckling and postbuckling behavior of thin-walled beams considering shear deformation

The static stability of thin-walled composite beams, considering shear deformation and geometrical non-linear coupling, subjected to transverse external force has been investigated in this paper. The theory is formulated in the context of large displacements and rotations, through the adoption of a shear deformable displacement field (accounting for bending and warping shear) considering moderate bending rotations and large twist. This non-linear formulation is used for analyzing the prebuckling and postbuckling behavior of simply supported, cantilever and fixed-end beams subjected to different load condition. Ritz's method is applied in order to discretize the non-linear differential system and the resultant algebraic equations are solved by means of an incremental Newton-Rapshon method. The numerical results show that the beam loses its stability through a stable symmetric bifurcation point and the postbuckling strength is in relation with the buckling load value. Classical predictions of lateral buckling are conservative when the prebuckling displacements are not negligible and the non-linear buckling analysis is required for reliable solutions. The analysis is supplemented by investigating the effects of the variation of load height parameter. In addition, the critical load values and postbuckling response obtained with the present beam model are compared with the results obtained with a shell finite element model (Abaqus).     

压电智能复合材料层合梁的力电耦合模型及层间应力分析

由于非凡的物理性能,石墨烯纳米片(GPL)被认为是最有吸引力的复合材料增强材料之一.GPL增强材料可以明显提高聚偏氟乙烯(PVDF)压电性能和力学性能.在力电载荷作用下,对含均匀石墨烯薄片增强(GSR)智能压电复合材料层合梁层间应力预测至关重要.若对受到力电耦合作用且层与层之间材料性能突变的压电层合梁层间剪切变形预测有误,则其层间应力过大可能导致层间失效.因此,论文提出一种适于分析此类问题且满足层与层之间相容性条件的有效力电耦合模型,用于含GSR致动器的复合材料层合梁层间应力分析.应用Reissner混合变分原理(RMVT),可以提高考虑力电耦合效应的横向剪应力预测精度.三维(3D)弹性理论和所选模型计算结果将用于评估所提梁模型性能.此外,还从力电载荷、压电层厚度、石墨烯体积分数和长厚比等方面对含GSR致动器复合材料层合梁力学响应特性进行了系统的研究.     

Buckling analysis of two layer delaminated beams with bridging

Stitching has been used as through-thickness reinforcement to reduce the effects of delamination. In stitching, the delamination will be held by stitches in the form of crack/interface bridging. In the present work, the reinforcement of stitching threads is assumed to provide continuous linear restoring tractions opposing the delamination opening. A generalized mathematical model is developed to study the buckling analysis of two layer delaminated beams with bridging by using Rayleigh–Ritz energy method. The delaminated beam is analyzed as four interconnected beams using the delamination as their boundary. Lagrange multipliers are used to enforce the boundary and continuity conditions between the junctions of the interconnected beams. The developed mathematical model is solved as an eigenvalue problem in which the lowest eigenvalue gives the buckling load. Effective-bridging modulus, a new nondimensionalized parameter, is introduced to study the influence of bridging on the delamination buckling. It is shown that bridging strongly influences the buckling load of the delaminated beams and a monotonic relation is observed between the buckling load and the effective-bridging modulus. Parametric studies in terms of delamination sizes and locations along spanwise and thicknesswise positions on the buckling load have been carried out. The bridging is found to be effective for shallow delaminations of moderate length, and for deep and long delaminations. Spanwise positions of delamination strongly influence the buckling loads. In addition, an analytical model for obtaining upper bounds of the buckling load is developed by using Euler–Bernoulli beam theory. Effective-slenderness ratio, a new nondimensionalized parameter is defined and it is found to be controlling the buckling mode configurations, i.e., local, global and mixed modes.     

光弹性贴片法研究钢纤维活性粉末混凝土断裂性能

采用预制裂缝的三点弯曲试件,应用光弹性贴片法研究了不同纤维掺量活性粉末混凝土RPC200的断裂性能.实验获取了光弹贴片所显示的裂缝扩展全过程,由光弹性条纹分析了不同纤维掺量试件的初裂荷载及临界有效裂缝长度的变化规律.实验表明,利用光弹性贴片法可以有效的获取钢纤维混凝土裂缝扩展的全过程;随着钢纤维掺量的增加,试件的初裂荷载和峰值荷载得到相应提高,且峰值荷载呈近似线性的增加;当纤维掺量为1%时,临界有效裂缝长度值最大;纤维掺量继续增加,其分布均匀性下降,试件的韧性降低,临界有效裂缝长度减少.     

Suggestion of a new dimensionless number for dynamic plastic response of beams and plates

Summary A dimensionless number, termed response number in the present paper, is suggested for the dynamic plastic response of beams and plates made of rigid-perfectly plastic materials subjected to dynamic loading. It is obtained at dimensional reduction of the basic governing equations of beams and plates. The number is defined as the product of the Johnson's damage number and the square of the half of the slenderness ratio for a beam; the product of the damage number and the square of the half of the aspect ratio for a plate or membrane loaded dynamically. Response number can also be considered as the ratio of the inertia force at the impulsive loading to the plastic limit load of the structure. Three aspects are reflected in this dimensionless number: the inertia of the applied dynamic loading, the resistance ability of the material to the deformation caused by the loading and the geometrical influence of the structure on the dynamic response. For an impulsively loaded beam or plate, the final dimensionless deflection is solely dependent upon the response number. When the secondary effects of finite deflections, strain-rate sensitivity or transverse shear are taken into account, the response number is as useful as in the case of simple bending theory. Finally, the number is not only suitable to idealized dynamic loads but also applicable to dynamic loads of general shape. Received 17 October 1997; accepted for publication 19 March 1998