Natural frequencies of plates with square holes when subjected to in-plane uniaxial, biaxial or shear loading

The finite element method is used to determine the natural frequencies of flat square plates containing eccentrically located square holes. The plates are subjected to in-plane uniaxial, biaxial or uniformly distributed shear along the four outer edges. These edges are either simply supported or clamped.

In order to evaluate the stiffness and mass matrices, the non-conforming rectangular displacement element is used to model the out-of-plane behaviour of the plate. The in-plane stress distribution within the plate, required in the analysis, is determined by using a rectangular finite element having the only essential degrees of freedom at each of the four corner nodes. The element displacement functions are based on assumed strains and satisfy the exact requirements of strain free rigid-body modes of displacements.

The variation of the natural frequency with the size and location of the hole is first investigated in the absence of any in-plane stresses. This analysis is then repeated for a series of values of the applied in-plane stresses. When uniform shear is applied, tension and compression zones are produced in the plate and hence the effect of locating the hole in each of the regions is also investigated. The values of the applied in-plane stresses ranged up to the point that would cause the plates to buckle. In this way a comprehensive set of results can be obtained.     

Shear Lag and Effective Breadth in Rectangular Plates with Material Orthotropy. Part 1: Analytical Formulation

Symbolically derived closed-form solutions for the integration constants in series solutions for rectangular orthotropic plates under in-plane boundary shear are derived, enabling the exact stress distribution for such problems to be readily obtained. The ensuing expressions complement an earlier derivation for in-plane normal loadings along longitudinal boundaries, so that totally arbitrary stresses on these boundaries can now be studied.

Simple formulae for the longitudinal stress distribution are listed, and these provide the basis for a subsequent parametric investigation of shear lag and effective breadths in wide orthotropic flanges.     

Effect of interfacial imperfection on bending behavior of composites and sandwich laminates by an efficient C0 FE model

The bending behavior of composites and sandwich plates having imperfections at the layer interfaces is investigated by a refined higher order shear deformation plate theory (RHSDT) and a Least Square Error (LSE) method. In this theory, the in-plane displacement field is obtained by superposing a globally varying cubic displacement field on a zig-zag linearly varying displacement field. This plate theory represents parabolic through thickness variation of transverse shear stresses which satisfy the inter-laminar continuity condition at the layer interfaces and zero transverse shear stress condition at the top and bottom of the plate. In this plate model, the interfacial imperfection is represented by a liner spring-layer model. Finite element method is adopted and an efficient C⁰ continuous 2D finite element (FE) model is developed based on the above mentioned plate theory for the static analysis of composites and sandwich laminates having imperfections at the layer interfaces. In this model, the first derivatives of transverse displacement have been treated as independent variables to circumvent the problem of C¹ continuity associated with the above plate theory (RHSDT). The LSE method is applied to the 3D equilibrium equations of the plate problem at the post-processing stage, after in-plane stresses are calculated by using the above FE model based on RHSDT. The proposed model is implemented to analyze the laminated composites and sandwich plates having interfacial imperfection. Many new results are also presented which should be useful for the future research.     

Dynamic in-plane transversal normal stresses in the concrete face of CFRD

Severe earthquakes can induce damages to Concrete Face Rockfill Dams (CFRDs) such as concrete cracking and joint’s water stops distressing where high in-plane transversal normal stresses develop. Although these damages rarely jeopardize the dam safety, they cause large water reservoir leakages that hinder the dam functioning. This issue can be addressed using well know numerical methods; however, given the wide range of parameters involved, it would seem appropriate to develop a simple yet reliable procedure to get a close understanding how their interaction affects the CFRD’s overall behavior. Accordingly, once the physics of the problem is better understood one can proceed to perform a detailed design of the various components of the dam. To this end an easy-to-use procedure that accounts for the dam height effects, valley narrowness, valley slopes, width of concrete slabs and seismic excitation characteristics was developed. The procedure is the dynamic complement of a method recently developed to evaluate in-plane transversal normal stresses in the concrete face of CFRD’s due to dam reservoir filling [¹]. Using these two procedures in a sequential manner, it is possible to define the concrete slab in-plane normal stresses induced by the reservoir filling and the action of orthogonal horizontal seismic excitations acting at the same time upstream-downstream and cross river. Both procedures were developed from a data base generated using nonlinear static and dynamic three-dimensional numerical analyses on the same group of CFRD’s. Then, the results were interpreted with the Buckingham Pi theorem and various relationships were developed. In the above reference, the method to evaluate the concrete face in-plane transversal normal stresses caused by the first reservoir filling was reported. In this paper, the seismic procedure is first developed and then through an example the whole method (dam construction, reservoir filling plus seismic loading) of analysis is assessed.     

双向剪压作用下弹性板临界屈曲应力的简化计算公式

旨在开发一个简化公式,用于双向剪压作用下简支板的临界屈曲应力计算。运用经典板理论和里兹法对不同面积比的板临界应力进行计算。根据二维平面内应力关系,由经验判断推出四维临界应力公式,该公式表现为3个平面内应力和面积比的关系。计算结果表明:1)面积比在1~2时,临界应力与面积比成线性关系,2~5时为非线性关系;2)当剪切应力接近其临界值时,临界应力关系呈现更明显的线性变化趋势,同时面积比对其影响减弱。     

水泥固化体淋滤液对GCL防渗性能的影响

水泥固化/稳定化是危险废弃物处理的经济、高效方法,然而,水泥固化体的淋滤液中含有大量Ca~(2+),其长期渗透有可能导致填埋场底部土工合成黏土衬垫(geosyntheticclayliner,GCL)的防渗性能下降,从而引发二次污染。使用柔性壁渗透仪,测定有效应力和水泥固化体淋滤液共同作用下GCL的渗透系数,探讨了淋滤液浓度以及不同有效应力对GCL渗透系数的影响。试验结果表明:当有效应力为24kPa时,水泥固化体淋滤液的持续渗透会使GCL的渗透系数增大179～721倍,淋滤液中Ca~(2+)浓度越高,GCL渗透系数增大的幅度越大。通过增加有效应力,可以降低固化体淋滤液对GCL防渗性能所造成的负面影响,当有效应力增大至438 kPa时,固化体淋滤液对GCL防渗性能所造成的负面影响全部被抵消。     

Manufacturing effects on the hydraulic properties of needlepunched nonwoven geotextiles

Needlepunched nonwoven geotextiles are entangled to form a complex three-dimensional structure by random fibers, accounting for its bulky nature, wide range of pore size distribution, and good drainage. With needlepunched nonwoven geotextiles, water can move in both the vertical and horizontal directions. This paper examines two types of needlepunched nonwovens: one produced from polyester staple fiber and the other made from polyester spunbond continuous filaments. Experimental results indicate that the permittivity of staple needlepunched nonwoven geotextiles varies from 1.77-4.51 s⁻¹; the permeability coefficient varies from 0.63-2.87 × 10⁻² m/s. The permittivity of spunbond needlepunched nonwoven geotextiles varies from 1.13-1.97 s⁻¹; the permeability coefficient varies from 0.48-1.09 × 10⁻² m/s. In addition, the transmissivity of needlepunched nonwoven geotextiles decrease to an essentially constant value as the normal stress is increases. The transmissivity of needlepunched nonwoven geotextiles examined varies from 155-2.75 × 10⁻⁶ m²/s over the normal stress range examined (5-200 kN/m²). The AOS value of 3 denier staple fiber needlepunched nonwovens is less than 0.074 mm, the AOS value of spunbonded 7 denier and, 15 d and 20 d needlepunched nonwovens are 0.21 mm, 0.25 mm and 0.30 mm, respectively.     

Large deflection analysis of flexible plates by the meshless finite point method

The classical finite difference technique and methods based on series expansions can only be adopted for solving plates with simple geometry, loading and boundary conditions. In contrast, the finite element method has been widely used for general analysis of bending and flexible plates (coupled bending and in-plane effects). Lack of stress continuity and relatively expensive mesh generation and remeshing schemes have led to the emergence of meshless methods, such as the finite point method (FPM). FPM is a strong form solution which combines the moving least square interpolation technique on a domain of irregularly distributed points with a point collocation scheme to derive system governing equations. In this study, coupled nonlinear partial differential equations of fourth order are solved to analyse large deflection behaviour of plates subjected to lateral and in-plane loadings. Several plate problems are solved and compared with analytical solution and other available numerical results to assess the performance of the proposed approach.     

A simplified method for elastic large deflection analysis of plates and stiffened panels due to local buckling

A computational model for analysis of local buckling and postbuckling of stiffened panels is derived. The model provides a tool that is more accurate than existing design codes, and more efficient than nonlinear finite element methods. Any combination of biaxial in-plane compression or tension, shear, and lateral pressure may be analysed. Deflections are assumed in the form of trigonometric function series. The deformations are coupled such that continuity of rotation between the plate and the stiffener web is ensured, as well as longitudinal continuity of displacement. The response history is traced using energy principles and perturbation theory. The procedure is semi-analytical in the sense that all energy formulations are derived analytically, while a numerical method is used for solving the resulting set of equations, and for incrementation of the solution. The stress in certain critical points are checked using the von Mises yield criterion, and the onset of yielding is taken as an estimate of ultimate strength for design purposes.     

Concise formula for the critical buckling stresses of an elastic plate under biaxial compression and shear

This study aims to develop a concise formula for the critical buckling stresses of a simply supported plate under biaxial compression and shear. The critical stresses are obtained for different aspect ratios using classical plate theory and the Ritz method. The four-dimensional critical stress formula, which is expressed in terms of the three in-plane stresses and the aspect ratio, is developed empirically according to the two-dimensional relationships between the in-plane stresses. The findings that are of interest are: (1) the critical stress relationship is linear for the aspect ratios within the range 1 to and nonlinear for the aspect ratios within the range to 5; and (2) as shear stress approaches its critical value, the critical stress relationship becomes increasingly linear and less dependent on aspect ratio.     

复变函数法分析盾构隧道开挖引起的土体位移和衬砌变形

盾构隧道开挖引起的地层变形历来是人们所关注的重要课题。目前,既有成果较少考虑隧道衬砌与土体相互作用所带来的影响,尤其是较少针对衬砌变形进行分析,就此基于隧道椭圆化变形边界条件,提出了考虑衬砌与土体两种不同介质相互作用下的地层位移和衬砌变形复变函数解答。在该方法中,隧道埋深只影响共形映射后圆环域的环壁厚度,而解析区域依然保持圆形,具有不会对函数解析产生影响的优势;此外,该法经共形映射后保证了边界连续性,避免了既有应力函数法为保证隧道扰动土体无穷远处位移为零,而对解析解进行修正所导致物理意义不明确的缺陷。通过实例分析,得到了隧道开挖引起的地表沉降,并与实测数据进行了对比验证;通过参数分析,获取了扰动地层和隧道衬砌变形的影响规律。结果表明:复变函数解答得到的土体位移曲线与实测值吻合较好,且地表最大沉降值更接近于实测值;隧道的埋深和半径对土体位移和衬砌变形均有较大影响,衬砌厚度对其影响虽然较小,但仍不可忽略;衬砌径向位移曲线呈仰卧的鸭蛋形,关于90°/270°轴对称,拱顶和拱底被压扁,拱顶压缩量明显大于拱底,左、右两侧压缩量小于上、下两侧,表现为收缩之后又被压扁向左、右两侧突出,且随着埋深的增大,衬砌整体上浮;衬砌环向位移曲线呈侧立的苹果形,关于0°/180°轴对称,且在90°和270°处取值为零,随着隧道埋深的增大,环向位移绝对值增大。     

土的σ1/3空间滑动面强度准则及其与传统准则的比较研究

土的抗剪强度与其剪切破坏面上的正应力一般呈线性关系,反映了土的剪切强度本质特性。常用的强度准则有Mohr-Coulomb准则、Drucker-Prager屈服准则、Matsuoka-Nakai准则,分别对应于与大主应力呈45°+φ/2的剪切破坏面、八面体面和空间滑动面（SMP）上的剪应力比为常数的关系。本文提出了一种由κσ₁^1/3,κσ₂^1/3,κσ₃^1/3确定土单元大、中、小主应力轴交点的空间滑动面,称为σ^1/3空间滑动面;建立了σ^1/3空间滑动面剪应力比为常数的准则,称为σ^1/3空间滑动面强度准则,该准则在应力空间描述的强度破坏面为平面上呈曲边三角形形态的光滑锥面。进行了Mohr-Coulomb强度准则、Drucker-Prager强度准则、Matsuoka-Nakai强度准则与Lade-Duncan强度准则、σ^1/3空间滑动面强度准则在应力空间描述强度破坏面的比较分析,以及不同平面上Lade-Duncan准则和σ^1/3空间滑动面强度准则随b值的变化规律。结果表明Lade-Duncan强度准则与σ^1/3空间滑动面强度准则近似一致,从而揭示了Lade-Duncan强度准则的物理本质基础：Lade-Duncan强度准则实质上近似服从土破坏时σ^1/3空间滑动面上剪应力与正应力呈线性变化的规律。即Lade-Duncan强度准则描述土单元剪切破坏时的空间滑动面近似为σ^1/3空间滑动面。根据4种原状黄土固结排水条件下的真三轴压缩试验结果,验证了σ^1/3空间滑动面强度准则的合理性与可靠性。     

Effects of microstructures on dynamic compression of Barre granite

The distribution and characteristics of microstructures (microcrack and grain) of Barre granite (BG) were investigated, and three orthogonal weak planes associated with the preferred orientations of microcracks were identified. It has been demonstrated that both the fracture toughness and the longitudinal wave speed depend on the direction of these weak planes. In this study, disk samples cut from one BG block are prepared for split Hopkinson pressure bar (SHPB) test. The axial directions of the samples are chosen to be parallel to the preferred direction of microcracks and the samples are grouped and denoted by Y (lowest P-wave velocity), Z (highest P-wave velocity), and X (intermediate P-wave velocity). Pulse-shaper technique is adopted to achieve equilibrium of dynamic stresses on both ends of the sample and constant strain rate during the dynamic loading. For samples within the same orientation group, the maximum stress achieved shows clear strain-rate sensitivity. The effect of microcracks on the dynamic compressive response of BG depends on the strain rate for a fixed loading duration (230 μs). For low strain-rate loading (70 s⁻¹) and high strain-rate loading (130 s⁻¹), the maximum dynamic stress achieved is not sensitive to the microcrack orientation; for intermediate strain rate (100 s⁻¹) loading, the maximum achieved stress for Y-samples is the largest. In addition, three dynamic compressive rock failure modes are identified: quasi-elastic, cracked, and fragmented. The correlation between the failure modes and the shape of the stress–strain curves is discussed.     

双坡楔形偏压柱平面内稳定分析

本文利用ANSYS程序,在弹塑性、大挠度范围内,建立考虑板件间相关屈曲作用的双坡楔形偏压柱的有限元模型,并模拟实际情况,在模型中引入初始几何缺陷和残余应力,研究几何参数及残余应力对其稳定承载力的影响.     

Dynamic instability of laminated sandwich plates using an efficient finite element model

For the first time, the dynamic instability of laminated sandwich plates subjected to in-plane edge loading is studied using an efficient finite element plate model, which is developed recently by the authors. The plate model is based on a refined higher order shear deformation plate theory. In this theory, the transverse shear stresses are continuous at the layer interfaces with stress free conditions at plate top and bottom surfaces. It is interesting to note that the plate model having all these refined features requires unknowns at the reference plane only. However, this theory requires C¹ continuity of transverse displacement at the element edges, which is difficult to satisfy arbitrarily in any existing finite element. To deal with this, a new triangular element developed by the authors is used in the present paper.     

串/并联运行下能源管廊相对热效率及热致应力现场试验

依托南京雨花台区软件谷杆线迁移地下综合管廊工程,在管廊的底板、侧板及顶板内埋设换热管形成能源管廊,并通过恒定输入功率加热循环液体,对明挖施工能源管廊的换热规律进行现场试验; 实测能源管廊的换热系统进/出口水温、底板温度及热致应力等变化规律,初步探讨并联和串联的能源管廊段连接形式下,系统运行过程中的相对热效率及热致应力响应性能,以及能源管廊段运行过程中对周围管廊段结构造成的影响。结果表明:试验条件下并联和串联运行下能源管廊的相对线热效率分别为39.68、31.27 kW?m^-1,并联较串联运行模式提高了约26.9%,即并联运行的换热性能相对较好; 并联和串联运行过程中底板产生的最大轴向热致应力分别为1.30、1.24 MPa(两者相差小于10%),由于叠加效应,邻近管廊段产生0.33 MPa的最大压应力,对地下综合管廊结构安全性的影响较小; 相关结论可为依托城市地下综合管廊开展能源管廊或隧道的设计和计算提供参考。     

A semi-analytical model for global buckling and postbuckling analysis of stiffened panels

A computational model for global buckling and postbuckling analysis of stiffened panels is derived. The loads considered are biaxial in-plane compression or tension, shear, and lateral pressure. Deflections are assumed in the form of trigonometric function series, and the principle of stationary potential energy is used for deriving the equilibrium equations. Lateral pressure is accounted for by taking the deflection as a combination of a clamped and a simply supported deflection mode. The global buckling model is based on Marguerre’s nonlinear plate theory, by deriving a set of anisotropic stiffness coefficients to account for the plate stiffening. Local buckling is treated in a separate local model developed previously. The anisotropic stiffness coefficients used in the global model are derived from the local analysis. Together, the two models provide a tool for buckling assessment of stiffened panels. Implemented in the computer code PULS, developed at Det Norske Veritas, local and global stresses are combined in an incremental procedure. Ultimate limit state estimates for design are obtained by calculating the stresses at certain critical points, and using the onset of yielding due to membrane stress as the limiting criterion.     

Vacuum glazing—A new component for insulating windows

The substantial progress in the science and technology of vacuum glazing that has occurred over the past few years is reviewed. Vacuum glazing up to 1 m × 1 m in size has been produced with an air-to-air, mid-device thermal conductance as low as 0.90 W m⁻² K⁻¹, compared with 1.3 W m⁻² K⁻¹ for high performance double glazing. The mechanical tensile stresses in vacuum glazing due to pressure and temperature differentials are well understood, and appear to be tolerably small. The internal vacuum is high, and extremely stable over long times at moderate temperatures. The likely cost of volume production of vacuum glazing should be only slightly greater than for high performance double glazing.     

天津滨海吹填泥浆的自重沉降固结特性研究

以天津滨海新区吹填泥浆为研究对象,对初始含水率w_0=200%~2000%的泥浆开展长达100 d的自然沉降模型试验,研究吹填泥浆的自重沉降固结规律与形成土的微观结构特性,据此提出吹填工程设计的控制指标,为吹填工程的设计与施工提供可靠的技术支撑。结果表明,天津吹填泥浆的沉降类型主要是沉积沉降和固结沉降,沉积沉降过程分为絮凝阶段、阻碍沉降阶段、自重固结阶段。含水率临界值(或土的形成含水率)w_0*=400%,且w_0*与液限w_L具有较好的线性关系。初始含水率w_0≤w_0*,发生固结沉降,沉降量可以用一维固结理论计算;w_0w_0*,发生沉积沉降,沉降量可以用沉积规律计算。土的形成孔隙比e_0*=10.92;沉降稳定时间Tc可用Tc=159(w_0/w_L)~(-1)计算;稳定孔隙比e_c可由分段公式计算,e_c=0.08+5.4(e_0≥13.65),e_c=0.4+1.03(e_013.65);絮凝屈服应力P_s=0.3 k Pa,界限孔隙比e_s=6.4。研究还表明,泥浆沉降过程其实是絮凝屈服应力与有效应力相互影响的过程,进而产生不同的沉降特征;吹填形成土在平行于沉降方向为絮凝结构,而垂直沉降方向呈堆叠结构。     

Field evaluation of geonet flow rate (transmissivity) under increasing load

This paper presents data from a full scale field test of a geonet placed between two geomembranes used as a leak detection system for a solid waste landfill. The cell under investigation is 1·54 ha in area, with the geonet covering 0·87 ha of the base of the cell. The remaining sideslope area was also covered by geonet, but did not contribute to the flow rate testing. Approximately 2300 liters of water were injected at three different times; i.e., at landfill waste heights corresponding to 12, 153 and 311 kPa normal stresses. The percentages of recovered water within a 15-h period were 93·9%, 89·6% and 81·2% respectively. The calculated transmissivity values reflected the increased normal stress as would have been anticipated, i.e., transmissivity values decreased from 45·2 to 43·5 to 40·0 × 10⁻⁴ m²/s, respectively. These decreases were anticipated due to the elastic intrusion of the geomembranes into the geonet under the gradually increasing normal stresses. The results indicate that geonets are viable drainage materials under actual full-scale field conditions and should certainly be considered as drainage replacements for natural granular soil drainage media.