Bending moment calculation for single lap joints with composite laminate adherends including bending-extensional coupling

This work deals with the analytical determination of section forces and moments in adhesively bonded single lap joints with composite laminate adherends including bending-extensional coupling. The analysis is also valid for unbalanced joints and the adhesive thickness is taken into account in the model. Several types of boundary conditions can be applied, e.g. simply supported ends, fixed ends, bonded doubler and single strap joints. Various configurations are studied and the results are compared to finite element analyses and other analytical approaches. Good agreement is achieved over a wide range of configurations. A closed form analytical solution is given for the section forces and moments at the overlap ends.     

局部应力计算方法的对比研究(下)

在压力容器设计中经常需要考虑管道通过接管而施加于设备上的力和力矩,这些外力和外力矩会在容器与接管连接的局部区域产生高应力,从而有可能使得该区域的强度不够而使容器失效。长期以来,工程中计算局部应力最常用的方法为WRC107和WRC297公报中提供的方法。当超出这两个方法的范围时,一般会采用有限元分析的方法。在2002年颁布的欧盟压力容器设计标准EN13445中,提供了另一种局部应力计算方法。在这些方法重叠的适用范围内,设计人员可以自行确定选用哪一个方法。通过对这四种方法计算结果的对比,分析这些方法在工程应用中的安全性和经济性,以给设计人员在方法选择时提供参考。通过对大量算例的结果比较,可以确定,EN方法的结果作为壳体强度评定的依据是足够安全的,但不能作为接管强度评定的依据;WRC297方法的应力计算结果一般总是偏于保守;而WRC107方法的结果,一方面没有给出接管的应力,另一方面,在大部分情况下,计算得到的壳体应力往往偏小。从理论上讲,用有限元方法可以得到最可靠的应力分析结果,但该方法相对其他方法而言,总是更费时费力。因此,通过分析,对给定的壳体与接管连接结构及载荷工况下如何合理选择另外三种方法中的一种给出了一些推荐意见,从而使得在保证安全的前提下,可以降低综合设计成本。     

局部应力计算方法的对比研究(上)

在压力容器设计中经常需要考虑管道通过接管而施加于设备上的力和力矩,这些外力和外力矩会在容器与接管连接的局部区域产生高应力,从而有可能使得该区域的强度不够而使容器失效.长期以来,工程中计算局部应力最常用的方法为WRC 107和WRC 297公报中提供的方法.当超出这两个方法的范围时,一般会采用有限元分析的方法.在2002年颁布的欧盟压力容器设计标准EN 13445中,提供了另一种局部应力计算方法.在这些方法重叠的适用范围内,设计人员可以自行确定选用哪一个方法.通过对这四种方法计算结果的对比,分析这些方法在工程应用中的安全性和经济性,以给设计人员在方法选择时提供参考.通过对大量算例的结果比较,可以确定.EN方法的结果作为壳体强度评定的依据是足够安全的,但不能作为接管强度评定的依据;WRC 297方法的应力计算结果一般总是偏于保守;而WRC 107方法的结果,一方面没有给出接管的应力,另一方面,在大部分情况下,计算得到的壳体应力往往偏小.从理论上讲,用有限元方法可以得到最可靠的应力分析结果,但该方法相对其他方法而言,总是更费时费力.因此,通过分析,对给定的壳体与接管连接结构及载荷工况下如何合理选择另外三种方法中的一种给出了一些推荐意见,从而使得在保证安全的前提下,可以降低综合设计成本.     

基础沉降量对三鞍座卧式容器的影响

本文从理论上 ,将基础沉降量对三鞍座卧式容器中的支承反力与弯矩的影响进行尝试性公式推导。供参考。     

施釉机器人静力学分析的研究

根据6自由度施釉机器人的终端受力，利用雅可比矩阵，求解出各转动关节在稳定平衡状态下的受力和所需的驱动力矩，为设计施釉机器人确定各转轴的电机及其他动力元件提供了可靠的依据。     

三支座硬聚氯乙烯卧式贮槽的计算

本文结合贮槽系列５０三支座卧式贮槽的计算,对三支座硬聚氯乙烯塑料卧式贮槽的弯矩、支座反力、轴向应力、剪切应力、周向应力进行计算与校核。     

Numerical Simulation of Baffle-Supported Tube Bundle Vibration by the Method of Finite Differences

Tube bundles in heat exchangers are often damaged due to flow-induced vibrations. To simulate the fluid-structure interaction between the tubes and the flow field, which seems to be the only reliable way to predict flow-induced vibration of tube bundles, a coupled numerical solver for the governing Navier-Stokes equations of the flow field as well as for the structural response has to be used. Since commercial codes still require a large computational effort to calculate the fluid-structure interaction, one has to develop special program codes for certain technical problems. This paper deals with a numerical method to calculate the structural response of baffle-supported heat exchanger tubes due to outer forces such as flow and contact forces. The equations of motion for a cylindrical tube including torsional movement are developed. They are discretized in space by the means of Finite Differences and in time by Newmark′s method of constant acceleration. Non-linear frictional impact forces due to the baffle supports are introduced as additional line loads and line moments. Flow forces at this stage of development are modeled by simplified assumptions concerning vortex shedding. Numerical examples show the consistency of the calculated solutions. The algorithm is stable and converges for parameters of practical importance. Only little mathematical effort is needed compared to the Finite Element technique or modal analysis. A Navier-Stokes flow solver already developed can now be integrated into the vibration simulation code.     

轮胎力和力矩建模、试验与仿真（续完）

（接上期） 5汽车轮胎力和力矩试验 汽车轮胎六分试验是进行轮胎结构设计和车辆性能优化的常规步骤[1]。尽管测试设备的成本高昂,但试验手段目前依然是整车研究开发应用最为直接的方法。此外由前面对轮胎一车辆建模的相关讨论可知,试验手段对各种轮胎模型的参数确定也具有至关重要的作用。     

Analysis of adhesive-bonded single-lap joint with an interfacial crack and a void

We use the first-order shear deformation plate theory (FSDT) to analyze stresses in two layers bonded together with an adhesive as recommended by the ASTM D3165 standard, except that we also include a void within the adhesive. Depending upon the number of notches and voids, the specimen is divided into several regions. Assuming that a plane strain state of deformation prevails in the specimen, we write the balance of forces and moments for each section and impose the continuity of displacements, forces and moments at the interfaces between the adjoining sections. By taking the Laplace transform of the resulting ordinary differential equations we get a system of simultaneous linear algebraic equations that can be easily solved. The inverse transform of the solution of the algebraic equations provides stresses and displacements in the adhesive and the substrates, which are found to agree well with those obtained by the finite element method (FEM). It is also found that the order of the stress singularity at the corner of the free surface of the adhesive and the substrate, and the strain energy release rate computed from the solution of the problem with the FSDT agree well with those determined from the solution of the problem by the FEM. We note that the computational effort required to analyze the problem with the FSDT is considerably less than that needed to solve the problem by the FEM.     

结构和载荷相对于跨中截面非对称双鞍座卧式容器壁中的应力计算

工程上存在一些结构或载荷相对于跨中截面为非对称的双鞍座卧式容器,这些容器的设计计算超出了ＧＢ１５０－８９的范围,目前国内也尚无其它标准可引用。本文采用材料力学中梁的受力分析方法给出了这类容器中支座反力和最大轴向弯矩计算方程。结合Ｚｉｃｋ法的基本假设,这些方程为工程上解决这类容器的设计提供提供了一种可行的方法,该方法可作为过程设备设计工程师的一种参考。     

加热盘管应力分析

运用CAESARII应力分析软件程序对加热盘管管系进行了整体应力分析。根据ASMEB31．3《工艺管道》标准要求及工程实践经验,考虑了管系在内压、自重、热胀等载荷作用下的应力分布和各个支吊点、设备管口的受力情况,为炉管支吊架设计提供了解决方案。     

Einsatzgrenzen von T‐Stücken mit Abzweigen gleichen Durchmessers

Limitations of Tees with Branches of Equal Diameter Welded and necked‐out tees are frequently used in pressure vessel and piping design. Standard calculations based on the Kellog method are merely applicable for pressure loading. Supplementary forces and moments are excluded in this case. The application of numerical methods of structural analysis is extremely helpful in this situation. However, detailed modelling of the geometry is quite complicated and standard models of the cylinder‐cylinder intersection type cannot be used. Special models of the welded and necked‐out design variants have to be generated and parametrized in order to be applicable for different nominal sizes. Tees as structural components have to be considered under various aspects with respect to their mechanical behaviour. The following investigation proposes methods for design under static and cyclic loading conditions based on detailed FE analyses. The results reveal a considerable potential of tees which has to be proved by analysis.     

Effect of polarity on the adsorption of dichlorobenzene isomers

The influence of reference vapor polarity on the characterization of microporous carbon adsorbents using the Dubinin equations was investigated. Polarity may be an important parameter for reference vapor selection due to the influence of electrostatic forces on the adsorption of polar vapors. Adsorbate polarity was investigated by evaluating the adsorption isotherms and characteristic curves for the three isomers of dichlorobenzene and the heats of adsorption for the two liquid isomers. The three isomers are very similar in terms of molecular weight, vapor pressure, density, and electronic polarizations. The major difference is the range of dipole moments: 1,2-dichlorobenzene, 2.50 D; 1,3-dichlorobenzene, 1.72 D; and 1,4-dichlorobenzene, 0.00 D. If adsorbate polarity has a major influence on adsorption, the three characteristic curves should have different slopes. The slopes of the three curves were not statistically different at the 95% level, and no difference in the heats of adsorption was observed. It was concluded, therefore, that electrostatic forces do not have a major influence on vapor adsorption when adsorbate polarities are between 0 and 2.50 D. Therefore, a single reference vapor may be adequate for characterization of microporous carbon adsorbents.     

Crystal structures of azo colorants derived from pyrazolone: a review

The crystal structures of five azo colorants derived from pyrazolone have been determined by single crystal X-ray diffraction techniques. An examination of these crystal structures indicates the presence of certain common features. In the solid state the molecules do not exist in the azo form but in the form of the hydrazone tautomer. The hydrogen atom in the hydrazone group and one in one of the phenyl rings take part in intramolecular hydrogen bonding, which holds the molecule in a more or less planar configuration. The molecules stack in columns linked by van der Waals forces. Molecule dipole moments and shortest intermolecular distances in the crystal structures are tabulated in an attempt to explain the different solubilities of these solvent dyes and pigments.     

Comparison of Eulerian QBMM and classical Eulerian–Eulerian method for the simulation of polydisperse bubbly flows

The spatial gas distribution of poly-disperse bubbly flows depends greatly on the bubble size. To reflect the resulting polycelerity, more than two momentum balance equations (typically for the gas and liquid phases) have to be considered, as done in the multifluid approach. The inhomogeneous multiple-size group model follows this approach, also combined with a population balance model. As an alternative, in a previous work, an Eulerian quadrature-based moments method (E-QBMM) was implemented in OpenFOAM; however, only the drag force was included. In this work, different nondrag forces (lift, wall lubrication, and turbulent dispersion) are added to enable more complex test cases to be simulated. Simulation results obtained using E-QBMM are compared with the classical E–E method and validated against experimental data for different test cases. The results show that there is good agreement between E-QBMM and E–E methods for mono-disperse cases, but E-QBMM can better simulate the separation and segregation of small and large bubbles.     

Treatment of size-dependent aerosol transport processes using quadrature based moment methods

The use of moment methods for simulation of aerosol settling and diffusion phenomena in which the settling velocity and diffusion coefficient are functions of the size of the particles leads to difficult computational problems, especially if the moment equations need to be closed. In this study, a simple one dimensional problem of aerosol diffusion and gravitational settling is carried out using quadrature method of moments (QMOM) and the direct quadrature method of moments (DQMOM). Analytical solutions can be obtained for the number density function, and issues related to the integration of the solutions to get the moments are discussed. Comparison of the solutions of the moment equations to the moments obtained from the analytical solutions reveals that solutions depend on the initial choice of moments. Results also indicate that the proper choice of moments of the initial number density function may be a significant factor in obtaining more accurate solutions from QMOM or DQMOM.     

Quadrature-based moment methods for the population balance equation: An algorithm review

The dispersed phase in multiphase flows can be modeled by the population balance model (PBM). A typical population balance equation (PBE) contains terms for spatial transport, loss/growth and breakage/coalescence source terms. The equation is therefore quite complex and difficult to solve analytically or numerically. The quadrature-based moment methods (QBMMs) are a class of methods that solve the PBE by converting the transport equation of the number density function (NDF) into moment transport equations. The unknown source terms are closed by numerical quadrature. Over the years, many QBMMs have been developed for different problems, such as the quadrature method of moments (QMOM), direct quadrature method of moments (DQMOM), extended quadrature method of moments (EQMOM), conditional quadrature method of moments (CQMOM), extended conditional quadrature method of moments (ECQMOM) and hyperbolic quadrature method of moments (HyQMOM). In this paper, we present a comprehensive algorithm review of these QBMMs. The mathematical equations for spatially homogeneous systems with first-order point processes and second-order point processes are derived in detail. The algorithms are further extended to the inhomogeneous system for multiphase flows, in which the computational fluid dynamics (CFD) can be coupled with the PBE. The physical limitations and the challenging numerical problems of these QBMMs are discussed. Possible solutions are also summarized.     

A new improved high‐order theory for analysis of free vibration of sandwich panels

A new improved high‐order theory is presented to investigate the dynamic behavior of sandwich panels with flexible core. Shear deformation theory is used for the face sheets, whereas the three‐dimensional elasticity theory is used for the core. Displacements in the core are assumed as polynomial with unknown coefficients. Inertia forces, moments of inertia and shear deformations in the core, and the face sheets are taken into consideration. Unlike the previous improved theory, the in‐plane normal and shear stresses in the core are considered. The governing equations and the boundary conditions are derived by Hamilton's principle. Closed form solution is achieved using the Navier method and solving the eigenvalues. The numerical results of present analysis compared with the available results in the literature. It indicates that the present new modified theory is more accurate than the other developed theories for sandwich panels. In this study, the variation of the nondimensional natural frequency with respect to the various parameters is presented. POLYM. COMPOS., 31:2042–2048, 2010. © 2010 Society of Plastics Engineers     

Analytical Derivation of Moment Equations in Stochastic Chemical Kinetics

The master probability equation captures the dynamic behavior of a variety of stochastic phenomena that can be modeled as Markov processes. Analytical solutions to the master equation are hard to come by though because they require the enumeration of all possible states and the determination of the transition probabilities between any two states. These two tasks quickly become intractable for all but the simplest of systems. Instead of determining how the probability distribution changes in time, we can express the master probability distribution as a function of its moments, and, we can then write transient equations for the probability distribution moments. In 1949, Moyal defined the derivative, or jump, moments of the master probability distribution. These are measures of the rate of change in the probability distribution moment values, i.e. what the impact is of any given transition between states on the moment values. In this paper we present a general scheme for deriving analytical moment equations for any N-dimensional Markov process as a function of the jump moments. Importantly, we propose a scheme to derive analytical expressions for the jump moments for any N-dimensional Markov process. To better illustrate the concepts, we focus on stochastic chemical kinetics models for which we derive analytical relations for jump moments of arbitrary order. Chemical kinetics models are widely used to capture the dynamic behavior of biological systems. The elements in the jump moment expressions are a function of the stoichiometric matrix and the reaction propensities, i.e. the probabilistic reaction rates. We use two toy examples, a linear and a non-linear set of reactions, to demonstrate the applicability and limitations of the scheme. Finally, we provide an estimate on the minimum number of moments necessary to obtain statistical significant data that would uniquely determine the dynamics of the underlying stochastic chemical kinetic system. The first two moments only provide limited information, especially when complex, non-linear dynamics are involved.