考虑材料拉压异性的固支圆板塑性极统一解

本文采用最新的统一强度理论求出了固支圆板的塑性极限荷载,内力场及速度的统一解;得出了强度理论参数b及材料的不同拉压比α对塑性极限的影响曲线,所给出的解可以灵活地适用于各种不同特性的材料及机械、土木、航空等工程的相关结构中,文献中已有的Tresca解,Mises解和双剪统一屈服准则解均为本文的特例,本文的统一解还给出了一系列新的结果,统一解大于Tresca,Mohr-Coulomb的单剪理论解,它可以更好地发挥材料的强度潜力,工程应用可以取得明显的经济效益。     

Nonsteady sink and source in a rotating fluid

The effect of the Coriolis force on the nonsteady two-dimensional sink or source flow has been studied theoretically. With the assumptions of incompressibility and invisddity of fluid, the equations governing the flow are still non-linear. However, a set of analytical and exact solutions is obtained for the velocity and pressure distributions. The result shows that no significant vortex flow can be induced by a source flow, the circulation produced there mainly is because the observer is moving with the rotating system; however, a sink will always induce a vortex, the strength of circulation in the sink flow is simply in proportion to the rotating speed of the system and the time integrated sink strength. As the system is under a constant rotating speed, the circulation will vanish only when the time integrated sink strength vanishes. Several special cases of sink strength are examined and their results are presented in this paper. The purpose of this study is mainly to relate the strength of circulation with the strength of sink and source. Consequently, it- can be applied to the weather forecast for hurricanes or tornadoes.     

基于统一强度理论的组合厚壁圆筒弹塑性统一解

基于统一强度理论,考虑中间主应力效应及拉压不等特性,对双层和多层厚壁圆筒进行弹塑性分析,分别建立了材料相同双层厚壁圆筒最佳分层半径、套装压力和套装过盈量的基本解,以及组合厚壁圆筒的弹塑性统一解,得出统一强度理论参数、拉压比、半径比和组合筒体层数对统一解的影响特性。该结果具有通用性,适用于拉压异性组合厚壁圆筒压力容器的相关问题;考虑中间主应力的影响,能充分发挥组合筒体的强度潜能,为组合厚壁筒的设计及工程应用提供一定的参考。     

Flow and heat transfer over a generalized stretching/shrinking wall problem—Exact solutions of the Navier-Stokes equations

In this paper, we investigate the steady momentum and heat transfer of a viscous fluid flow over a stretching/shrinking sheet. Exact solutions are presented for the Navier-Stokes equations. The new solutions provide a more general formulation including the linearly stretching and shrinking wall problems as well as the asymptotic suction velocity profiles over a moving plate. Interesting non-linear phenomena are observed in the current results including both exponentially decaying solution and algebraically decaying solution, multiple solutions with infinite number of solutions for the flow field, and velocity overshoot. The energy equation ignoring viscous dissipation is solved exactly and the effects of the mass transfer parameter, the Prandtl number, and the wall stretching/shrinking strength on the temperature profiles and wall heat flux are also presented and discussed. The exact solution of this general flow configuration is a rare case for the Navier-Stokes equation.     

不同化学溶液下砂岩I型断裂韧度及其强度参数相关性的试验研究

本文通过长期浸泡的方法,以陕西铜川新区龙潭水库典型的库岸边坡的砂岩为研究对象,研究了浸泡在不同化学溶液下砂岩的力学特性及其损伤劣化机制,分析了经不同化学溶液腐蚀后试样的物理力学特性随化学腐蚀时间的劣化规律。研究发现：化学腐蚀后砂岩的物理力学特性均发生不同程度的劣化,其随化学腐蚀时间的劣化规律基本一致;但不同化学溶液下试样物理力学特性的劣化程度有所差异,酸性溶液（pH=3.0）加剧了砂岩的劣化程度,中性化学溶液对其损伤劣化程度也有一定的影响,试验初期,强碱性溶液下砂岩的劣化程度最小,但随着化学腐蚀时间的加长,强碱性溶液下的劣化程度逐渐加剧,大于中性溶液下的,但仍小于酸性溶液。化学腐蚀后砂岩试样均呈现出明显的弱化趋势,其断裂韧度KIC、抗压强度和抗拉强度的劣化程度显著,但各力学特征的劣化程度存在明显的差异,其中抗压强度的劣化程度相对减小,而其KIC的劣化程度较大;同时,化学腐蚀后砂岩的断裂韧度与抗拉强度、抗压强度间的一致性比较明显,存在明显线性关系。可以利用不同化学溶液下砂岩的裂纹扩展半径r来间接说明其力学特征发生损伤劣化的程度。     

A modified multi-objective particle swarm optimization approach and its application to the design of a deepwater composite riser

A modified multi-objective particle swarm optimization method is proposed for obtaining Pareto-optimal solutions effectively. Different from traditional multi-objective particle swarm optimization methods, Kriging meta-models and the trapezoid index are introduced and integrated with the traditional one. Kriging meta-models are built to match expensive or black-box functions. By applying Kriging meta-models, function evaluation numbers are decreased and the boundary Pareto-optimal solutions are identified rapidly. For bi-objective optimization problems, the trapezoid index is calculated as the sum of the trapezoid’s area formed by the Pareto-optimal solutions and one objective axis. It can serve as a measure whether the Pareto-optimal solutions converge to the Pareto front. Illustrative examples indicate that to obtain Pareto-optimal solutions, the method proposed needs fewer function evaluations than the traditional multi-objective particle swarm optimization method and the non-dominated sorting genetic algorithm II method, and both the accuracy and the computational efficiency are improved. The proposed method is also applied to the design of a deepwater composite riser example in which the structural performances are calculated by numerical analysis. The design aim was to enhance the tension strength and minimize the cost. Under the buckling constraint, the optimal trade-off of tensile strength and material volume is obtained. The results demonstrated that the proposed method can effectively deal with multi-objective optimizations with black-box functions.     

冲击荷载作用下简支圆板的塑性动力响应统一解

采用统一强度理论求解了简支圆板在中等脉冲荷载作用下的动力响应问题,得出了统一的动力塑性极限荷载、内力场和速度场,并给出了上限解和下限解。讨论了静力许可条件和运动许可条件。利用本文的解还得出了简支圆板在静力荷载作用下的极限荷载、内力场和速度场。根据选择不同的拉压比参数,本文所给出的解可以适用于各种拉压异性和拉压同性材料。Tresca解、Mohr Coulomb解和双剪统一屈服准则解是本文的特例,Mises解是本文当=1和b=0.5时的线性逼近。研究结果表明,拉压比和强度理论参数b对动力解的影响要大于对静力解的影响,所以,根据材料的不同选择合适的强度理论,对于更好的发挥材料的强度潜力,减轻结构的重量具有重要的意义。     

Hardness-packing density scaling relations for cohesive-frictional porous materials

Recent progress in instrumented nanoindentation makes it possible today to test in situ phase properties and structures of porous materials that cannot be recapitulated ex situ in bulk form. But it requires a rigorous indentation analysis to translate indentation data into meaningful mechanical properties. This paper reports the development and implementation of a multi-scale indentation analysis based on limit analysis, for the assessment of strength properties of cohesive-frictional porous materials from hardness measurements. Based on the separation-of-scale condition, we implement an elliptical strength criterion which results from the nonlinear homogenization of the strength properties of the constituents (cohesion and friction), the porosity and the microstructure, into a computational yield design approach to indentation analysis. We identify the resulting upper bound problem as a second-order conical optimization problem, for which advanced optimization algorithms became recently available. The upper bound yield design solutions are benchmarked against solutions from comprehensive elastoplastic contact mechanics finite element solutions and lower bound solutions. Furthermore, from a detailed parameter study based on intensive computational simulations, we identify characteristic hardness-packing density scaling relations for cohesive-frictional porous materials. These scaling relations which are developed for two pore-morphologies, a matrix-pore morphology and a polycrystal (perfect disordered) morphology, are most suitable for the reverse analysis of the strength parameters of cohesive-frictional solids from indentation hardness measurements.     

一个弹-粘塑性问题的统一解析解

采用统一强度理论对平面应变轴对称问题在弹－粘塑性状态下的解析解进行了分析,由此得到的统一解可以蜕化成一系列从Ｍｏｈｒ－Ｃｏｕｌｏｍｂ单剪强度理论到双剪强度理论的平面应变轴对称问题解析式。献中已有的关于弹－粘塑性问题的单剪解为本的特例,统一强度理论可以给出更符合各种不同材料特性的合理解。     

Continuum modeling of a porous solid with pressure-sensitive dilatant matrix

The pressure-sensitive plastic response of a material has been studied in terms of the intrinsic sensitivity of its yield stress to pressure and the presence and growth of cavities. This work focuses on the interplay between these two distinctly different mechanisms and the attendant material behavior. To this end, a constitutive model is proposed taking both mechanisms into account. Using Gurson's homogenization, an upper bound model is developed for a voided solid with a plastically dilatant matrix material. This model is built around a three-parameter axisymmetric velocity field for a unit sphere containing a spherical void. The void is also subjected to internal pressure; this can be relevant for polymeric adhesives permeated by moisture that vaporizes at elevated temperatures. The plastic response of the matrix material is described by Drucker–Prager's yield criterion and an associated flow rule. The resulting yield surface and porosity evolution law of the homogenized constitutive model are presented in parametric form. Using the solutions to special cases as building blocks, approximate models with explicit forms are proposed. The parametric form and an approximate explicit form are compared against full-field solutions obtained from finite element analysis. They are also studied for loading under generalized tension conditions. These computational simulations shed light on the interplay between the two mechanisms and its enhanced effect on yield strength and plastic flow. Among other things, the tensile yield strength of the porous solid is greatly reduced by the internal void pressure, particularly when a liquid/vapor phase is the source of the internal pressure.     

Mechanical properties of three variations of a wire-woven metal subjected to shear

In this study, two variations of WBC (Wire-woven Bulk Cross), named semi-WBC and straight-WBC, are introduced. In the variations, helically formed wires in an ordinary WBC are partly or totally replaced with straight wires to obtain higher shear strength and modulus, and the fabrication processes are modified to enhance productivity. Analytic solutions of the relative density, shear strength and modulus for the three variations of WBCs including the ordinary WBC with X-orientation are derived. And CAD modeling, shear tests and FEA were performed to prove the analytic solutions. The effects of the curviness of the struts loaded or floating between face sheets, and the offset at the joints are evaluated. The semi- and straight WBCs had equivalent shear strengths and moduli comparable to those of typical aluminum honeycombs, and all the three variations of WBCs maintained their strengths at low densities down to 1%.     

Stress state and strength of an inhomogeneous plastic strip with a defect in a stronger part

We consider discontinuous solutions of a boundary value problem for a system of plastic equilibrium equations under plane strain and use these solutions to study the stress state and strength of an inhomogeneous strip with a defect in the form of a transverse cut in a stronger part of the junction.     

Strength evaluation of a cement sheath adjacent to a production wellbore

A model for predicting the strength of a cement sheath adjacent to a production wellbore without consideration of internal and temperature stresses is proposed based on solutions of the Lamé problems for one- and two-layer tubes and the Huber–Mises yield criterion using the model of a perfectly plastic isotropic body.     

Biorthogonal stretching and shearing of an impermeable surface in a uniformly rotating fluid system

The flow induced by an impermeable flat surface executing orthogonal stretching and orthogonal shearing in a rotating fluid system is investigated. Both the stretching and shearing are linear in the coordinates. An exact similarity reduction of the Navier–Stokes equations gives rise to a pair of nonlinearly-coupled ordinary differential equations governed by three parameters. In this study we set one parameter and analyze the problem which leads to flow for an impermeable surface with shearing and stretching due to velocity u along the x-axis of equal strength a while the shearing and stretching due to velocity v along the y-axis of equal strength b. These solutions depend on two parameters—a Coriolis (rotation) parameter \(\sigma = \Omega /a\) and a stretching/shearing ratio \(\lambda =b/a\). A symmetry in solutions is found for \(\lambda = 1\). The exact solution for \(\sigma = 0\) and the asymptotic behavior of solutions for \(|\sigma | \rightarrow \infty\) are determined and compared with numerical results. Oscillatory solutions are found whose strength increases with increasing values of \(|\sigma |\). It is shown that these solutions tend to the well-known Ekman solution as \(|\sigma | \rightarrow \infty\).     

Displacement of surrounding rock in a deep circular hole considering double moduli and strength-stiffness degradation

The problem of cavity stability widely exists in deep underground engineering and energy exploitation. First, the stress field of the surrounding rock under the uniform stress field is deduced based on a post-peak strength drop model considering the rock's characteristics of constant modulus and double moduli. Then, the orthogonal non-associative flow rule is used to establish the displacement of the surrounding rock under constant modulus and double moduli, respectively, considering the stiffness degradation and dilatancy effects in the plastic region and assuming that the elastic strain in the plastic region satisfies the elastic constitutive relationship. Finally, the evolution of the displacement in the surrounding rock is analyzed under the effects of the double modulus characteristics, the strength drop, the stiffness degradation, and the dilatancy. The results show that the displacement solutions of the surrounding rock under constant modulus and double moduli have a unified expression. The coefficients of the expression are related to the stress field of the original rock, the elastic constant of the surrounding rock, the strength parameters, and the dilatancy angle. The strength drop, the stiffness degradation, and the dilatancy effects all have effects on the displacement. The effects can be characterized by quantitative relationships.     

A modified model for isothermal homogeneous and heterogeneous reactions in the boundary-layer flow of a nanofluid

The homogeneous and heterogeneous reactions in the boundary-layer of a flat surface are considered. The autocatalysts are assumed to be of regular sizes, while the solution is a dilute nanofluid. The heat release due to the chemical reactions is taken into account. The Buongiorno's model is used to describe the behaviors of this reaction system. This configuration makes the current model be different from all previous publications. Multiple solutions are given numerically to the rescaled nonlinear system, whose stability is verified. The results show that the strength coefficients of the homogeneous and heterogeneous reactions are key factors to cause the appearance of the multiple solutions in the distribution of the chemical reactions. Nanofluids enhance the diffusion of heat and help maintain the stability of chemical reactions.     

Enrichment of surface charge contributes to the stability of surface nanobubbles

Surface nanobubbles are spontaneously formed at the interface between hydrophobic surfaces and aqueous solutions, which show extraordinarily longer lifetime than that was predicted by the classical thermodynamics model. In the present work, by using a surface plasmon resonance microscopy (SPRM) to quantitatively measure the dissolution kinetics of individual surface nanobubbles in real time, we explored the effects of ionic strength and pH value on the dissolution rates (lifetime) of nanobubbles. The results revealed that nanobubbles could exist stably for a long time in low-concentration electrolyte solutions or high-concentration non-electrolyte solutions, while they dissolved quickly in high-concentration electrolyte solutions. With the increase of ionic strength, the dissolution rates were accelerated by 2–3 orders of magnitude, and thus the lifespan of these surface nanobubbles was significantly shortened. In addition to ionic strength, it was further found that, with the increase of acidity or alkalinity of the solution, the dissolution rates of the surface nanobubbles were faster than that in neutral solution. These results demonstrated that the interfacial charge enrichment significantly contributed to the extraordinary stability of the surface nanobubbles.     

不同拉压特性的厚壁圆筒极限内压统一解

厚壁圆筒在实际工程领域中应用广泛,若能精确计算出极限内压,对预防事故发生,降低风险有重要意义.工程中存在许多材料,其拉压强度和拉压模量均存在差异,这些差异对极限内压的大小有显著影响.以往研究表明,仅考虑拉压强度与拉压模量的一个方面,计算结果与实际情况存在一定的误差.本文基于双剪统一强度理论,综合考虑中间主应力效应及材料拉压强度和拉压模量的不同,推导了内压作用下厚壁圆筒的弹、塑性状态的应力分布及弹性极限内压、塑性极限内压与安定极限内压的统一解,通过与其他文献对比分析验证了本文计算结果的正确性,分析了半径比、统一强度理论参数、拉压强度比与拉压模量系数对弹性极限内压、塑性极限内压及安定极限内压的影响.结果表明:统一解均随半径比和统一强度理论参数的增大而增大,随拉压强度比的增大而减小,弹性极限内压随材料拉压模量系数的增大而减小,当壁厚增加到一定值后,安定极限内压随材料拉压模量系数的增大而减小;材料的拉压模量不同、拉压强度差异对厚壁圆筒的安定性影响显著,考虑中间主应力效应可使材料的潜能得到更充分发挥,极限内压随半径比的变化规律可为选择合理壁厚提供参考,该结论可为厚壁圆筒的工程应用提供理论依据.     

Maximum channel pressure of a nanosecond pulsed anode discharge in a KCl crystal

The breakdown channel pressure is estimated for the initial stage of breakdown of a KCl crystal using experimental data on the fracture of KCl crystals upon anode pulsed discharges, the known strength of this crystal, and solutions of the corresponding static boundaryvalue problem of the anisotropic theory of elasticity.