Shakedown theory for elastic plastic kinematic hardening bodies

Shakedown static and kinematic theorems for elastic–plastic (generally nonlinear) kinematic hardening solids are derived in classical (path-independence) spirit with new constructions. The generally plastic-deformation-history-dependent hardening curve is assumed to be limited by the initial yield stress and ultimate yield strength, and to obey a positive hysteresis postulate for closed plastic cycles, but else can be arbitrary and unspecified. The theorems reveal that the shakedown of structures is not affected by the particular form of the hardening curve, but just by the initial and ultimate yield stresses. While the ultimate yield strength is clearly defined macroscopically and attached to the incremental collapse mode with unbounded plastic deformations, the initial yield stress, which is responsible for the bounded cyclic plasticity collapse mode, should not be taken as the convenient one at a fixed amount of plastic deformation (0.2%), but is suggested to be taken as low as the fatigue limit to preserve the classical load-history-independence spirit of the shakedown theorems. Otherwise, for our pragmatic application purpose, it may be given empirical values between the low fatigue limit and high ultimate yield stresses according to particular loading processes considered, which may range anywhere between the high-cycle and low-cycle ones. The theorems appear as simple as those of Melan and Koiter for perfect plasticity but applied to the much larger class of more realistic kinematic hardening materials.     

基于能量法组合梁倒塌工况下的抗力分析

框架结构在竖向承重构件突然发生破坏的情况下主要通过两个抗倒机制防止连续倒塌的发生,分别为小变形状态下的梁机制以及大变形状态下的悬链线机制.组合楼板由于平面刚度大,可以显著提高框架结构的抗倒性能.将混凝土楼板-钢框架结构简化为组合梁结构进行分析.对已有研究得到的抗力曲线进行适当简化,并运用能量法分析抗倒各个阶段的受力特征以得到曲线各个阶段的表达式.随后应用大型有限元分析软件ANSYS对理论公式的可靠性进行算例验证,说明提出的分析方法较为合理,同时可以发现楼板对结构抗倒有明显的的加强作用.     

基于广义非线性统一强度理论的隧道塌落拱分析

基于广义非线性统一强度的剪切破坏理论,在平面应变状态下,根据极限上限定理和隧道顶部的围岩塌落机制,在耗散能中引入了包含曲线型破裂面方程的目标函数,建立了围岩中任意断面的隧道顶部围岩的塌落机制。基于塑性位势理论,考虑塑性应变增量与塑性势函数的应力梯度成正比,由此得出了在速度间断线上任意点内能的耗散率;再运用虚功原理,建立内能耗散率和外力做功相等的关系式,从而通过变分原理得出了隧道顶部塌落面的解析表达式,由该表达式计算出隧道顶部塌落面的形状。以圆形断面隧道为例,对影响塌落拱形状的隧道半径和中间主剪应力系数等相关参数进行了讨论分析。由此得出:在平面应变状态下,隧道顶部围岩塌落体的宽度和高度随着中间主剪应力系数的不断增大而减小;塌落面的高度随着广义非线性统一强度参数的不断增大而增大,而塌落面的宽度则不断减小;塌落宽度和塌落高度随隧道半径的增大而增大。     

Gravitational Collapse of a Spherical Star with Heat Flow as a Possible Energy Mechanism of Gamma-Ray Bursts

We investigate the gravitational collapse of a spherically symmetric, inhomogeneous star, which is described by a perfect fluid with heat flow and satisfies the equation of state p=ρ/3 at its center. In the process of the gravitational collapse, the energy of the whole star is emitted into space. And the remaining spacetime is a Minkowski one without a remnant at the end of the process. For a star with a solar mass and solar radius, the total energy emitted is at the order of 10⁵⁴ erg, and the time-scale of the process is about 8 s. These are in the typical values for a gamma-ray burst. Thus, we suggest the gravitational collapse of a spherical star with heat flow as a possible energy mechanism of gamma-ray bursts.     

Transformation of alkynyl sulfones into alkynylphosphonates with trialkyl phosphites

1-Alkynylphosphonates were obtained in good to high yields by simple heating of 1-alkynyl sulfones with trialkyl phosphites.     

Bridging contributions to polyelectrolyte brush collapse in multivalent salt solutions

Polyelectrolyte brushes are essential in many aspects of surface functionality, particularly for colloidal stabilization and lubrication in biological and materials science applications. It has been shown experimentally that the brushes undergo an abrupt shrinkage in the presence of multivalent counter-ions. This transition is studied here using a phenomenological mean-field approach with a model that specifically includes bridging of the polyelectrolyte chains by the multiple charges on the multivalent counter-ions. Using an energy balance represented by the sum of electrostatic, polymeric and entropic mean-field terms, additional parameterized phenomenological terms are introduced for counter-ion condensation and for the attractive interaction between adjacent polyelectrolyte chains to account for the bridging effect. The free energy is minimized with respect to the counter-ion populations and the brush height. In agreement with experimental observations, increasing the concentration of multivalent ions leads to a sharp collapse of the polyelectrolyte brush height. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016, 54, 284–291     

聚环氧乙烷在水和叔丁醇溶液中分子构型变化的研究

在聚合物溶液中,聚合物单体和溶剂分子之间的相互作用会影响聚合物高分子的尺寸和结构。本文使用动态光散射实验系统研究了聚环氧乙烷在水+TBA二元混合溶液中的分子尺寸变化,实验结果表明聚环氧乙烷分子会呈现出收缩-膨胀的奇异性构型变化。本文也系统分析了产生该现象的原因,依次分析了在二元混合溶液中可能对聚合物分子尺寸产生影响三个原因:溶剂非理想性影响(Shultz-Flory理论)、临界涨落影响以及水+醇溶液所呈现出来的奇异性性质。结合这三个因素,本文较好地解释了实验所观测到的奇异现象。     

Spectral Determinant of the Two-Photon Quantum Rabi Model

The various generalized spectral determinants (G-functions) of the two-photon quantum Rabi model are analyzed with emphasis on the qualitative aspects of the regular spectrum. Whereas all of them yield at least a subset of the exact regular eigenvalues, only the G-function proposed by Chen et al. in 2012 exhibits an explicitly known pole structure which dictates the approach to the collapse point. This function is derived rigorously employing the ${\mathbb{Z}}_4$-symmetry of the model and shown that its zeros correspond to the complete regular spectrum.     

Interaction of non-ionic hydrogels with weak aromatic acids

Measurements are reported of the swelling behaviour at 20°C of poly (N isopropylacrylamide) (PNIPA) gels in aqueous solutions of two weak aromatic acids, phenol and resorcinol. For solute concentrations below 45 mmol/l the uptake of these solutions is similar. Due to selective solvation phenol exhibits an excess equilibrium concentration inside the gel of 5% over that in the surrounding bath, while for resorcinol, the excess is found to be 12%. At 50 mmol/l solute concentration, both systems display a volume transition accompanied by expulsion of the solvent. The solubility limits in water of these aromatic compounds, which are significantly different from each other (870 mmol/l and 9080 mmol/l respectively), are far above this critical concentration. In the collapsed condition the expelled liquid spreads on the surface of the phenol treated gel, while an ordered arrangement of separate droplets is generated in the case of resorcinol. In the latter case an acute contact angle was observed. It is also shown by acid-base titration that the PNIPA/water system may exhibit a slight ion exchanging character.