解梁书院清代刻书考

解梁书院是明代嘉靖年间由解州府设立的官方书院,也是明清时期河东地区重要的教育场所,曾经刊刻了大量图书,为后世留下珍贵的典籍文献,其刻书之富,可谓清代晋省书院翘楚。但是,有关解梁书院的刻书情况却鲜有记载。近年来,随着一批清代名人稿本陆续披露,作者在曾任解梁书院山长的阎敬铭信札中,发现了一些与解梁书院相关的记录,成为了解解梁书院刻书的重要依据。本文依据现有资料,从解梁书院的概况、刻印图书的传本调查、阎敬铭与解梁书院刻书的关系三个方面论述了清代解梁书院的刻书情况。

关于“连续梁弯曲变形的截断多项式解法”一文之管见

自从沈云程的文章发表后,出现了不同的见解。本文就此谈几点粗浅看法,以便抛砖引玉,共同商榷. 一、 文章和初参数法的联系 文章是用截断多项式来讨论问题的,研究如何求解梁的弹性线微分方程,与初参数法用的同一原理.文章导出的梁的普遍的挠曲线方程是用截断多项式表示的,公式的形式与单跨梁相一致.所以,文章与初参数法有紧密的联系.可是在文章中未提及初参数法这个名称显然是欠妥的。

求解超静定梁的打靶法

《打靶法求梁变形的数值解》[1]叙述了打靶法解线性微分方程的原理以及各种载荷情况下梁弯矩方程的通式,并给出了打靶法求解梁变形的算例。但在工程实际中,超静定梁是应用极为普遍的结构之一。对于超静定梁的求解,无论是解析法还是数值法,都已有很多种.本文在力法原理的基础上,以打靶法为手段来求解超静定梁.此法程序简单,精度高,实用性强,不仅是求解静定梁变形的简便数值方法,也是求解各种超静定梁的一种有效数值方法。

浅谈虞乡政区沿革

"虞乡"位于黄河文明发源地晋南地区。上古时期有虞氏就在此地生息繁衍,春秋至隋,虞乡与解州合称解梁。隋唐以降,虞乡置县。元明时期遭裁撤,清至民国重新置县。本文拟将其历史沿革划分为上古"有虞氏、或者虞国"时期、东周至隋的河东解梁、唐宋金清民时期的虞乡置县、元明虞乡临晋合并期几个历史时期。试图解读虞乡的沿革历史,以初步厘清"虞乡"的历史发展脉络。

An Existence Theorem of Positive Solution for Fourth-order Superlinear Semipositone Eigenvalue Problems

In this paper we investigate the existence of positive solution for a class of fourth_order superlinear semipositone eigenvalue problems. This class of problems usually describes the deformation of the elastic beam whose both end_points are fixed.

Travelling Wave Solutions to Stretched Beam's Equation: Phase Portraits Survey

In this paper, following the phase portraits analysis, we investigate the integrability of a system which physically describes the transverse oscillation of an elastic beam under end-thrust. As a result, we find that this system actually comprises two families of travelling waves： the sub- and super-sonic periodic waves of positive- and negative- definite velocities, respectively, and the localized sub-sonic loop-shaped waves of positive-definite velocity. Expressing the energy-like of this system while depicting its phase portrait dynamics, we show that these multivaiued localized travelling waves appear as the boundary solutions to which the periodic travelling waves tend asymptotically

Solving Nonlinear Differential Equation Governing on the Rigid Beams on Viscoelastic Foundation by AGM

In the present paper a vibrational differential equation governing on a rigid beam on viscoelastic foundation has been investigated. The nonlinear differential equation governing on this vibrating system is solved by a simple and innovative approach, which has been called Akbari-Ganji＇s method （AGM）. AGM is a very suitable computational process and is usable for solving various nonlinear differential equations. Moreover, using AGM which solving a set of algebraic equations, complicated nonlinear equations can easily be solved without any mathematical operations. Also, the damping ratio and energy lost per cycle for three cycles have been investigated. Furthermore, comparisons have been made between the obtained results by numerical method （Runk45） and AGM. Results showed the high accuracy of AGM. The results also showed that by increasing the amount of initial amplitude of vibration （A）, the value of damping ratio will be increased, and the energy lost per cycle decreases by increasing the number of cycle. It is concluded that AGM is a reliable and precise approach for solving differential equations. On the other hand, it is better to say that AGM is able to solve linear and nonlinear differential equations directly in most of the situations. This means that the final solution can be obtained without any dimensionless procedure Therefore, AGM can be considered as a significant progress in nonlinear sciences.

Lateral-torsional buckling of box beam with corrugated steel webs

Corrugated steel web is folded along the longitudinal direction and has the mechanical properties such as axial compression stiffness corrugation effect, shear modulus corrugation effect, similar to that of an accordion. In order to study the lateral-torsional buckling of box beams with corrugated steel webs (BBCSW) under the action of bending moment load, the neutral equilibrium equation of BBCSW under the action of bending moment load is derived through the stationary value theory of total potential energy and further, along with taking Kollbrunner-Hajdin correction method and the mechanical properties of the corrugated web into consideration. The analytical calculation formula of lateral-torsional buckling critical bending moment of BBCSW is then obtained. The lateral-torsional buckling critical bending moment of 96 BBCSW test specimens with different geometry dimensions are then calculated using both the analytical calculation method and ANSYS finite element method. The results show that the analytical calculation results agree well with the numerical calculation results using ANSYS, thus proving the accuracy of the analytical calculation method and model simplification hypothesis proposed in this paper. Also, compared with the box beams with flat steel webs (BBFSW) with the same geometry dimensions as BBCSW, within the common range of web space-depth ratio and web span-depth ratio, BBCSW’s lateral-torsional buckling critical bending moment is larger than that of BBFSW. Moreover, the advantages of BBCSW’s stability are even more significant with the increase of web space-depth ratio and web depth-thickness ratio.

Analytical solution for evaluating deformation response of existing metro tunnel due to excavation of adjacent foundation pit

The excavation of foundation pit generates soil deformation around existing metro tunnel with shield driving method,which may lead to the deformation of tunnel lining.It is a challenge to evaluate the deformation of shield tunnel accurately and take measures to reduce the tunnel upward displacement as much as possible for geotechnical engineers.A new simplified analytical method is proposed to predict the longitudinal deformation of existing metro tunnel due to excavation unloading of adjacent foundation pit in this paper.Firstly,the additional stress of soils under vertical axisymmetric load in layered soil is obtained by using elastic multi-layer theory.Secondly,the metro tunnel is regarded as a Timoshenko beam supported by Winkler foundation so that the shear effect of tunnels can be taken into account.The additional stress acting on the tunnel due to excavation unloading in layered soil are compared with that in homogeneous soil.Additionally,the effectiveness of the analytical solution is verified via two actual cases.Moreover,parametric analysis is conducted to investigate the responses of the metro tunnel by considering such factors as the variation of subgrade coefficient,offset distance from the excavation center to tunnel longitudinal axis as well as equivalent shear stiffness.The proposed method can be used to provide theoretical basis for similar engineering project.

Elasticity solution of laminated beams with temperature-dependent material properties under a combination of uniform thermo-load and mechanical loads

An exact solution for simply-supported laminated beams with material properties variable with temperature under a combination of uniform thermo-load and mechanical loads was investigated,based on the two-dimensional(2-D)thermo-elasticity theory.Firstly,the beam was divided into a series of layers with uniform material properties along the interfaces of the beam.The uniform thermo-load acted on each layer was transformed into a combination of the normal surface forces acted at the two ends and the transverse thermo-load.Secondly,the state space method was employed to obtain the general solutions of displacements and stresses in an arbitrary layer.Thirdly,based on the interfacial continuity conditions between adjacent layers,the relations of displacement and stress components between the top and bottom layers of the beam were recursively derived by use of the transfer-matrix method.The unknowns in the solutions can be solved by the mechanical loads acted on the top and bottom surfaces.The convergence of the present solutions was checked.The comparative study of the present solutions with the Timoshenko’s solutions and the finite element(FE)solutions was carried out.The effects of material properties variable with temperature on the thermo-elastic behavior of laminated beams were discussed in detail.

Elasticity solution of laminated beams subjected to thermo-loads

According to the two-dimensional(2-D) thermo-elasticity theory, the exact elasticity solution of the simply supported laminated beams subjected to thermo-loads was studied. An analytical method was presented to obtain the temperature, displacement and stress fields in the beam. Firstly, the general solutions of temperature, displacements and stresses for a single-layered simply supported beam were obtained by solving the 2-D heat conduction equation and the 2-D elasticity equations, respectively. Then, based on the continuity of temperature, heat flux, displacements and stresses on the interface of two adjacent layers, the formulae of temperature, displacements and stresses between the lowest layer and the top layer of the beam were derived out in a recurrent manner. Finally, the unknown coefficients in the solutions were determined by the use of the upper surface and lower surface conditions of the beam. The distributions of temperature, displacement and stress in the beam were obtained by substituting these coefficients back to the recurrence formulae and the solutions. The excellent convergence of the present method has been demonstrated and the results obtained by the present method agree well with those from the finite element method. The effects of surface temperatures, thickness, layer number and material properties of the plate on the temperature distribution were discussed in detail. Numerical results reveal that the displacements and stresses monotonically increase with the increase of surface temperatures. In particular, the horizontal stresses are discontinuous at the interface.

The analytical solutions for orthotropic cantilever beams (II):Solutions for density functionally graded beams

In this paper, the specific solutions of orthotropic plane problems with body forces are derived. Then, based on the general solution in the case of distinct eigenvalues and the specific solution for density functionally graded orthotropic media, a series of beam problem, including the problems of cantilever beam with body forces depending only on z or on x coordinate and expressed by z or x polynomial is solved by the principle of superposition and the trial-and-error method.

Positive solutions of nonlinear elastic beam equations with a fixed end and a movable end

The existence of n positive solutions is studied for a class of fourth-order elastic beam equations where one end is fixed and other end is movable. Here, n is an arbitrary natural number. Our results show that the class of equations may have n positive solutions provided the “heights” of the nonlinear term are appropriate on some bounded sets.

Analytical solution for functionally graded anisotropic cantilever beam under thermal and uniformly distributed load

The bending problem of a functionally graded anisotropic cantilever beam subjected to thermal and uniformly dis-tributed load is investigated,with material parameters being arbitrary functions of the thickness coordinate. The heat conduction problem is treated as a 1D problem through the thickness. Based on the elementary formulations for plane stress problem,the stress function is assumed to be in the form of polynomial of the longitudinal coordinate variable,from which the stresses can be derived. The stress function is then determined completely with the compatibility equation and boundary conditions. A practical example is presented to show the application of the method.

访常平村关帝家庙

去年夏天,我到晋南运城地区参访了世称武庙之冠的解州关帝庙和常平村的关帝家庙。常平村北临银波万顷的运城盐池,南靠山峦起伏的中条山脉,为人崇敬的“关圣帝君”就出生在这一“风水宝地”。据《关圣帝君传》云:“关羽河东解梁宝池里下冯村人也。”下冯村也就是现在的常平村。村里有这样一个传说:这个村子本来叫下冯村,后来因有人在天庭的玉皇大帝那里告了状,说是下冯村的人不尊敬老年人,品行不端。玉帝大怒。

普贤莊

佛像/佛具/沉香/红木/木雕/珠宝武财神关公即关羽,在整个华人文化圈内都是一个妇孺皆知、家喻户晓的人物。徐道在《历代神仙通鉴》中说,关公的前生本是"解梁老龙",汉桓帝时,河东连年大旱,老龙悯民心切,是夜汲黄河水兴云施雨。玉帝见老龙公然违反天命,擅取封水,令天曹以法剑斩之,掷头于地。解县僧普静。

Forward-backward doubly stochastic differential equations and related stochastic partial differential equations

The notion of bridge is introduced for systems of coupled forward-backward doubly stochastic differential equations （FBDSDEs）. It is proved that if two FBDSDEs are linked by a bridge, then they have the same unique solvability. Consequently, by constructing appropriate bridges, we obtain several classes of uniquely solvable FBDSDEs. Finally, the probabilistie interpretation for the solutions to a class of quasilinear stochastic partial differential equations （SPDEs） combined with algebra equations is given. One distinctive character of this result is that the forward component of the FBDSDEs is coupled with the backvzard variable.

Progress in rectifying-based RRAM passive crossbar array

Resistive random access memory(RRAM) with crossbar structure is receiving widespread attentions due to its simple structure,high density,and feasibility of three-dimensional(3D) stack.It is an extremely promising solution for high density storage.However,a major issue of crosstalk restricts its development and application.In this paper,we will first introduce the integration methods of RRAM device and the existing crosstalk phenomenon in passive crossbar array,and then focus on the 1D1R(one diode and one resistor) structure and self-rectifying 1R(one resistor) structure which can restrain crosstalk and avoid misreading for the passive crossbar array.The test methods of crossbar array are also presented to evaluate the performances of passive crossbar array to achieve its commercial application in comparison with the active array consisting of one transistor and one RRAM cell(1T1R) structure.Finally,the future research direction of rectifying-based RRAM passive crossbar array is discussed.