The Minimum Energy Principle in Description of Nonlinear Properties of Orthotropic Material

In this paper the conception of theoretical determine the relations between material experimental characteristics is presented. On the base of stress-strain relations for nonlinear elastic anisotropic material and geometrical interpretation of deformation state, the general form of strain energy density function was introduced. Using this function and variational methods the relations between material characteristics were achieved. All considerations are illustrated by a short theoretical example.

Numerical simulation of dense particle-gas two-phase flow using the minimal potential energy principle

A simulation method of dense particle-gas two-phase flow has been developed. The binding force is introduced to present the impact of particle clustering and its expression is deduced according to the principle of minimal potential energy. The cluster collision, break-up and coalescence models are proposed based on the assumption that the particle cluster are treated as one discrete phase. These models are used to numerically study the two-phase flow field in a circulating fluidized bed （CFB）. Detailed results of the cluster structure, cluster size, particle volume fraction, gas velocity, and particle velocity are obtained. The correlation between the simulation results and experimental data justifies that these models and algorithm are reasonable, and can be used to efficiently study the dense particle-gas two-phase flow.

Applied principle of minimum potential energy in analyzing buckle phenomenon of cold rolled strip

When solving buckling type based on minimum potential energy, it is first to make hypothesis for strip buckling type. Under the simple strain condition, buckling type and strain distribution have a certain similarity, so the hypothesis is reasonable comparatively. However, under the complicated strain condition, it is difficult to give more reasonable buckling type. Moreover, the existing algorithms usually ignore the effect which the transverse stress and the shear stress have on the buckling type. After assuming strip was only affected by shear stress for the edge wave and affected by both transverse stress and the shear stress for the center wave in the paper, the buckling form of strip under simple strain situation was calculated. It was seen from the calculating result that wave height and half wavelength were smaller than those of the existing algorithms, and the wave height and half wavelength of edge wave were all bigger than those of center wave in the same stress distribution. Secondly, a more reasonable hypothesis method of buckling type for the complicated stress distribution was put forward. After analyzing, the result showed that it was more reasonable by using the optimizing algorithm.

GENERALIZED VARIATIONAL PRINCIPLES OF THE VISCOELASTIC BODY WITH VOIDS AND THEIR APPLICATIONS

From the Boltzmann's constitutive law of viscoelastic materials and the linear theory of elastic materials with voids, a constitutive model of generalized force fields for viscoelastic solids with voids was given. By using the variational integral method, the convolution-type functional was given and the corresponding generalized variational principles and potential energy principle of viscoelastic solids with voids were presented. It can be shown that the variational principles correspond to the differential equations and the initial and boundary conditions of viscoelastic body with voids. As an application, a generalized variational principle of viscoelastic Timoshenko beams with damage was obtained which corresponds to the differential equations of generalized motion and the initial and boundary conditions of beams. The variational principles provide a way for solving problems of viscoelastic solids with voids.

Heuristic algorithm based on the principle of minimum total potential energy(HAPE):a new algorithm for nesting problems

We present a new algorithm for nesting problems.Many equally spaced points are set on a sheet,and a piece is moved to one of the points and rotated by an angle.Both the point and the rotation angle constitute the packing attitude of the piece.We propose a new algorithm named HAPE(Heuristic Algorithm based on the principle of minimum total Potential Energy) to find the optimal packing attitude at which the piece has the lowest center of gravity.In addition,a new technique for polygon overlap testing is proposed which avoids the time-consuming calculation of no-fit-polygon(NFP).The detailed implementation of HAPE is presented and two computational experiments are described.The first experiment is based on a real industrial problem and the second on 11 published benchmark problems.Using a hill-climbing(HC) search method,the proposed algorithm performs well in comparison with other published solutions.

A nonlinear rheological model of backfill material for retaining roadways and the analysis of its stability

The long-term stability of backfill material is the key to retaining roadways successfully. In order to study the rheological deformation of backfill material and its long-term stability, given the visco-elastoplastic properties of this material, we introduced a softening and a hardening function for a new nonlinear the- ological model with time-varying parameters. Based on this, we presented the instability condition of this model by using the principle of minimum potential energy. Combined with engineering practice, we cal- culated the urlstable time period of backfill material. The results show that the time of instability of the backfill material relate to the initial parameters of the material, ＂the coefficients decided by temperature and the ratio of the plastic zone of the backfill material. Based on the results of our analysis from the point of view of energy, we can quickly obtain the time of instability of this model from our graphical analysis. The time of instability of the backfill material obtained from our investigation coincides with an actual project.

THE DERIVATION OF EXACT STATIC CONDITIONS AT THE CORNER POINTS FOR THE BENDING OF THICK RECTANGULAR PLATES

In this paper, exact static conditions at the corner points for the bending of thickrectangular ptates are strictly. derived from the theorem of minimum potentialenerg[1].

Strong Interaction and Newtonian Potential Energy

The central part of the nuclear potential energy is shown to depend on the interacting masses of the nuclear matter. This mass dependent potential energy reduces to the usual Newtonian potential energy of the interacting masses when both the interacting masses are more than a certain limiting mass. This strong potential energy results when both the interacting masses are less than the limiting mass. The potential energy is applied to two more systems here and out of which one nucleus is in the middle of periodic table.

A Study of the Pit-Aided Construction of Egyptian Pyramids

Pyramids,symbols of the Ancient Egyptian civilization,are visited by tourists and studied by researchers from all around the world.However,the techniques used by Ancient Egyptians to construct the pyramid,specifically,how such a tall structure could have been constructed from huge blocks of stone with the limited productive forces at the time,remains a mystery to the world.Though numerous theories,such as the use of ramps,levers,pulleys,fluid buoyancy,and cast-in-place concrete,have been proposed in academia,no consensus has been reached to date.Based on mechanical principles and the productive forces available at the time,the famous Pyramid of Khufu is used as a case study in this paper to propose a theory of pit-aided construction.The main steps include the digging of the pit,the transportation of stone blocks into the pit,the layer-by-layer construction,and the layer-by-layer filling of soil until the top of the pyramid is completed.The main idea of the pit-aided construction was to use the self-weight of the stone material to achieve the transportation of stone blocks by converting potential energy to kinetic energy,thereby avoiding the large amounts of work that must be done to elevate the huge blocks of stone.The proposed theory of pit-aided construction is consistent with the cultural custom of burial that is associated with tomb construction,namely laying the deceased to rest through burial,and is also consistent with the productive forces available in Ancient Egypt at the time.

基于磁各向异性的管壁应力集中区域检测方法

针对应力集中导致管壁发生屈服失效的问题,提出了利用磁各向异性检测管壁应力集中区域的方法。从能量角度出发,研究了应力导致管壁产生磁各向异性的机理,建立了管壁当量应力与磁各向异性探头输出电压信号的数学模型,通过计算管壁的当量应力判断其是否发生屈服失效,搭建了应力检测实验平台。实验结果表明,应力会导致管壁产生磁各向异性,磁各向异性检测方法能够检测出管壁当量应力的变化趋势和主应力方向所在延长线的角度,进而判断管壁是否产生应力集中区域。

预应力UHPC-NC组合梁结合面徐变剪应力分析

在恒载应力作用下,预应力UHPC-NC组合梁因两种材料不同的徐变特性及加载龄期的差异导致结合面产生徐变剪应力,分别采用解析法和有限元法对结合面徐变剪应力进行分析。在解析法中,用三角级数表示UHPC-NC结合面的应力分布,基于结合面上的变形协调,利用最小余能原理推导出结合面徐变剪应力计算公式。在有限元法中,将组合梁UHPC层与NC层均划分成四边形平面应力单元,对结合面则采用等效杆单元模拟。以T形截面预应力UHPC-NC组合梁为例进行计算方法的验证,两种方法的计算结果吻合良好,且研究发现徐变剪应力最大值位于梁端;在此基础上对影响结合面徐变剪应力分布的UHPC层压应力、梁高、计算龄期、环境年平均相对湿度等参数进行分析,结果表明:结合面徐变剪应力最大值随着UHPC层压应力、计算龄期、环境年平均相对湿度的增大而增大,但基本不随梁高变化;结合面徐变剪应力最大值的位置随着梁高的增大而逐步向跨中靠近,其他因素不影响应力最大值的位置。研究结果可为UHPC-NC组合梁结合面的抗剪设计提供参考。

基于综合赋权与云熵优化的园区综合能源系统评价

综合能源系统(integrated energy system,IES)作为能源转型中的重要环节已得到越来越多国家的广泛关注。构建一套匹配中国国情的综合能源系统评价体系和评价方法不仅能够为综合能源系统规划后评价打下基础,以此对规划方案进行优劣排序;还能够提高综合能源系统项目的管理水平,在制定统一、完整的综合能源系统综合评价标准时提供参考。为此,首先结合园区IES基本特征以及运行特性,构建包含经济性、可靠性、环保性以及智能友好性4个方面的综合评价指标体系;然后为解决IES在运行中的不确定性问题,对基于传统云物元模型的综合评价体系提出云熵优化,即考虑不同评价者对模糊性的可接受程度;为解决单一赋权方法可能导致的评价结果过于主观或过于客观的问题,选择基于最小鉴别信息原理将决策实验室法与熵权法相结合的综合赋权法,并采用变权法进一步完善综合评价指标;最后通过算例分析,验证所提综合评价体系的科学正确性。

高速铁路桥梁结构变形与轨面几何形态的空间映射模型研究

高速铁路桥梁附加变形会导致轨面几何形态的变化,加剧列车和轨道-桥梁结构之间的动态相互作用,影响桥上行车安全性。以32 m简支梁桥-CRTSⅡ型板式无砟轨道结构为研究对象,将箱梁看作耦合板结构,选取改进傅里叶级数作为结构的试函数,通过输入梁体的附加变形值,基于势能驻值原理求解轨道各结构层的垂、横向变形函数,建立桥梁结构变形与轨面几何形态的空间映射模型。研究考虑底板脱空情况下桥梁典型横、竖向组合变形下轨面几何形态的变形规律。研究表明:空间映射模型与有限元模型得到的钢轨变形曲线吻合较好。映射模型经过少量的迭代便可以求出底板脱空的位置、幅值与面积。钢轨在梁体横、竖向组合变形下存在耦合变形效应,梁体横向转角幅值对钢轨垂向变形影响较大,并会导致左右两块底板脱空区域的范围与幅值发生相反变化趋势,进而使底板上方两侧钢轨“上翘”处以及“下凹”处最大变形值发生改变。桥墩垂向沉降值基本不会影响其钢轨横向变形。

静置工况条件下掺氢天然气浓度分布规律

利用天然气管道进行掺氢输送已成为氢能及天然气输送领域的热点和重点,但当前业界对于掺氢天然气在管道输送和停输静置过程中是否会自发分层一直存在较大争议。为了厘清该问题,以掺氢天然气在管道中静置这一极端工况为例,基于热力学能量最小原理,推导了在重力场作用下掺氢天然气浓度分布数学模型,并采用Peng-Robinson真实气体状态方程对该数学模型进行了求解,最后研究了甲烷—氢气二元组分混合气体在4种典型场景高度和5种掺氢比下氢浓度随高度的分布规律。研究结果表明:(1)在重力影响下管道顶部和底部的氢浓度存在差异,但其受高度差的影响显著,对于米级的水平管道、几十米级的一般城镇楼宇天然气立管、百米级的高层楼宇天然气立管,氢浓度随高度变化的差异微小,可完全忽略氢分层;(2)对于千米级大落差的掺氢天然气管道,当掺氢比不超过20%时,氢分层仍可忽略,但当掺氢比很高时(例如50%)管道顶部和底部的氢浓度差将超过1%,此时需考虑工程实际情况评估能否忽略氢分层;(3)西气东输某管道考虑真实气体组成、掺氢比20%、管道落差200 m时,各气体组分的浓度随落差高度的分布规律揭示了在实际工程中此类落差高度的掺氢天然气氢分层可忽略。结论认为,对于掺混均匀的掺氢天然气在静置这种最容易发生分层的极端工况下,如果不存在千米级极端大落差和极端大掺氢比,掺氢天然气管道分层现象可完全忽略;该认识从理论上厘清了目前关于掺氢天然气分层现象的争议,对掺氢天然气管道安全输送具有重要指导意义。

一种研究高铁轨面-桥梁横向变形映射关系的精细化解析模型

强震后的桥墩和支座不可避免会产生一定残余变形,引起钢轨的几何不平顺,直接影响行车安全性和舒适性。该文基于势能驻值原理推导了CRTS-Ⅱ型纵连式无砟轨道横向变形与桥梁结构横向变形之间的映射解析表达式,提出了可考虑层间各构件刚度贡献的解析映射模型。通过有限元模型和文献解析模型验证了该文解析映射模型,进而基于该模型定量分析了层间构件对钢轨横向映射变形的影响。结果表明:梁体横向错台下的钢轨映射变形呈现明显非对称性,且跟随主梁变形的特性较差;扣件对钢轨映射变形的影响很小;CA砂浆层对梁体错台下钢轨映射变形幅值的影响很大,滑动层次之,而对钢轨映射变形范围的影响则弱于滑动层;剪力齿槽对钢轨映射变形的影响最大,侧向挡块次之;剪切钢筋对钢轨映射变形的影响可以忽略;桥梁抗弯刚度对钢轨映射变形范围有一定影响,而对钢轨映射变形幅值的影响几乎可以忽略。

Application of stiffness matrix of a beam element considering section distortion effect

According to the stationary principle of potential energy and the generalized coordinate method, a stiffness matrix of a beam element considering distortion effects is derived. Using the stiffness matrix of the beam element, a finite element program for computing thin-walled box steel beams is developed. And the program can take the section distortion and warping effects into account. The influences of diaphragm spacing on the mechanical behavior of thin-walled box beams are analyzed by the program. The numerical analysis shows that setting diaphragms have the greatest influence on the distortion normal stress, while there is very little influence on the bending normal stress. Only when the distance of adjacent diaphragms decreases to a certain value, will the distortion normal stress in the thin-walled box beam obviously reduce under the distortion load. Finally, a distortion-warping coefficient γ is introduced for simplifying the calculation of the longitudinal normal stress of thin-walled box beams. When the ratio of diaphragms adjacent space L to the maximum section dimension H is less than 2, the distortion-warping coefficient γ tends to one, which means that the distortion normal stress of the thin-walled box beam tends to zero, and the effect of the section distortion can be ignored.

基于庞特里亚金极小值原理的柴电混合动力船舶能量管理策略

提升混合动力船舶的能源利用率,制定合适的能量管理策略以实现功率合理分配、减小船舶燃油消耗、节约成本,是混合动力船舶的亟需解决的关键技术问题。本文基于Matlab/Simulink仿真建模软件,建立对象船舶的动力系统仿真模型,研究不同功率需求下对柴油发电机和超级电容的控制要求。考虑动力源特性和船舶功率需求,本文提出了一种基于庞特里亚金极小值的能量管理策略对目标船舶进行合理的功率分配。仿真结果表明:基于庞特里亚金极小值原理的能量管理策略能够优化船舶柴油机组原动机的工作状态,使其在比油耗较低的点工作。在该策略的控制下,航行工况内的柴油发电机组原动机平均比油耗为207.2 g/(kW·h),总燃油消耗量为204.1 kg。本文方法不仅对船舶减小燃油消耗具有积极的作用,同时对提高船舶运行经济性具有重要意义。

基于最小势能原理的双渐开线齿轮载荷分布研究

双渐开线齿轮接触线上的载荷非均匀分布,使得载荷计算困难。采用现有的方法或过于简化导致精度不足,或过于复杂使得计算量大、耗时长,并不适用于双渐开线齿轮载荷分布研究。为此,将双渐开线齿轮接触线等分为若干段,建立了双渐开线齿轮载荷分布模型,综合有限元法对轮齿载荷分布进行了研究。首先,根据双渐开线齿轮的啮合特点,求解了时变接触线,将每一啮合时刻下的齿轮接触线“分段”;然后,基于最小势能原理,建立了双渐开线齿轮的载荷分布模型,综合有限元法对齿轮轮齿载荷分布进行了研究;最后,对双渐开线齿轮与普通渐开线齿轮的载荷分布进行了对比分析,并研究了输入扭矩、齿宽对双渐开线齿轮轮齿载荷分布的影响。研究结果表明:载荷分布模型与有限元仿真结果之间的误差在10%之内,载荷分布模型合理可靠;双渐开线齿轮沿接触线方向载荷分布不均匀,节线附近载荷值最大;同参数、同工况下的双渐开线齿轮载荷波动幅度小于普通渐开线齿轮;输入扭矩增加,双渐开线齿轮节线附近载荷分布发生突变;齿宽增加,双渐开线齿轮沿接触线载荷分布不均匀程度增加。

基于势能原理基面力元法的橡胶混凝土损伤分析

以势能原理基面力元的方法为基础,对橡胶混凝土的细观力学性能展开了分析,建立了橡胶混凝土随机圆骨料模型,模拟了橡胶混凝土单轴静态受压的破坏过程,对破坏机理进行了分析,研究了不同橡胶掺量下对橡胶混凝土抗压强度的影响。数值模拟结果表明,橡胶混凝土单轴受压过程中的应力应变变化受骨料随机分布影响较小,并且随着橡胶掺量的提高,抗压强度明显降低。与物理试验对比发现,该细观损伤模型较好地模拟出了橡胶混凝土的抗压强度和开裂过程,为今后分析橡胶混凝土的细观力学性能提供了新的思路。

基于变形机动分析的薄壁箱梁畸变效应研究

提出一种通过角点位移分析箱梁畸变效应的理论解析法。基于变形机动分析,以分解的角点位移描述和分析箱梁畸变行为;根据应变假设和闭合箱室满足的翘曲位移连续性条件推导畸变翘曲位移及应力分布模式;根据势能驻值原理,建立以角点位移为未知量的畸变控制微分方程。通过数值算例,验证解析理论和计算方法的正确性。结果表明:按翘曲模式分析的截面翘曲位移沿板宽按直线分布,翘曲正应力的分布与在板元弯曲假设下的应力分布规律相同;考虑泊松比影响后的横向弯矩相比于忽略泊松比时增大未超过0.6%;角点沿垂直顶(底)板方向的畸变位移大于其沿垂直腹板方向的位移分量;腹板与顶板交点处的翘曲正应力和横向弯矩小于腹板与底板交点处的相应值;腹板倾角变化对翘曲正应力和横向弯矩有显著影响,合理减小腹板倾角可一定程度减小翘曲正应力和横向弯矩。