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复杂条件下地基承载力系数N_γ的上限解 总被引:1,自引:0,他引:1
由地基土重量引起的地基承载力系数N_γ的真实解答至今尚未获取.本文根据极限分析法与极限平衡法的等效性,构造出最危险的运动许可滑动机构,得出N_γ尽可能小的上限解.分别定量分析了在荷载倾斜、基底倾斜、地表倾斜对N_γ的影响,提出了近似影响系数公式,并与现有研究结果进行比较. 相似文献
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隧洞式内衬储气库是一种新型能源储存方法,有助于平衡供需,推动国家由化石能源向绿色能源的持续过渡,有利于国家“碳中和、碳达峰”目标的实现.本文采用极限平衡方法和弹塑性分析方法推导隧洞式内衬储气库极限储存压力的解析解.在极限平衡方法中,考虑上覆围岩自重、破裂面受力和极限储存压力,选用刚性锥模型,推导了上限压力表达式;在弹塑性分析方法中,根据围岩中应力分布规律和剪切、抗拉强度,推导获得了弹塑性条件下上限与下限压力表达式.最终综合考虑两方法求得的结果,确定极限储存压力解析解.结果表明:极限平衡方法求得上限压力与埋深呈二次函数关系,且随着侧压力系数的增大而增大;弹塑性分析方法确定的上限压力和下限压力与埋深呈线性关系,下限压力随着侧压力系数的增大而减小,且Ⅰ级围岩条件下的内衬储气库不用考虑下限压力.在侧压力系数λ=1.2时上限压力最大,因此应尽量在侧压力系数为1.2的围岩条件下修建隧洞式储气库.最后根据典型工况下上限和下限压力曲线给出内衬洞室推荐压力范围. 相似文献
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本文提出了有限条塑性系数增量初应力法,用于分析钢压杆的弹塑性稳定极限承载力,该法采用分级加载,用有限条法建立结构的增量平衡方程;在塑性范围,引入截面的塑性系数对弹性刚度进行折减得到结构的弹性刚度矩阵;用修正的Newto-Raphson方法迭代求解,数值结果表明,本法效率较高,与钢压杆试验结果吻合良好,可以考虑残余应力和载荷偏心的影响,可望实现大型超静定结构的极限载力分析。 相似文献
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求解冷弯开口薄壁截面短柱的极限承载力是一个板组结构的大挠度弹塑性分析问题,板件之间相互作用和纵向面内加载方式对其局部屈曲后性能和稳定极限承载力有很大的影响。本文应用大挠度弹塑性有限条分析方法系统地研究了冷弯薄壁槽形截面柱的极限承载能力和它们的优化性能,并对荷载偏心距为常数和位移梯度为常数的两种加载条件下的薄壁开口短柱局部屈曲后性能和极限承载力进行了对比分析和探讨。 相似文献
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本文利用岩土塑性力学的滑移场理论,建立了任意剖面的地基极限承载力的一般解,并考虑土体自重等因素进行了修正,结果与L.Prandtl,K.Terzaghi解的结果吻合良好 相似文献
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《应用力学学报》2021,(5)
针对洞跨对下伏空洞岩石地基极限承载力影响问题,对含空洞岩石地基极限承载力计算方法进行了推导和试验验证。首先采用极限分析上限法构建了一种空洞岩石地基破坏时的机动许可速度场,通过求解功能方程得到了地基极限承载力随空洞跨度变化的一般计算方法。通过参数分析研究了不同空洞跨度、顶板厚度对空洞岩石地基极限承载力的影响,并导得了空洞临界跨度与顶板厚度的关系表达式。最后进行了不同空洞跨度和厚度下的空洞地基极限承载力模型试验研究,并与理论进行了对比验证分析。结果表明:当厚径比h/d一定时,空洞岩石地基极限承载力随空洞跨度l的增加逐渐减小;存在一个临界跨度l_(cr),当超过临界跨度l_(cr)时空洞跨度的增加对空洞岩石地基极限承载力系数N_σ的影响较小且N_σ趋于稳定;当空洞跨度l为0.5d且厚径比h/d为1.0~2.5时,尚需考虑洞体对地基极限承载力的影响;同一空洞跨度l下,初始冲切角随着厚径比h/d的增加而减小。其他参数相同时,空洞地基极限承载力系数N_σ随GSI的增大而提高。 相似文献
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曲梁极限承载力涉及弯扭强度和稳定两方面的问题.尤其是曲梁进入弹塑性阶段后,截面上弯曲应力和扭转应力将不再保持原有的比例关系,问题变得更为复杂.水平曲梁在弹性和弹塑性阶段工作特性的研究成果为其工程应用提供了理论依据.在总结不同曲梁稳定极限承载力公式的基础上,通过对已有有限元计算结果的非线性回归,得到了工程实用的曲梁极限承载力估算公式. 相似文献
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采用极限分析下限原理求解了岩土工程中基础的极限载力和边坡的安全系数。求解过程中把有限元法和非线性规划相结合,把整个结构离散化,设定每个结点的应力,把原问题变成一个以边坡的稳定安全系数或基础的极限承载力为目标函数,以结点应力为优化变量,以对可静应力场的各种制约为约束条件的非线性规划问题。采用序列二次规划法求解该非线性规划问题,得到了人为构造的严格满足应力边界条件、平衡微分方程、不违反Mohr-Coulomb或Drucker-Prager屈服准则的应力场,解决了三维可静应力场的构造问题。算例分析表明,本文的方法是正确、可行的。 相似文献
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The analysis of the stresses in one-, two- and three-dimensional spinning bodies is discussed in a systematic and comprehensive way. First elastic solutions are derived for rods, for elliptical-shaped flat disks and for ellipsoidal solid bodies spinning about their sideways axes. Then the spins for first plastic yield are found in each case using each of the Tresca and the von Mises yield conditions. Then upper and lower bounds on the maximum allowable limit spins where the body would globally fail assuming perfectly plastic behavior are derived. The elastic solutions at first yield always give a lower bound to that limit spin, but global failure generally does not occur until the spin is increased. A way to calculate an improved lower bound is illustrated. Upper bounds are found in a simple and new way. The method uses the fact that the volume-averaged stresses can be calculated directly from the loadings without the need for any actual stress solutions, and then it is proved that the use of those average stresses in the yield functions always gives an upper bound to the limit loads. That use of the statically determinate average stresses to obtain meaningful plastic upper bounds to limit loads is though to be a new method, and can be applied to any shape. Finally, several finite element calculations are used to determine the quantitative relations between the lower and upper bounds and the actual limit spins for ellipsoidal bodies.The results are of interest in the spin of planetary bodies, where they explain the nature of an average-stress approximate method, and in the analysis of spinning bodies in general. In addition, the approach gives a very interesting example of the utility of the limit analysis approaches of plasticity theories. 相似文献
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Liu Yinghua Cen Zhangzhi Xu Bingye 《Acta Mechanica Solida Sinica》1995,8(3):263-276
A numerical investigation of the limit loads is carried out for pressurevessels with part-through slots using a general computational method for the limitanalysis of 3-D structures.The limit pressures are given for a comprehensive range ofgeometric parameters.Some of the calculated results are compared with the results of3-D elastic-plastic finite element analysis and existing numerical solutions.The effectsof various shapes and sizes of part-through slots on the load carrying capacity ofcylindrical shells are investigated and evaluated.Two kinds of typical failure modescorresponding to different dimensions of slots are studied.Based on the numericalresults,a geometric parameter G which combines the slot dimensions and the cylindergeometry is presented.It reasonably reflects the overall effect of slots on the limit loadsof cylinders.An empirical formula for estimating the limit pressures of cylindricalshells with part-through slots is obtained. 相似文献
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《International Journal of Solids and Structures》1999,36(8):1193-1207
Limit analysis has been rendered versatile in many structural and metal forming problems. In metal forming analysis, the slip-line method and the upper bound method have filled the role of limit analysis. As a breakthrough of the previous work, a computational approach to limit solutions is considered as the most challenging area.In the present work, a general algorithm for limit solutions of plastic flow is developed with the use of finite element limit analysis. The algorithm deals with a generalized Hölder inequality, a duality theorem, and combined smoothing and successive approximation in addition to a general procedure for finite element analysis. The algorithm is robust such that from any initial trial solution, the first iteration falls into a convex set which contains the exact solution (s) of the problem. The idea of the algorithm for limit solutions is extended from rigid⧹perfectly plastic materials to work-hardening materials by the nature of the limit formulation, which is also robust with numerically stable convergence and highly efficient computing time. 相似文献
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关于蜂窝芯体面外等效剪切模量的讨论 总被引:2,自引:0,他引:2
对于六边形蜂窝芯体,其面内等效参数具有确定的解析式,便于应用;相比之下,对于面外等效剪切模量,现有工作只能给出其上下限,由于没有确定的取值,给工程计算带来了困扰。为克服这一矛盾,本文通过Y型蜂窝胞元,针对薄面板的情况,重新分析了芯材的面外等效剪切模量。针对直壁板与斜壁板厚度为1:1和2:1的情况,给出了近似的弹性力学解答,并由此确定出面外等效剪切模量的上限。本方法所确定的剪切模量的上限与文献给出的剪切模量的下限是相同的,从而使该模量也具有确定的解析表达式,方便了数值计算和分析。试验数据和有限元数值分析均验证了本文结论的正确性。 相似文献
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基于自然单元法的极限上限分析 总被引:2,自引:0,他引:2
自然单元法是一种基于离散点集的Voronoi图和Delaunay三角化几何信息,以自然邻近插值为试函数的新型数值方法.相对于一般无网格法中常采用的移动最小二乘近似而言,自然邻近插值不涉及到复杂的矩阵求逆运算,更不需要任何人为的参数,可以提高计算效率.采用该方法构造的形函数满足Delta函数的性质,可以像有限元一样准确地施加边界条件,可以方便处理场函数及其导数的不连续性的问题.论文将自然单元法应用到极限上限分析中,编制了相应的计算程序,通过极限分析的几个经典算例进行了验证,同时采用类似于分片应力磨平的方式,编制相应的磨平程序,由计算点上的塑性耗散功外推得到了节点上的塑性耗散功的值,从而画出了极限状态下结构的塑性耗散功的分布云图.计算结果表明采用自然单元法求解极限上限分析具有稳定性好,精度高,收敛快等优点. 相似文献
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极限分析和安全分析的近代发展方向是寻找通用性强,计算效率高的数值方法。本文介绍将有限单元法和数学规划法相结合的、同时适用于极限分析和安全分析的统一数值方法,包括下限格式和上限格式。 相似文献