共查询到19条相似文献,搜索用时 213 毫秒
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1.历史的回顾1.1 早期的工作数学规划方法用于结构优化设计问题,有相当短但生动的历史。1958年以前,这一领域的研究建立在塑性设计原理上。简要地说,这种方法是在结构受到按比例加大使用载荷而得到的过载作用下,防止塑性破坏并探求重量最轻。在塑性设计原理中,一类重要的结构优化问题可公式化成线性规划。线性规划方法早期用于以塑性破坏理论为基础的平面框架最小重量设计,它并没有考虑多种加载或交替的加载情况。后来,认识到在塑性设计原理中需要处理交替加载情况并成功地进行了处理。早期数学规划方法用于最优结构设计是取线性规划的形式,因为它们是在简化塑性破坏设计原理范围内用公式表述的。 相似文献
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超静定梁的弹塑性分析 总被引:9,自引:0,他引:9
通过虚功原理和单位载荷法分析了超静定梁的弹塑性加载过程,给出了加载过程中外
载荷与约束反力的非线性关系,并据此对塑性力学中超静定梁的塑性极限分析的编写提出了
建议. 相似文献
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多孔材料塑性极限载荷及其破坏模式分析 总被引:4,自引:1,他引:4
运用塑性力学中的机动极限分析理论,研究韧性基体多孔材料的塑性极限承载能力和破坏模式。以多孔材料的细观结构为研究对象,将细观力学中的均匀化理论引入到塑性极限分析中,并结合有限元技术,建立细观结构极限载荷的一般计算格式,并提出相应的求解算法。数值算例表明:细观孔洞对材料的宏观强度影响明显;在单向拉伸作用下,孔洞呈现膨胀扩大规律;多孔材料破坏源于基体塑性区的贯通。 相似文献
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"超静定梁的塑性极限分析" 作为塑性力学教材中的一节内容,阐述了如何用"机动法" 和"静力法" 求最终的塑性极限破坏载荷,却没有分析超静定梁的弹塑性加载变形过程. 通过把结构力学中计算弹性位移的单位载荷法扩展应用到超静定梁的弹塑性加载过程,以均布载荷作用下两端固支超静定梁的弹塑性加载和变形全过程分析为例,构建了超静定梁弹塑性加载过程分析的教学内容,给出了两端固支超静定梁在均布载荷加载过程中弯矩内力和挠度随外载荷而变化的解析公式. 主要目的是引导学生掌握超静定梁复杂的非线性弹塑性加载变形全过程的分析方法,可供塑性力学教材改编时参考引用. 相似文献
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《International Journal of Plasticity》2006,22(10):1962-1987
Employing repeating unit cell (RUC) to represent the microstructure of periodic composite materials, this paper develops a numerical technique to calculate the plastic limit loads and failure modes of composites by means of homogenization technique and limit analysis in conjunction with the displacement-based finite element method. With the aid of homogenization theory, the classical kinematic limit theorem is generalized to incorporate the microstructure of composites. Using an associated flow rule, the plastic dissipation power for an ellipsoid yield criterion is expressed in terms of the kinematically admissible velocity. Based on nonlinear mathematical programming techniques, the finite element modelling of kinematic limit analysis is then developed as a nonlinear mathematical programming problem subject to only a small number of equality constraints. The objective function corresponds to the plastic dissipation power which is to be minimized and an upper bound to the limit load of a composite is then obtained. The nonlinear formulation has a very small number of constraints and requires much less computational effort than a linear formulation. An effective, direct iterative algorithm is proposed to solve the resulting nonlinear programming problem. The effectiveness and efficiency of the proposed method have been validated by several numerical examples. The proposed method can provide theoretical foundation and serve as a powerful numerical tool for the engineering design of composite materials. 相似文献
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《International Journal of Solids and Structures》2005,42(14):4058-4076
In this paper, a nonlinear numerical technique is developed to calculate the plastic limit loads and failure modes of frictional materials by means of mathematical programming, limit analysis and the conventional displacement-based finite element method. The analysis is based on a general yield function which can take the form of the Mohr–Coulomb or Drucker–Prager criterion. By using an associated flow rule, a general nonlinear yield criterion can be directly introduced into the kinematic theorem of limit analysis without linearization. The plastic dissipation power can then be expressed in terms of kinematically admissible velocity fields and a nonlinear optimization formulation is obtained. The nonlinear formulation only has one constraint and requires considerably less computational effort than a linear programming formulation. The calculation is based entirely on kinematically admissible velocities without calculation of the stress field. The finite element formulation of kinematic limit analysis is developed and solved as a nonlinear mathematical programming problem subject to a single equality constraint. The objective function corresponds to the plastic dissipation power which is then minimized to give an upper bound to the true limit load. An effective, direct iterative algorithm for kinematic limit analysis is proposed in this paper to solve the resulting nonlinear mathematical programming problem. The effectiveness and efficiency of the proposed method have been illustrated through a number of numerical examples. 相似文献
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The symmetric Galerkin boundary element method (SGBEM) instead of the finite element method is used to perform lower bound
limit and shakedown analysis of structures. The self-equilibrium stress fields are constructed by a linear combination of
several basic self-equilibrium stress fields with parameters to be determined. These basic self-equilibrium stress fields
are expressed as elastic responses of the body to imposed permanent strains and obtained through elastic-plastic incremental
analysis. The complex method is used to solve nonlinear programming and determine the maximal load amplifier. The limit analysis
is treated as a special case of shakedown analysis in which only the proportional loading is considered. The numerical results
show that SGBEM is efficient and accurate for solving limit and shakedown analysis problems.
Project supported by the National Natural Science Foundation of China (No. 19902007), the National Foundation for Excellent
Doctorial Dissertation of China (No. 200025) and the Basic Research Foundation of Tsinghua University. 相似文献
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IntroductionThelimitanalysisofstructuresisoneofthemostpracticalandusefulbranchesinplasticity .Ithasimportantapplicationbackgroundforproblemssuchasthedeterminationofloadcarryingcapacityandplasticformingofmetal.Thepurposeofthelimitanalysisofstructuresistoprovidereliabletheoreticalbasesforengineeringdesignandsafetyassessment.Asasimplifiedmethodforelastoplasticproblems,limitanalysisneednotrequirethehistoryofloadandcancomputethelimitloadsdirectlyinsteadofelastoplasticincrementalcomputationwhichisus… 相似文献
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《International Journal of Solids and Structures》2006,43(21):6594-6614
This paper develops a novel nonlinear numerical method to perform shakedown analysis of structures subjected to variable loads by means of nonlinear programming techniques and the displacement-based finite element method. The analysis is based on a general yield function which can take the form of most soil yield criteria (e.g. the Mohr–Coulomb or Drucker–Prager criterion). Using an associated flow rule, a general yield criterion can be directly introduced into the kinematic theorem of shakedown analysis without linearization. The plastic dissipation power can then be expressed in terms of the kinematically admissible velocity and a nonlinear formulation is obtained. By means of nonlinear mathematical programming techniques and the finite element method, a numerical model for kinematic shakedown analysis is developed as a nonlinear mathematical programming problem subject to only a small number of equality constraints. The objective function corresponds to the plastic dissipation power which is to be minimized and an upper bound to the shakedown load can be calculated. An effective, direct iterative algorithm is then proposed to solve the resulting nonlinear programming problem. The calculation is based on the kinematically admissible velocity with one-step calculation of the elastic stress field. Only a small number of equality constraints are introduced and the computational effort is very modest. The effectiveness and efficiency of the proposed numerical method have been validated by several numerical examples. 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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基于有限元重分析技术,考虑载荷对结构的综合影响,从失效元漂移问题和结构极限承载能力角度出发,对结构可靠性分析中,增量载荷法的加载方式进行了分析和改进,并通过有限元程序进行了对比验证,文后提供了算例。结果表明,改进后的分析方法具有更广泛的应用性,其分析结果具有满意的精确度和良好的稳定性,更适合于实际工程中大型结构系统在多种载荷共同作用下的可靠性失效模式分析。 相似文献
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功能梯度材料板件三维分析的半解析梯度有限元法 总被引:1,自引:0,他引:1
将半解析有限元与梯度有限元相结合,形成一种半解析梯度有限元来求解功能梯度材料板件问题。该方法兼有有限元法的适应性强、程序统一,半解析有限元法的节省单元与计算工作量,梯度有限元法的适应构件内部材料性能任意梯度分布等特点,并实现用一维数值计算给出构件三维分析结果。算例分析表明了方法的精度、功能与上述特点,充分揭示了功能梯度材料板件力学响应的三维形态。半解析梯度有限元法可推广应用到其他功能梯度材料面结构的各类分析中。 相似文献