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首页> 外文期刊>International Journal of Solids and Structures >A comparison between analytical calculations of the shakedown load by the bipotential approach and step-by-step computations for elastoplastic materials with nonlinear kinematic hardening
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A comparison between analytical calculations of the shakedown load by the bipotential approach and step-by-step computations for elastoplastic materials with nonlinear kinematic hardening

机译：双势方法的减振载荷解析计算与具有非线性运动硬化的弹塑性材料的逐步计算之间的比较

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摘要

The class of generalized standard materials is not relevant to model the nonassociative constitutive equations. The bipotential approach, based on a possible generalization of Fenchel's inequality, allows the recovery of the flow rule normality in a weak form of an implicit relation. This defines the class of implicit standard materials. For such behaviours, this leads to a weak extension of the classical bound theorems of the shakedown analysis. In the present paper, we recall the relevant features of this theory. Considering an elastoplastic material with nonlinear kinematic hardening rule, we apply it to the problem of a sample in plane strain conditions under constant traction and alternating torsion in order to determine analytically the interaction curve bounding the shakedown domain. The aim of the paper is to prove the exactness of the solution for this example by comparing it to step-by-step computations of the elastoplastic response of the body under repeated cyclic loads of increasing level. A reliable criterion to stop the computations is proposed. The analytical and numerical solutions are compared and found to be closed one of each other. Moreover, the method allows uncovering an additional '2 cycle shakedown curve' that could be useful for the shakedown design of structure. (c) 2005 Elsevier Ltd. All rights reserved.
机译：广义标准材料的类别与非关联本构方程的建模无关。基于Fenchel不等式的可能推广，双势方法允许以隐式关系的弱形式恢复流规则正态性。这定义了隐式标准材料的类别。对于这样的行为，这导致了精简分析的经典界定理的弱扩展。在本文中，我们回顾了该理论的相关特征。考虑具有非线性运动硬化规则的弹塑性材料，我们将其应用于恒定应变和交替扭转的平面应变条件下的样本问题，以便分析确定边界区域的相互作用曲线。本文的目的是通过与逐步增加水平的反复循环载荷下人体弹塑性响应的逐步计算进行比较，以证明该示例解决方案的准确性。提出了一个可靠的准则来停止计算。比较了解析解和数值解，发现它们彼此是封闭的。此外，该方法还可以揭示一条额外的“ 2周期振动曲线”，这对于结构的振动设计可能是有用的。 （c）2005 Elsevier Ltd.保留所有权利。

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