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Non-linear programming in shakedown analysis with plasticity and friction

机译：具有塑性和摩擦力的减振分析中的非线性编程

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摘要

Complete frictional contacts, when subjected to cyclic loading, may sometimes develop a favourable situation where slip ceases after a few cycles, an occurrence commonly known as frictional shakedown. Its resemblance to shakedown in plasticity has prompted scholars to apply direct methods, derived from the classical theorems of limit analysis, in order to assess a safe limit to the external loads applied on the system. In circumstances where zones of plastic deformation develop in the material (e.g., because of the large stress concentrations near the sharp edges of a complete contact), it is reasonable to expect an effect of mutual interaction of frictional slip and plastic strains on the load limit below which the global behaviour is non dissipative, i.e., both slip and plastic strains go to zero after some dissipative load cycles. In this paper, shakedown of general two-dimensional discrete systems, involving both friction and plasticity, is discussed and the shakedown limit load is calculated using a non-linear programming algorithm based on the static theorem of limit analysis. An illustrative example related to an elastic-plastic solid containing a frictional crack is provided.
机译：完全的摩擦接触在承受周期性载荷时，有时可能会产生有利的情况，即在几个循环后停止滑动，这种现象通常称为摩擦振动。它与可塑性的降低相似，促使学者应用从极限分析经典定理推导的直接方法，以评估对系统上施加的外部载荷的安全极限。在材料中出现塑性变形区域的情况下（例如，由于在完整接触的尖锐边缘附近的应力集中较大），可以合理预期摩擦滑移和塑性应变的相互作用对载荷极限的影响低于此值，则整体行为是非耗散的，即，在一些耗散的载荷循环之后，滑移应变和塑性应变都变为零。本文讨论了同时涉及摩擦和塑性的二维离散系统的减振问题，并基于极限分析的静态定理，采用非线性规划算法计算了减振极限载荷。提供了涉及包含摩擦裂纹的弹塑性固体的说明性示例。

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