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首页> 外文期刊>Journal of University of Science and Technology Beijing >Instability criterion for the system composed of elastic beam and strain-softening pillar based on gradient-dependent plasticity
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Instability criterion for the system composed of elastic beam and strain-softening pillar based on gradient-dependent plasticity

机译：基于梯度相关塑性的弹性梁与应变软化柱组成的系统的失稳判据

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摘要

A mechanical model is proposed for the system of elastic beam and strain-softening pillar where strain localization is initiated at peak shear stress. To obtain the plastic deformation of the pillar due to the shear slips of multiple shear bands, the pillar is divided into several narrow slices where compressive deformation is treated as uniformity. In the light of the compatibility condition of deformation, the total compressive displacement of the pillar is equal to the displacement of the beam in the middle span. An instability criterion is derived analytically based on the energy principle using a known size of localization band according to gradient-dependent plasticity. The main advantage of the present model is that the effects of the constitutive parameters of rock and the geometrical size of structure are reflected in the criterion. The condition that the derivative of distributed load with respect to the deflection of the beam in the middle span is less than zero is not only equivalent to, but also even more concise in form than the instability criterion. To study the influences of constitutive parameters and geometrical size on stability, some examples are presented.
机译：针对弹性梁和应变软化柱的系统，提出了一个力学模型，其中在剪切应力峰值时开始了应变局部化。为了获得由于多个剪切带的剪切滑移引起的柱的塑性变形，将柱分成几个狭窄的切片，将压缩变形视为均匀。根据变形的相容条件，支柱的总压缩位移等于梁在中间跨度中的位移。根据能量原理，使用已知大小的定位带根据梯度相关的可塑性，通过分析得出不稳定性标准。本模型的主要优点是，岩石的本构参数和结构的几何尺寸的影响反映在准则中。相对于中跨中梁的挠度，分布载荷的导数小于零的条件不仅与不稳定性准则等效，而且在形式上比不稳定性准则更为简洁。为了研究本构参数和几何尺寸对稳定性的影响，给出了一些例子。

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