静载荷作用下橡胶-金属块的应力分布

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引用次数: 0

摘要

摘要研究了圆柱型橡胶-金属块在静载荷作用下的应力-应变状态的确定问题。提出了一个数学模型,该模型假设当一个块被垂直载荷压缩时,其水平部分保持水平,块的金属部件是刚性的,不可变形的,位于垂直线上的点在加载过程中保持在抛物线上,并且橡胶被认为是不可压缩的。可接受的假设为获得沿对称轴运动的表达式提供了机会,该表达式提供了橡胶-金属块在压缩过程中期望的抛物线性,并满足不可压缩条件。导出了块体压缩过程中产生的法向应力和切向应力的计算公式,该公式满足基本体积平衡微分方程和胡克定律,并考虑了橡胶体两侧的边界条件。考虑到砌块的几何参数和橡胶的机械特性,可以根据静载荷的程度计算其压降,并分析砌块中发生的法向和切向应力的分布。开发的压缩过程数学模型允许,作为一个例子,分析BRM - 102型橡胶-金属块的应力-应变状态,该块的制造使用了51 - 1562品牌的橡胶。通过对该问题的求解,绘制了在荷载作用下危险截面(橡胶体上下两侧)的法向、切向和总应力分布图。结果表明,最大的正应力和最大的总应力出现在砌块的纵对称轴上;最大切向应力在角点实现。接收这种类型的插图的能力使您能够在视觉上确定哪个更合理:一个块的水平截面为200(100毫米)或两个块的尺寸为100(100毫米)。该数学模型可用于研究橡胶-金属块体在压缩条件下的应力-应变状态,也可用于具有预定特性的块体的设计。关键词:橡胶-金属块,应力-应变状态,位移,应力,相对变形,数学模型
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Stress distribution in a rubber-metal block under compression by static load
Abstract. The problem of determining the stress-strain state of a prismatic rubber-metal block when it is compressed by a static load is considered. A mathematical model is proposed, which assumes that when a block is compressed by a vertical load, its horizontal sections remain horizontal, the metal components of the block are rigid, non-deformable, points located on a vertical line during loading remain on a parabola, and rubber is considered incompressible. Accepted assumptions provided an opportunity to obtain expressions for movements along the axes of symmetry, which provide the expected parabolicity during compression of the rubber-metal block and satisfy the condition of incompressibility. The formulas for normal and tangential stresses arising during block compression are derived, which satisfy the differential equation of equilibrium of the elementary volume, Hooke’s law, and take into account the boundary conditions on the sides of the rubber body. Given the geometric parameters of the block and the mechanical characteristics of the rubber, it was possible to calculate its drawdown depending on the degree of static load, as well as to analyze the distribution of normal and tangential stresses that occur in the block. The developed mathematical model of the compression process allowed, as an example, to analyze the stress-strain state of a rubber-metal block of the BRM‑102 type, for the manufacture of which rubber of the brand 51‑1562 was used. As a result of solving the problem, distribution diagrams of normal, tangent, and total stresses arising in dangerous sections (on the upper or lower sides of the rubber body) under loading are constructed. It was found that the maximum normal stresses and maximum total arise on the vertical axis of symmetry of the block; maximum tangential stresses are realized at corner points. The ability to receive this type of illustration allows you to visually determine which is more rational to use: one block with a horizontal section of 200(100 mm or two blocks with a size of 100(100 mm. The proposed mathematical model allows us to study the stress-strain state of a rubber-metal block under compression, and can also be used in the design of a block with predetermined characteristics. Keywords: rubber-metal block, stress-strain state, displacements, stresses, relative deformation, mathematical model.
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