Abstract

A spatial non-stationary contact problem with moving boundaries of the interaction region for a thin elastic cylindrical shell and an absolutely solid impactor bounded by a smooth convex surface is considered. A closed mathematical formulation is given and a system of resolving equations is constructed. The latter is based on the spatio-temporal integral equation resulting from the principle of superposition and contact conditions. The core of this equation is the influence function for the cylindrical shell. To a closed system of resolving equations, it is supplemented by a kinematic relation for determining the moving boundary of the contact region and the equation of motion of the impactor as an absolutely rigid body. An algorithm for solving the spatial non-stationary contact problem for an infinitely long cylindrical shell and absolutely solid impactor in the case of a normal impact on the side surface of the shell is constructed and implemented. Examples of calculations are given.

中文翻译：

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圆柱壳和刚性刚体的空间非平稳接触问题

摘要

考虑了一个空间非平稳接触问题，该问题具有相互作用的边界，该相互作用区域为薄的弹性圆柱壳和由光滑凸面为边界的绝对固体撞击器。给出了一个封闭的数学公式，并构造了一个方程组求解系统。后者基于由叠加原理和接触条件得出的时空积分方程。该方程式的核心是圆柱壳的影响函数。对于一个封闭的方程式求解系统，它补充了运动学关系，用于确定接触区域的运动边界和作为绝对刚体的冲击器的运动方程。构造并实现了一种算法，该算法用于解决无限长的圆柱壳和绝对固体冲击器在正常作用在壳侧面上时的空间非平稳接触问题。给出了计算示例。