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首页> 外文期刊>Journal of Engineering Mechanics >Unilateral contact problem for aging viscoelastic beams
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Unilateral contact problem for aging viscoelastic beams

机译：粘弹性梁老化的单边接触问题

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摘要

The frictionless unilateral contact problem of a viscoelastic Bernoulli-Euler beam resting on a viscoelastic soil is studied. The mathematical formulation involves equilibrium equations, compatibility equations, and constitutive laws, with an aging integral-type form. The unilateral nature of the contact is imposed through a compatibility inequality, which allows the determination of the contact imprint at each time. Further, the governing integro-differential equation for the unknown contact pressure is derived. As special cases, the elastic Winkler-type soil and the rigid soil conditions are discussed. A numerical approach is presented, which employs the finite difference method along space and an adaptive step-by-step algorithm along time. The procedure allows for time discontinuities of both external loads and contact pressure. Several selected numerical examples are. presented and the influence of the most important material and geometrical parameters are shown. For the simplest situations, it was possible to compare the results obtained with known analytical solutions.
机译：研究了粘弹性土上的粘弹性贝努利-欧拉梁的无摩擦单边接触问题。数学公式涉及具有老化积分型形式的平衡方程，相容性方程和本构定律。接触的单边性质是由相容性不平等引起的，该不相容性允许每次确定接触的烙印。此外，推导了未知接触压力的控制积分微分方程。作为特殊情况，讨论了弹性Winkler型土壤和刚性土壤条件。提出了一种数值方法，该方法采用沿空间的有限差分法和沿时间的自适应逐步算法。该程序允许外部负载和接触压力的时间不连续。有几个选定的数值示​​例。展示了最重要的材料和几何参数的影响。对于最简单的情况，可以将获得的结果与已知的分析解决方案进行比较。

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