弹性曲梁的非局部力学
On nonlocal mechanics of curved elastic beams
摘要：
弯曲梁是纳米机电系统的基本结构部件，其设计需要对尺度效应进行适当的建模。本文采用应力驱动的非局部连续介质力学方法研究了弯曲弹性纳米梁的尺寸相关静态行为。轴向应变和弯曲曲率场是平衡轴向力和弯矩场与平均核之间的积分卷积。这里制定的非局部积分方法是[Int. J. Eng. Science 115（2017）14-27]中限于直梁的处理的弯曲结构的推广。相应的非局部微分问题，补充非标准的边界条件，突出显示，并导致数学良定的纳米工程问题。因此，理论预测，表现出硬化的非本地行为，是适当的，以显着模拟各种各样的小规模的纳米技术感兴趣的设备。非局部的方法是利用分析建立的弯曲的弹性纳米传感器和纳米致动器，由小尺度的特征参数驱动的尺寸相关的响应。
英文摘要：
Curved beams are basic structural components of Nano-Electro-Mechanical-Sistems (NEMS) whose design requires appropriate modelling of scale effects. In the present paper, the size-dependent static behaviour of curved elastic nano-beams is investigated by stress-driven nonlocal continuum mechanics. Axial strain and flexural curvature fields are integral convolutions between equilibrated axial force and bending moment fields and an averaging kernel. The nonlocal integral methodology formulated here is the generalization to curved structures of the treatment in [Int. J. Eng. Science 115 (2017) 14-27] confined to straight beams. The corresponding nonlocal differential problem, supplemented with non-standard boundary conditions, is highlighted and shown to lead to mathematically well-posed problems of nano-engineering. The theoretical predictions, exhibiting stiffening nonlocal behaviours, are therefore appropriate to significantly model a wide range of small-scale devices of nanotechnological interest. The nonlocal approach is exploited by analytically establishing size-dependent responses of curved elastic nano-sensors and nano-actuators that are driven by the small-scale characteristic parameter.
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