弹性梁的非局部应变梯度扭转：变分形式和本构边界条件
Nonlocal strain gradient torsion of elastic beams: variational formulation and constitutive boundary conditions
摘要：
非局部应变梯度连续介质力学是一种广泛应用于纳米结构尺寸效应研究的方法。尽管如此，不适当的高阶边界条件（HOBC）规定关闭相应的弹性静力问题。在本研究中，它被证明，HOBC必须被替换为一致的变分公式建立的本构型的唯一确定的边界条件。在弹性梁扭转的框架内发展的处理方法，提供了一种有效的方法来评估规模越来越小的设备的工程利益的现象。采用一种简单的解析方法研究了纳米梁的弹性扭转响应和扭转自由振动。它还强调，非局部应变梯度模型，如果配备了不适当的HOBC，可能会导致扭转结构的反应，不可接受的不表现出非局部性。所提出的变分策略，而不是能够表征显着特有的软化和硬化行为的结构中所涉及的现代纳米机电系统（NEMS）。
英文摘要：
Nonlocal strain gradient continuum mechanics is a methodology widely employed in literature to assess size effects in nanostructures. Notwithstanding this, improper higher-order boundary conditions (HOBC) are prescribed to close the corresponding elastostatic problems. In the present study, it is proven that HOBC have to be replaced with univocally determined boundary conditions of constitutive type, established by a consistent variational formulation. The treatment, developed in the framework of torsion of elastic beams, provides an effective approach to evaluate scale phenomena in smaller and smaller devices of engineering interest. Both elastostatic torsional responses and torsional free vibrations of nano-beams are investigated by applying a simple analytical method. It is also underlined that the nonlocal strain gradient model, if equipped with the inappropriate HOBC, can lead to torsional structural responses which unacceptably do not exhibit nonlocality. The presented variational strategy is instead able to characterize significantly peculiar softening and stiffening behaviours of structures involved in modern Nano-Electro-Mechanical-Systems (NEMS).
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