Abstract

It is well-acknowledged by the scientific community that Eringen’s nonlocal integral theory is not applicable to nanostructures of engineering interest due to conflict between equilibrium and constitutive requirements. In this paper, a well-posed two-phase nonlocal integral elasticity with the bi-Helmholtz kernel is developed to study the size-dependent buckling response of Bernoulli-Euler beams under non-uniform temperatures. The governing equation is derived by invoking the variational principle of virtual work, and the temperature effect is equivalent to the thermal load along the axial direction, which is determined by nonlocal heat conduction. The two-phase nonlocal integral constitutive equation is transformed into a differential one equipped with four constitutive boundary conditions, and then exact solutions for the buckling loads of the beam with various boundary edges are obtained. Numerical results are validated by comparing them with those from local elasticity. Moreover, the effects of parameters related to the two-phase nonlocal elastic model and the nonlocal heat conductive model are investigated.

摘要

科学界普遍承认，由于平衡和本构要求之间的冲突，Eringen 的非局部积分理论不适用于具有工程意义的纳米结构。在本文中，开发了具有双亥姆霍兹核的适定两相非局部积分弹性来研究非均匀温度下伯努利-欧拉梁的尺寸相关屈曲响应。控制方程是通过虚功变分原理推导出来的，温度效应相当于沿轴向的热载荷，由非局部热传导决定。将两相非局部积分本构方程转化为具有四个本构边界条件的微分方程，然后得到了具有各种边界边的梁的屈曲载荷的精确解。数值结果通过与局部弹性的结果进行比较来验证。此外，研究了与两相非局部弹性模型和非局部导热模型相关的参数的影响。