论文标题
通过非局部考虑的应变梯度弹性
The strain gradient elasticity via nonlocal considerations
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
Strain gradient elasticity and nonlocal elasticity are two enhanced elastic theories intensively used over the last fifty years to explain static and dynamic phenomena that classical elasticity fails to do. The nonlocal elastic theory has a clear differentiation from the classical case by considering stresses in a point of the continuum as an integral of all stresses defined in the treated elastic body. On the other hand, strain gradient elasticity is characterized as a non-classical theory because considers both potential and kinetic energy densities as not only functions of strains and velocities, respectively but also functions of their gradients. Although the two considerations seem to be completely different from each other, it is a common belief that strain gradient elasticity has a lot in common with nonlocal elasticity. The goal of the present work is to derive all the strain gradient elastic theories appearing so far in the literature via nonlocal definitions of the potential and kinetic energy densities. Such a derivation demonstrates the common roots of the two theories and explains the nature of the involved intrinsic parameters in strain gradient elastic theories. For the sake of simplicity and brevity, only one-dimensional wave propagation phenomena are considered.
