基于Neumann展开的非完整结构参数化非线性降阶降阶模型
An enhanced parametric nonlinear reduced order model for imperfect structures using Neumann expansion
摘要：
我们提出了一个增强版本的参数非线性降阶模型的形状缺陷的结构动力学，我们在以前的工作研究[1]。该模型是侵入式计算的，没有训练，使用有关结构的标称几何形状的信息和一些用户定义的位移场表示形状缺陷，即从标称几何形状的小偏差由它们各自的振幅参数化。这些人工位移的线性叠加描述了缺陷的几何形状，并且可以以这样的方式嵌入应变公式中，即，最终，非线性内部弹性力可以表示为这些缺陷场和实际位移场的多项式函数。通过这种方式，可以获得内力的张量表示，并且由于Galerkin投影给出的模型尺寸减小，可以实现高仿真速度。我们表明，通过采用严格的变形框架，我们能够实现更好的精度相比，以前的工作。特别是，利用Neumann展开的定义中的格林-拉格朗日应变张量，我们表明，我们以前的模型是一个较低的阶近似相对于我们现在提出的。两个数值例子的夹紧梁和MEMS陀螺仪最后证明了该方法的好处，在速度和精度的提高。
英文摘要：
We present an enhanced version of the parametric nonlinear reduced order model for shape imperfections in structural dynamics we studied in a previous work [1]. The model is computed intrusively and with no training using information about the nominal geometry of the structure and some user-defined displacement fields representing shape defects, i.e. small deviations from the nominal geometry parametrized by their respective amplitudes. The linear superposition of these artificial displacements describe the defected geometry and can be embedded in the strain formulation in such a way that, in the end, nonlinear internal elastic forces can be expressed as a polynomial function of both these defect fields and the actual displacement field. This way, a tensorial representation of the internal forces can be obtained and, owning the reduction in size of the model given by a Galerkin projection, high simulation speed-ups can be achieved. We show that by adopting a rigorous deformation framework we are able to achieve better accuracy as compared to the previous work. In particular, exploiting Neumann expansion in the definition of the Green-Lagrange strain tensor, we show that our previous model is a lower order approximation with respect to the one we present now. Two numerical examples of a clamped beam and a MEMS gyroscope finally demonstrate the benefits of the method in terms of speed and increased accuracy.
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