微机电系统阵列的多尺度模型推导与仿真工具

Bin Yang, W. Belkhir, M. Lenczner, N. Ratier
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引用次数: 2

摘要

我们介绍了一个框架,用于计算机辅助推导专用于微系统阵列的多尺度模型。它依赖于在偏微分方程领域中使用的渐近方法与来自计算机科学的项重写技术的结合。在我们的方法中,多尺度模型推导的特征是在渐近分析中考虑的特征。它的表述包括一个与基本名义模型相关的参考模型的推导,以及一组应用于该证明的转换,直到它考虑到所需的特征。除了参考模型证明外,该框架还包括用于渐近模型推导的一阶重写原理和用于模型推导变换的二阶重写原理。我们应用该方法生成了一组具有周期系数的二阶椭圆方程的均质化模型,这些方程可以在多维域(可能是多域和/或薄域)中被提出。通过一个周期悬臂阵列模型的实例,说明了渐近模型在有限元软件包中的转换。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A multiscale model derivation and simulation tool for MEMS arrays
We introduce a framework for computer-aided derivation of multi-scale models dedicated to arrays of microsystems. It relies on a combination of a asymptotic methods used in the field of partial differential equations with term rewriting techniques coming from computer science. In our approach, a multi-scale model derivation is characterized by the features taken into account in the asymptotic analyses. Its formulation consists in a derivation of a reference model associated to an elementary nominal model, and in a set of transformations to apply to this proof until it takes into account the wanted features. In addition to the reference model proof, the framework includes first order rewriting principles designed for asymptotic model derivations, and second order rewriting principles dedicated to transformations of model derivations. We apply the method to generate a family of homogenized models for second order elliptic equations with periodic coefficients that could be posed in multi-dimensional domains, with possibly multi-domains and/or thin domains. The transfer of asymptotic models into a finite element software package is illustrated through an example of a model of periodic cantilever arrays.
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