析静电力作用下微梁大挠度变形的一种高精度计算模型与方法

A HIGH PRECISION COMPUTATIONAL MODEL AND METHOD FOR ANALYZING THE LARGE DEFLECTION OF MICROBEAMS DRIVEN BY ELECTROSTATIC FORCE

  • 摘要: 考虑静电力边缘效应的影响,通过薄板大挠度弯曲微分方程退化建立了微梁大挠度变形的一阶控制方程组,并采用打靶法将微梁大挠度变形的边值问题转化为初值问题,借助高精度迭代修正齐次扩容精细积分法建立了一种新的分析微梁大挠度变形的计算模型与方法。为了保证非线性代数方程组求解的收敛性和稳定性,该文根据微梁的受力特点提出了一种增量迭代的算法。数值算例表明:该文所提出的方法具有较高的精度和稳定性,是分析微梁大挠度变形的一种有效方法。

     

    Abstract: Considering the influence of electrostatic force edge effects, first order controlling equations of a large deflection bending microbeam was deduced by degenerating differential equations of a large deflection bending thin plate. The shooting method was adopted to change the large deflection, a boundary value problem, of the microbeam into an initial value problem. By means of the method of a high precision iterative refinement extended homogeneous capacity integration, a new computational model and method were established to analyze the deformation of a large deflection bending microbeam. In order to guarantee the convergence and stability in solving nonlinear algebraic equations, an incremental iterative algorithm was put forward according to the load characteristic. Numerical calculated results show that the proposed method is more accurate and stable, which is an effective method to analyze the large deflection deformation of a microbeam.

     

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