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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。
Considering the influence of the edge effect of electrostatic force, the first-order control equations of the large deflection of the micro-beam are established by degenerating the large-deflection bending differential equations. The boundary value problem of the large deflection of the micro-beam is transformed into the initial value problem by the shooting method, A new calculation model and method for analyzing the large deflection of micro-beam is established by means of high-precision iterative correction homogeneous expansion and fine integration method. In order to ensure the convergence and stability of nonlinear algebraic equations, this paper presents an incremental iteration algorithm based on the force characteristics of the micro-beam. Numerical examples show that the proposed method has high accuracy and stability and is an effective method to analyze the large deflection of the micro-beam.