中文摘要：

精密机电元件可化为非线性“非常规”平面梁柱有限元系统。基于这个系统的共同特征，构造了这类‘非常规。的通用数学模型及其迭加解法．基于不同的“非常规”条件，构造五类具体的迭加解法及同步为束算法．基于不同的系统特征，构造了三类具体系统安装到工作过程的数学模型．采用“非常规”非线性有限元与正交回归设计相结合的方法，建立了表征系统工作状态及具体性能的拟合算式，并对仿真方法的精度和系统寿命进行了讨论．

英文摘要：

The precise electromechanical components can be reduced to the nonlinear and unconventional plane beam finite element system. Firstly, the general mathematical model with its superposition solution was constructed based on the common characteristics of this system. Secondly, according to different unconventional conditions, five kinds of superposition and synchronization constrain solutions were given. Thirdly, based on different systemic features, three kinds of concrete systemic mathematical models for the system installation and working process were also provided. Furthermore, the composed formulas which denoted the system state and capability were established by combing the orthogonal regression method and unconventional nonlinear finite element. Lastly, the system life and precision of the simulation scheme were explored as well.