用于求解结构动力响应的不协调时间有限元法

An Incompatible Time Finite Element Method for Solving Structural Dynamic Responses

提出了一组用于求解结构动力响应的基于不协调时间有限元方法的算法公式，该组算法公式对位移、速度采用等阶插值并允许它们在时间离散点上不连续。证明了算法的强稳定特性，并从对该组算法公式的有限差分分析可知它们无条件稳定、有较高精度并且有好的耗散和超调特性，同时给出了与Ｎｅｗｍａｒｋ的梯形法则，ＨＨＴ－α，Ｈｏｕｂｏｌｔ，Ｐａｒｋ等方法的比较。

In this paper,a family of algorithm formula based upon the incompatible time finite element method is presented for solving the structural dynamic response.The displacement and velocity fields are interpolated independently by using time discontinuous functions.The L stability of the algorithm is proved.The unconditionally stability,higher order accuracy,good dissipation and dispersion,overshoot property are observed from a finite difference analysis of the algorithm formula which are compared with commonly used semidiscrete methods such as Newmarks trapezoidal rule,HHT α,Houbolt,Park etc.At last,the numerical calculation of the new algorithm is given.