离散系统运动方程的Galerkin有限元EEP法自适应求解

对于结构动力分析中的离散系统运动方程，现有算法的计算精度和效率均依赖于时间步长的选取，这是时间域问题求解的难点.基于EEP(element energy projection)超收敛计算的自适应有限元法，以EEP超收敛解代替未知真解，估计常规有限元解的误差，并自动细分网格，目前已对诸类以空间坐标为自变量的边值问题取得成功.对离散系统运动方程建立弱型Galerkin有限元解，引入基于EEP法的自适应求解策略，在时间域上自动划分网格，最终得到所求时域内任一时刻均满足给定误差限的动位移解，进而建立了一种时间域上的新型自适应求解算法.

An EEP Adaptive Strategy of the Galerkin FEM for Dynamic Equations of Discrete Systems

For the solution of structural dynamic equations, generally the accuracy of results and the efficiency of computation both depend on the selection of the time step lengths, which makes the key difficulty for efficient solution of time-dependent problems. With the element energy projection (EEP) super-convergent solution computed at the post-processing stage of the finite element method (FEM) to replace the unknown true solution and then to estimate the error of the conventional FEM solution, the so-called EEP adaptive method can automatically refine the solution mesh and has achieved success in various boundary-value problems with spatial coordinates as the arguments. Based on the Galerkin FEM solution of the weak form, the EEP self-adaptive strategy was introduced and applied to the dynamic equations of discrete systems. As a result, an adaptive mesh was automatically produced in the time domain, and a dynamic displacement solution satisfying the pre-specified error tolerance at any moment was obtained, which leads to a new adaptive computation approach for time-dependent problems.