空间几何构造分析的有限单元法

提出空间杆系几何构造分析的有限单元法，构造了两种单元(链杆单元和准梁单元)的几何约束矩阵，集成为整体矩阵并引入承条件后，通过对其阶数与秩的比较分析确定体系的几何可变性及静定性．本法原理简单，便于计算机实施，结果完备：对于几何不变体系，可指出多余约束的数目；对于几何可变体系，可给出体系的自由度数及相应的运动模态，并确定自由度的常变瞬变性质．     

基于最佳超收敛阶EEP法的一维有限元自适应求解

基于新近提出的具有最佳超收敛阶的单元能量投影(EEP)超收敛算法,提出用具有最佳超收敛阶的EEP超收敛解对有限元解进行误差估计,用均差法进行网格划分,用拟有限元解进行多次遍历而不反复求解有限元真解,形成一套新型的一维有限元自适应求解策略.该法理论上简明清晰,算法上高效可靠,对于大多数问题,一步自适应迭代便可给出按最大模度量逐点满足误差限的有限元解答.以二阶椭圓型常微分方程模型问题为例,介绍了该法的基本思想、实施策略及具体算法,并给出具有代表性的数值算例,以展示该法的优良性能和效果.     

Self-adaptive strategy for one-dimensional finite element method based on EEP method with optimal super-convergence order

Based on the newly-developed element energy projection （EEP） method with optimal super-convergence order for computation of super-convergent results, an improved self-adaptive strategy for one-dimensional finite element method （FEM） is proposed. In the strategy, a posteriori errors are estimated by comparing FEM solutions to EEP super-convergent solutions with optimal order of super-convergence, meshes are refined by using the error-averaging method. Quasi-FEM solutions are used to replace the true FEM solutions in the adaptive process. This strategy has been found to be simple, clear, efficient and reliable. For most problems, only one adaptive step is needed to produce the required FEM solutions which pointwise satisfy the user specified error tolerances in the max-norm. Taking the elliptical ordinary differential equation of the second order as the model problem, this paper describes the fundamental idea, implementation strategy and computational algorithm and representative numerical examples are given to show the effectiveness and reliability of the proposed approach.     

Self-adaptive one-dimensional nonlinear finite element method based on element energy projection method

The element energy projection （EEP） method for computation of super- convergent resulting in a one-dimensional finite element method （FEM） is successfully used to self-adaptive FEM analysis of various linear problems, based on which this paper presents a substantial extension of the whole set of technology to nonlinear problems. The main idea behind the technology transfer from linear analysis to nonlinear analysis is to use Newton＇s method to linearize nonlinear problems into a series of linear problems so that the EEP formulation and the corresponding adaptive strategy can be directly used without the need for specific super-convergence formulation for nonlinear FEM. As a re- sult, a unified and general self-adaptive algorithm for nonlinear FEM analysis is formed. The proposed algorithm is found to be able to produce satisfactory finite element results with accuracy satisfying the user-preset error tolerances by maximum norm anywhere on the mesh. Taking the nonlinear ordinary differential equation （ODE） of second-order as the model problem, this paper describes the related fundamental idea, the imple- mentation strategy, and the computational algorithm. Representative numerical exam- ples are given to show the efficiency, stability, versatility, and reliability of the proposed approach.