基于算法复杂度理论的拟力法计算效率评价

算法复杂度理论是一种算法效率定量评价方法，该方法通过度量算法的复杂度来客观反映其执行效率，避免了计算机系统性能等因素对效率评价的影响。拟力法是一种高效的结构非线性分析方法，以往研究工作只是在非线性分析过程和运行时间上对计算效率进行了探索，并没有从理论上量化分析。本文采用算法复杂度理论对拟力法和传统变刚度非线性求解方法进行分析，给出了两种方法的时间复杂度函数，并对比了其计算效率进行定量，从数学角度解释了拟力法计算效率高的根本原因。算例对两种方法的时间复杂度和计算时间进行对比分析，直观地说明了拟力法在计算效率方面的优越性。

The efficiency evaluation of force analogy method based on the algorithm complexity theory

The algorithm complexity theory is a method which can evaluate the efficiency of an algorithm quantitatively.The theory can avoid a number of factors,such as computer performance,which influence the algorithm efficiency evaluation through measuring the complexity of algorithm objectively.The force analogy method (FAM) is a structural nonlinear analysis method with high-efficiency.On computational efficiency of FEM,only focused on nonlinear calculation process and computation time has been explored,but no quantitative analysis in theory has been made.This paper analyzes the algorithm complexity of structural nonlinear analysis methods including FAM and conventional variable stiffness method.At the same time,the time complexity function of the two methods is given.Through quantitative comparison of the computational efficiency,this paper provides for the fundamental reason why FAM is computationally efficient from the view of mathematics.The efficiency advantage of FAM is intuitively demonstrated through the comparison of time complexity and computation time of a numerical example.