Non - oscillatory and non - free - parameters dissipative ( nnd ) finite difference scheme ( a total variation diminishing scheme ) with second order accuracy was adopted to solve the fluid dynamic equations , a finite rate chemical reaction model was developed to calculate ingredient producing rate , and an adi over relaxation iteration technique was used to solve the electromagnetic discretized equations 采用二阶精度nnd格式求解流体力学方程组，采用有限速率化学反应模型计算组分生成率，采用交替方向隐式( adi )超松弛迭代法求解电磁场离散方程。
This paper studied the material nonlinear problems , geometric nonlinear problems and double nonlinear problems , which includes both material and geometric nonlinear problems , of tall frames . at first i built up the stiffness equations of nonlinear problems by qr - method , then solved them by incremental iterative method , finally wrote the corresponding programs by c and calculated some examples 本文研究高层框架的材料非线性问题、几何非线性问题及双重非线性问题，即既含材料非线性问题又含几何非线性问题，先利用qr法建立非线性问题的刚度方程，然后利用增量迭代法求解非线性刚度方程，并用c语言编制计算程序，计算了一些例题。
Abstract : based on the integral creep constitutive relations of viscoelastic material with damages , a new increment finite element method to solve stress , strain and damage variables is developed by using equivalent stresses , three - dimension damage field can be analyzed and coupling stress and damage field can be solved by using iteration method 文摘:基于损伤的粘弹性材料积分蠕变型本构关系，建立了求解应力应变和损伤变量的一种新型增量型有限元法，引用当量应力，可以分析三维损伤场，采用迭代法求解相互耦合的应力和损伤场。
The direct solution for u ~ u and u ~ p form , the stagger solution for u ~ p form are compared in the convergency , stability and efficiency , from which it is concluded that the first solution used not widely before is characterized with weakly ill - conditioned stiffness and comparatively high efficiency . the finite element methods based on these three solving procedures are numerically implemented . the seabed soil under wave pressure with small amplitude can be viewed as elastic material 详细比较广义biot理论u u形式直接解法、 u p形式直接解法与交叉迭代法求解弹性、弹塑性问题的收敛性、稳定性与计算效率，认为以往较少应用的u u形式直接解法刚度阵病态性弱，求解效率高，更适合土工问题的数值模拟，小风浪作用下海床的动力响应特性可视为弹性的。
Secondly , a geometric nonlinear static finite element analysis program of cables , bars and beams is presented . an incremental iterative method based on the newton - raphson method is adopted here to solve the nonlinear equation . a calculation example is given to demonstrate the necessity of thinking over geometric nonlinear affect 其次，编制了索、梁、杆平面结构系统的几何非线性静力分析程序，计算中采用了基于newton - raphson法的增量迭代法求解非线性方程组，并给出了算例。
Iii ) the construction and solution of nonlinear finite element dynamics equations are analyzed , and the increment iteration method is used to solve them , in which newton - raphson or modified newton - raphson is adopted , also the stability of solution and convergence precision are discussed 3 、讨论了非线性有限元动力学方程的建立及其解法，提出了用增量逐步迭代法求解非线性有限元动力学方程组，在每一个载荷步内用newton - raphson法或修正的newton - raphson法进行迭代求解，并分析了解的稳定性和收敛精度。
