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The theory of geometrical non-linear finite element method is researched, which includes equilibrium equation, Lagrange formulation, assembled equations and tangent stiflhess matrix.

中文摘要:本文从大变形的基本理论出发,对几何非线性有限单元法的平衡方程、Lagrange格式、求解方程以及切线刚度矩阵进行了研究。

By the principle of penalt function, the irrotational fluid field is constrained, and author has proposed the Difference Method for distinguishing fluid vortex modes among the natural modes of coupled systems. Author has calculated the real frequencies with the extra deductive method, and discussed the influence of the numerical solution due to the irrotational constraint.

对于流体有限扰动时的非线性耦合系统的有限元分析作了一些探讨,给出了非线性系统的基本方程、变分原理及有限元方程,并具体地导出了三维几何非线性流体单元的切线刚度公式,采用增量形式的Newmark预报——校正逐步积分法计算系统的动力响应,由Newton-Raphson迭代法及其修正方法求解系统的非线性方程组,还列出了不平衡力余量检查和位移迭代增量检查等迭代收敛判断准则。

B Find the equation of the tangent to the curve at the point P.

求曲线在 P 的切线方程。 3 分

B Find the equation of the tangent to the curve at the poin t P.

求曲线在 P 的切线方程。 3 分

This paper analyses the tangent equation of space curve and the derivation process of the curved tangent plane equation in the higher-mathematics teaching-materials, and shows another method to extract the tangent equation of space curve.

分析高等数学教材中空间曲线的切线方程和曲面的切平面方程的推导过程,给出求空间曲线的切线方程的另一种方法。

Assume also that point corresponds the value of parameter t, then the equation of the tangent line to the curve L at point M is given by

假设对应到参数值,则L在点M的切线方程为。

If α had been determined,the dissociation and non-dissociation species photolysis rate constants could be calculated by the tangent equation of the power function.

任意解离度条件下的解离态和非解离态光解速率常数,可根据幂函数的切线方程来确定。

Then the element equation and unit tangent rigid matrix are deducted on the basis of description of UL coordiate and principle of imaginary, the balance equation and overall tangent rigid matrix are integrated via introduction of terminal condition, and the nonlinear equation group is finally parsed on the basis of combination method of Newton-Raphson and increment.

接着基于U.L 坐标描述,从虚功原理出发推导出单元的平衡方程和单元切线刚度矩阵,引入边界处理条件集成了整体结构的平衡方程和总切线刚度矩阵,并采用Newton—Raphson 法和增量法相结合的方法求解非线性方程组。

The method of slope deflection entails writing two equations for each member of a continuous frame, one at each end, expressing the end moment as the sum of four contributions:(1) the restraining moment associated with an assumed fixed-end condition for the loaded span,(2) the moment associated with rotation of the tangent to the elastic curves at the near end of the member,(3) the moment associated with rotation of the tangent at the far end of the member, and (4) the moment associated with translation of one end of the member with respect to the other.

边坡变形的方法需要编写的每一个成员连续帧两个方程,一个在每个月底,表示为四个贡献的总和:最后的时刻(1)限制矩假设固定结束条件相关的加载跨度,(2)目前相关的切线与旋转的弹性曲线在接近年底的成员,(3)目前的切线与旋转有关在该成员的尽头,和(4)时刻与1月底的会员与翻译相关的其他方面。

The method of slope deflection entails writing two equations for each member of a continuous frame, one at each end, expressing the end moment as the sum of four contributions:(1) the restraining moment associated with an assumed fixed-end condition for the loaded span,(2) the moment associated with rotation of the tangent to the elastic curves at the near end of the member,(3) the moment associated with rotation of the tangent at the far end of the member, and (4) the moment associated with translation of one end of the member with respect to the other.

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