查询词典 derived equation

By introducing special stress functions, we find solutions of eighth order homogeneous linear equation set with complex functions method and approach of undetermined coefficients, deduce calculation formulas of bi-material elastic constants for two dissimilar orthotropic composite materials. The expressions of stress intensity factors near finite interface crack tip subjected to symmetric loadings are derived. A engineering application numerical example is given.

通过引入特殊的应力函数，采用复变函数方法和待定系数法求解了八阶齐次线性方程组，推出了两种相异正交异性复合材料板的双材料弹性常数的计算公式，得到了受对称载荷作用的界面裂纹尖端应力强度因子的计算公式，给出了一个工程应用算例。

The expression of the least-squares solutions of the matrix equation A~TXA — B on the linear manifold is derived, too.

另外，利用矩阵对的商奇异值分解，给出了它的广义次对称最小二乘解的表达式。

Firstly,based on the lagrangian formulation and the relationship of the system linear momentum conversation,the dynamic equation of a free-floating space robot is derived.

首先，由系统动量守恒关系和拉格朗日第二类方法，建立了漂浮基空间机器人的系统动力学方程。

Firstly, with the Lagrangian formulation and the relationship of the system linear, angular momentum conversations, the full-controlled dynamics equation of the system was derived.

由拉格朗日第二类方法及系统动量、动量矩守恒关系，建立了漂浮基空间机械臂完全能控形式的系统动力学方程。

In this paper the stress analysis solution of parallel circular tunnels in elastic ground under any coefficient of lateral pressure is derived, and the stress field and displacement field of parallel circular opening subjected to continuous boundary stresses are first solved, and then the ground pressure and the internal force in lining are obtained, using the displacement compatibility equation between linin...

先求得连续洞周边界应力条件下双圆形洞室的应力场和位移场；再利用衬砌和围岩界面位移协调方程，获得平行圆形隧道的地层压力和衬砌内力公式，并可考虑开挖面的三维效应和洞室自由位移等因素。根据结论公式，对隧道间距、地层性质、衬砌厚度等诸因素进行了讨论，得到了单因素的一般规律，在此基础上，提出了平行圆形隧道最小间距的近似方法，并在某工程中予以应用，得到了满意的结果。本应力分析方法在平行圆形隧道的设计和施工中供作参考。

For the compressible materials, in order to satisfy the higher-order compatibility equation of the rate of deformation in the centered fan sector, which is a quite difficult problem unresolved in the previous studies, a particular term must be added to the expansions of the stress components in the regular logarithmic power series adopted by many researchers before. A higher-order near tip field with tangential velocity jump ahead of the crack tip is derived first, of which the dominant terms are the solution widely accepted.

对可压缩材料，本文首先采用非规则的对数幂级数渐近展开方法，克服了过去研究中存在的中心扇形区变形率协调方程的高次渐近式不能被满足的困难，并得到了一个切向速度在裂尖前方存在间断的高阶渐近解，该解的主项就是目前被广泛接受的关于可压缩材料的尖端场解。

The detailed comparisons between the higher—order near tip solution and the well—known modified Prandtl field are also given in this paper.For the compressible materials, in order to satisfy the higher-order compatibility equation of the rate of deformation in the centered fan sector, which is a quite difficult problem unresolved in the previous studies, a particular term must be added to the expansions of the stress components in the regular logarithmic power series adopted by many researchers before. A higher-order near tip field with tangential velocity jump ahead of the crack tip is derived first, of which the dominant terms are the solution widely accepted.

对可压缩材料，本文首先采用非规则的对数幂级数渐近展开方法，克服了过去研究中存在的中心扇形区变形率协调方程的高次渐近式不能被满足的困难，并得到了一个切向速度在裂尖前方存在间断的高阶渐近解，该解的主项就是目前被广泛接受的关于可压缩材料的尖端场解。

The factors that influence contour accuracy of the machine are analyzed. The equation ofcontour error due to feeding axis's dynamics is derived by circular contour motion of themachine, and a model of contour error is proposed.

五、研究了引起轮廓误差的各种因素，以圆弧轮廓为例推导了联动坐标轴动态特性对轮廓误差的影响公式，提出了轮廓误差模型。

The equation of magnetic line of force for current element is derived and the concluion is obtained that any magnetic line of force is a close circle and its center changing in straight line on three coordinate plane, the oblique rate is determined by current element.

导出了电流元的磁力线方程，发现任一磁力线是一闭合圆线，圆心在三个坐标平面上沿直线变化，斜率由电流元的取向决

The ion motion in such an electric field is derived,and the stability of ions is presented in the a-q diagram which is commonly used for sinusoidal wave quadrupole mass spectrometry in association with the solution of Mathieu Equation.

本文推导了离子在矩形波四极场中的运动规律，并以常用于正弦波四极场的马绍方程参量a，q来表出离子的稳定性。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。