数值方法

The Frechet derivative of the cost function is determined via the solution of an adjoint partial differential equation, and the boundary shape is then modified in a direction of descent. This process is repeated until an optimum solution is approached. The advantage is that the cost function variation is independent of the flow field variation, with the result that the gradient of cost function with respect to arbitrary number of design variables can be determined without the need for additional flow-field evaluations. So each design cycle requires the numerical solution of both the flow and the adjoint equations leading to a computational cost roughly equal to the cost of two flow solutions.

虽然他们的研究成果大多数都可以在公开性文献上看到，但是其中一些具体的细节问题的处理方法却没有透露，比如：伴随方程如何离散求解才能减小最终梯度计算中的误差，使得设计过程有效地进行；伴随方程与流动方程的边界条件是不同的，如何合理地处理伴随方程的边界条件，才能推动设计过程朝着设计目标而发展；在减阻问题中目标函数如何定义，求解梯度的具体数学公式如何推导，如何通过数值方法来实现它们等。

If the surface isrepresented by an implicit algebraic equation,the mapping can be constructed bythe theory of parametrization of algebraic surfaces;If the surface is represented byan parametric equation,the parameter values on the parameter plane can be solvedby numerical method or Grobner Basis method.

若曲面由代数隐式方程给出，可通过代数曲面参数化理论构造映射；若曲面由参数方程给出，可通过数值方法或Grobner基方法求解参数型值点。

The combination of analytic and numeric method s is an important approach to enhance computational efficiency.

解析方法与数值方法有效融合是提高计算效能的重要途径。

It is the purpose of this paper to review the contact problems and some recent developments using BEM.

本文回顾了使用边界元法处理接触问题的情况及目前的研究进展，详细叙述了处理这类问题的理论方法及相应的公式，然后讨论了解决这类问题所采用的边界元法的步骤和各种数值方法，同时给出了的大量的有关接触问题研究的参考文献及作者近期的研究工作，并提出一些有待进一步研究的问题

Compared with results of FEM and other methods, the results of BEM can satisfied the boundary conditions more accurately, It is very important for analyzing the rolling processes.

计算结果表明和有限元法及其他数值方法相比更能精确地满足边界条件，为精确分析轧制过程提供了一种新的计算方法。

It is related to the variational inequality problem, bilinear programming, nonlinear equation. So there is actual meaning and theories value to study how to solve it.In recent years, many algorithms for solving the generalized linear complementarity problem are put forward. But they basically belong to the traditional iterative methods, and may not be efficient since the computing time required for a solution is greatly dependent on the dimension, structure of the problem and the complexity of the algorithm used. Different from the traditional algorithms, the neural network has many advantages on calculations and real-time applications for its inherent massive parallelism and electric circuit implementation.

近年来，人们对广义线性互补问题提出了许多算法，但这些方法基本上属于传统的迭代法，由于它们的计算时间极大地依赖于问题的规模、维数以及所使用的算法，因此很难满足实时并行的要求，与传统数值方法不同，由于内在的并行分布处理信息的特点及电路实现的潜能，神经网络有着许多计算上的优势和实时性的应用，自Hopfield提出著名的人工神经网络模型-Hopfield神经网络，并将其成功应用于优化问题后，用神经网络求解优化问题得到了相当深入的研究，并取得了许多重要的成果。

The binomial tree is one of the numerical methods in common use.

二叉树方法就是比较常用的数值方法之一。

There are only several papers available on limit and shakedown analysis using the boundary element method.

到目前为止，绝大多数求解结构极限与安定问题的数值方法都基于有限元方法。

(1) The input of the internal fixation implant should be in accordance with the compressive trabeculae and be clingy with the femoral calcar, Abduction in small degree (10-30°) will improve the stress in femoral neck region. The stress distribution of the femur under extemal violence explained why the old people are easy to get the middle and low part fractures of the femoral neck and intertrochanteric fractures.(2) The finite element model of femoral neck fracture is good in orrowing various fixation methods for femoral neck fracture.

(1)三维有限元方法用于研究不规则物体是一种有效、准确的数值方法，不仅能考虑到所研究物体的几何形状，而且也考虑到物体的内部结构特性；股骨颈处的压力骨小梁和股骨距是重要的承载结构，内固定物的放置应循压力骨小梁方向尽量紧贴股骨距钻入；载荷主要通过压力骨小梁和股骨距传导至股骨干的中下1/3处；一定角度的下肢外展（10-30°）会较明显的增加股骨颈区的应力，而下肢的内收反而会减小此区的应力；暴力作用时股骨上端应力分布特点从生物力学角度说明老年人易于发生股骨颈中下段骨折和转子间骨折的原因。

Based on the load transmission mechanism of space truss, and referenced theanalysis of test materials, a formula for calculating the bearing capacity of reinforcedconcrete compression strut is introduced. By using the theory of plastic hinge-line, anupper limit solution of bent bearing capacity for four-pile cap, which coincidesprecisely with the practical measurements, is obtained. By utilizing the reaction ofthe soil under cap and by basing on the method of plastic ultimate analysis, an upperlimit solution of punching shear bearing capacity for pile cap is acquired, which. coincides precisely with the practical measurements, and the formula is similar to thecode.A brief discuss on cooperative work of strip beam of foundation and single rankof piles is made. Separately considering the pile-cap and the pile-group, thencoupling their matrix of rigidity, the inner force of pile-cap is solved by the numericalmethod under some reasonable supposition. In comparison with other method, thecalculating results are exact, reliable and convenient in using. The method provides apowerful tQol fOr further analysis and research on this kind of structure.

本文以空间桁架传力机理为基础，结合试验资料分析，推导了钢筋混凝土等边三桩承台受冲切承载力计算公式；根据塑性铰线理论，导得了与试验结果吻合良好的四桩承台受弯承载力的上限解；利用承台底土反力分布，根据塑性极限分析方法，导得了桩基承台受冲切承载力的上限解，在此基础上，通过简化假定，得到与规范公式相类似的承台受冲切承载力实用公式，该公式能方便考虑台底土反力作用，与试验结果的吻合程度比规范公式好；简要讨论了桩基条形承台梁与单排桩的协同工作分析；在一些合理假定的基础上，将承台与群桩分开考虑，分别得到其刚度矩阵后进行耦合，通过数值方法求解承台内力，算例表明，该方法结果准确，使用方便，为该类结构的进一步分析研究及工程设计提供了强有力的工具。

Singer Leona Lewis and former Led Zeppelin guitarist Jimmy Page emerged as the bus transformed into a grass-covered carnival float, and the pair combined for a rendition of "Whole Lotta Love".

歌手leona刘易斯和前率领的飞艇的吉他手吉米页出现巴士转化为基层所涵盖的嘉年华花车，和一双合并为一移交&整个lotta爱&。

This is Kate, and that's Erin.

这是凯特，那个是爱朗。