数值的

Using numerical simulation technology and method of orthogonal experiment design and single factor rotating optimization, this thesis makes a study of "lost core injection ", thus achieve the optimization of the parameters of molding process, to offer basic reference when developing production technology and mould of the plastics intake manifold. Based on the study of the status in quo and development trend of weight reduction on automobile, the application of plastics to automobile and intake manifold, then under the guidance of theory model and numerical simulation technology in the process of high polymer material, this thesis launches flowing main research work: First of all, on the basis of the three-dimensional model of the part and finite element net model, several designs of gating and running system are numerically simulated and analyzed via MPA of Moldflow.

本文在对当今汽车轻量化、零部件塑料化以及的汽车进气歧管塑料化的发展现状和发展趋势进行了研究和简要介绍，然后在高分子材料成型过程中的理论模型和数值计算方法的指导下，展开主要的研究工作：首先，在零件三维模型和有限元网格模型的基础上，使用Moldflow 的MPA模块对塑料进气歧管的多个浇注系统设计方案进行数值模拟，通过分析各个方案的充填质量、熔接线位置及数量等指标，得到了综合质量较高的4 个进料口的浇口位置及半限制型浇口大小的浇注系统。

Concretely, firstly with Timoshenko beams, the fundamental formulae of solutions of dynamical equations, boundary conditions and initial conditions have been transformed by Laplace transformation. Secondly, in the Laplace regions , we gain the analytical solutions of impact forces at the impact contact points, shear and maximum inverse stress of beams. Then, by using Durbin numerical inverse method, we gain the numerical solutions of Timoshenko beams under various restriction conditions. Moreover, the graphs about impact forces at the impact contact points, shear and maximum inverse stress of beams can be obtained too.

把Timoshenko梁力学模型动力学方程的基本解形式、边界条件以及初始条件进行Laplace变换，在Laplace区域得到了冲击接触处的冲击力、整个梁的最大弯曲应力和剪力的解析解，然后利用Durbin数值反演的方法得到了各种约束条件下的Timoshenko梁模型时间-空间的数值解，得到了冲击接触处的冲击力、梁各处的最大弯曲应力和剪力的曲线图。

The improved e-N method can also yield results well agree with those obtained by DNS.4 The transition prediction for boundary layers on cones with different key parameters such as angle of attack, cone half angle and the Mach number of the coming flow, have been made, to show the reliability of the modified e-N method.5 For the calculation of base flow, boundary layer equations can be used in the case of small angle of attack.

但是它要依赖于对初始扰动的正确预估，这显然又取决于更多飞行数据的积累和分析。e-N方法的转捩预测结果与直接数值模拟得到的结果也吻合较好。4通过对不同来流攻角、不同半锥角和不同马赫数的三维圆锥边界层的转捩位置进行预测，证实了改进的e-N方法对于三维边界层转捩预测是可靠的。5对于基本流的计算，边界层方程可以用于小攻角的情况，其计算量远远小于直接数值模拟，但背风面的剖面不可靠。

The axially symmetric torsion of rigid circular shaft of varying diameter embedded in an elastic half space is studied by line-loaded integral equation method, where the problem is formulated by distributions of fictitions fundamental loads PRCHS (point ring couple in half space) along the axis of symmetry in interval of the shaft and is reduced to a one-dimensional and non-singular Fredholm integral equation of the first kind and is easily solved numerically.

弹性半空间；本文用线载荷积分方程法研究嵌在弹性半空间的刚性变直径圆轴的轴对称扭转。利用将"半空间的点环力偶"这一虚的基本载荷沿对称轴的圆轴区间中分布就能使本问题归结为一个一维的非奇异的Ferdholm第一种积分方程，且很易用数值求解。文中给出刚性圆锥，圆柱，圆锥柱嵌在弹性半空间的扭转的数值计算的例并和他人的已知结果相比较。

In order to reasonably depict four basic problems with friction, one Coulomb friction new form in first Kirchhoff stress is proposed to deal with finite deformation problems, other Coulomb friction form in incremental mode to elastoplastic flow theory; Hilbert function spaces concerning elastoplastical problems with friction are established, so it makes all operations and calculations in the treatise standardized within the scope of reasonably topologic structure; In view of functional extremum, the equivalence between generalized variational inequalities principles in elastoplasticity with friction and corresponding basic problems are testified by inducing Lagrangian multipliers, so it provides a rationally theoretical basis for numerical methods in elastoplasticity with friction; From the viewpoint of variational inequality, the theory of generalized variational inequalities in elasticity and elastoplasticity with frictional constraint is studied, and the uniqueness and existence of the solution of FEM is proofed under the proposed conditions of stress compatibility, and them FEM approximation and a discrete solution are discussed; Based on the principles of generalized variational inequalities in elastoplasticity with friction, direct generalized variational inequalities methods is pretended, which is a natural generalization and development of direct variational methods; Using generalized variational inequalities methods, some examples in metal forming including plane deformation, upset and extrusion are analyzed and the results prove that all the theories and methods in the paper are right, feasible, accurate and advanced.

主要内容有：为了合理地描述金属塑性成形中摩擦约束弹性、弹塑性基本问题，提出和研究了有限变形下以Kirchhoff第一应力表示的Coulomb摩擦定律形式和弹塑性流动理论下以增量形式表示的Coulomb摩擦定律表示形式；系统建立了摩擦约束弹塑性问题的Hilbert函数空间，使本文规范在一个具有合理的代数拓扑结构内进行一切操作和运算；利用Lagrange乘子，从泛函极值的角度系统地阐述和论证了一系列摩擦约束弹性、弹塑性广义变分不等原理与相应的实际问题之间的等价性，它为处理摩擦约束的弹塑性力学数值方法提供了合理的理论基础；从变分不等式的角度出发，阐述了对应于摩擦约束弹性、弹塑性问题的广义变分不等式理论，首次提出了在应力相容性条件下，它的有限元解具有存在唯一性，进而讨论了其有限元近似及离散解法；基于摩擦约束弹塑性广义变分不等式原理，首次提出了直接广义变分不等式方法，这一方法是直接变分法的合理推广和发展；利用直接广义变分不等式方法对金属压力加工中的平面变形问题、镦粗、挤压等塑性成形问题进行了分析计算，验证了该理论和数值算法的正确性、实用性、精确性和优越性。

Firstly, Wavelet-Galerkin algorithm for solving the first kind of singular integral equation with the Hilbert kernel is proposed, we use the characteristic of periodic wavelet on L~2([0,1]) and Hilbert kernel to solve and make stiff matrix lower dimensions and become sparser through thresholding,thus the cost of computation is reduced. Because of the singularity of Hilbert kernel we use Tikhonov regularization method to solve the system of stiff equation. At last the convergence and numerical result of approximate solution are given. Secondly, an approach of regularization based on Fourier is presented for sideways heat equation; we give the theory proof and error estimate.

首先，提出了含Hilbert核的第一类奇异积分方程的小波伽辽金(Wavelet-Galerkin)数值算法，该算法中利用了L~2([0，1])上的周期小波和Hilbert核的特点进行处理，使得刚性矩阵维数降低并且通过阈值使得它更加稀疏，减少了计算量；由于Hilbert核的奇异性，通过Tikhonov正则化方法求解所得到的刚性方程组，给出了收敛性和数值结果；其次，对标准的一维逆热传导方程给出了一种基于Fourier正则化方法，给出了理论证明及其误差估计，解决了文献中算法与理论误差估计的不相匹配的现象，该正则化方法不仅保留了测量数据的部分高频成份，且与文献中的算法具有同样的计算量和误差估计。

The tensile strength and the elastic modulus were assumed to obey Weibull and logarithmic normal distribution and the other mechanical parameters were taken as constant values in the simulations of three-graded-concrete supported beam. The random aggregate random parameters model was established, which is very close to the actual structure. The results show that the nonlinear behavior of higher homogeneous specimen appears later obviously; the influence of random distribution of elastic modulus on the mechanical character is very little in linear range, while great in nonlinear range; random distribution of tensile strength affects the strength and the damage threshold of concrete obviously.

对三级配混凝土简支梁进行数值模拟时，假定各相材料的抗拉强度和弹性模量服从Weibull、对数正态两种随机分布，其他力学参数取定值，生成和实际结构比较接近的随机骨料随机参数模型，数值模拟结果表明材料均质度较高的试件出现非线性行为的时间要明显滞后于均质度较低的试件；弹性模量分布的随机性对材料线弹性段力学性能的影响极小，而对非线性区域的影响较大；材料强度分布的随机性对混凝土的强度和损伤阈值有较大的影响。

Establish the steady-state and transient model using the three hydrodynamics equations (Continuity equation, Momentum equation and Energy equation). By comparing different state equation, it selects the BWRS state equation which is considered the most accurate state equation in current natural gas measurement. It calculates compression factor, density and other Thermal parameters based on BWRS state equation. In Numerical solution of the steady-state and transient model, compression factor, friction coefficient and all the other Thermal parameters are recalculated in each small time step to reduce the numerical calculation error.

在稳态模型的建立上，利用流体力学三大方程(连续性方程、运动方程和能量方程)，通过比较不同的状态方程选用了目前被认为最精确的用于天然气计量的BWRS状态方程，并以此方程为基础进行压缩因子、密度等热物性参数的计算；在稳态模型的求解上，选用容易计算，精度较高的标准型龙格—库塔(Runge-Kutta)法进行数值求解，并且在迭代过程的每一小步都重新计算燃气的压缩因子，摩阻系数等所有的计算参数，以减少数值计算的误差。

The results of numerical experiments, using the four-dimensional variational data assimilation system of the nonhydrostatic mesoscale model MM5, show that: the tangent linear model and adjoint model conducted by keeping the "on-off" switches the same as the basic state, can provide a good approximation of the first-order information to the NLM perturbation and a good descent direction for the minimization procedure; switching on and off at every other time step in the Kuo cumulus parameterization scheme don"t impact the convergence rate of cost function; the existence of the switches don"t impact improvement to the MM5 model rainfall prediction because that not only specific humidity ,but also wind, temperature and pressure are assimilated into the model.

非静力中尺度数值模式MM5的四维变分资料同化系统进行的数值试验结果表明："开关"变量保持与基态一致，所构造的切向线性模式能够提供关于非线性模式扰动的一阶近似，伴随模式所计算的梯度值能够为最小化过程提供较好的下降方向；郭氏降水参数化方案中对流每隔一个积分步的交替发生并不影响目标函数最小化的收敛速度；"开关"变量的存在也不影响将风、温度、气压和比湿结合起来同化对MM5降水预报准确性的提高。

Based on this, a new WENO difference scheme which based on Dispersion-Relation-Preserving relation is developed, and representative test cases with this scheme for computational aeroacoustics problems has been implemented and compared in order to test capability of wave capturing; In addition, WENO schemes generally do not converge at high order in the presence of contact discontinuity of Euler equations, so a conservative front tracking technique coupling WENO schemes and Level Set method to simulate the translating density profile is presented here, and numerical simulation with this technique for representative test case has been implemented and results show the desired accuracy.

本文研究了高阶精度加权基本无振荡格式及其在双曲守恒律方程中的应用，在此基础上作了两个方面的工作：一是针对高频声波问题构造出一种基于保色散关系的WENO有限差分格式，并对计算气动声学问题的代表性算例进行了大量数值实验，比较了该格式捕捉波数的能力；另外，针对高阶WENO格式在处理Euler方程的接触间断时精度有所降低的问题，研究了利用界面追踪技术Level Set方法和高阶激波捕捉WENO格式相结合的一种守恒追踪方法，并且给出有代表性的密度滑移面问题的算例，得到一致高阶精度的数值模拟结果。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。