两类变量综合处理的结构形状优化设计方法

本文针对截面变量为离散变量为连续变量的结构优化问题提出了一种优化设计的方法,首先将单元内力作一阶近似,利用凝聚函数多约束问题转化了单约束问题。在解过程中,把定义在连续区间上的形状变量看成是在一些离散以值的离工用变量,然后将两类变量统一考虑并利用相对差商法求解。将该算法应用于几个经典的结构优化算例,运算结果显示了该方法是可行的,优化结果也比较满意。     

离散变量结构优化设计的相对差商-遗传算法

将相对差商法(RDQA)和遗传算法(GA)结合起来,提出一个离散变量结构优化设计的有效解法———相对差商-遗传算法。3个算例结果显示出其优于相对差商法与遗传算法:(1)大大提高了遗传算法搜索全局最优解的能力及计算效率;(2)间接证明了相对差商法具有足够的逼近全局最优解的能力。     

APPROACH FOR LAYOUT OPTIMIZATION OF TRUSS STRUCTURES WITH DISCRETE VARIABLES UNDER DYNAMIC STRESS, DISPLACEMENT AND STABILITY CONSTRAINTS

A mathematical model was developed for layout optimization of truss structures with discrete variables subjected to dynamic stress, dynamic displacement and dynamic stability constraints. By using the quasi-static method, the mathematical model of structure optimization under dynamic stress, dynamic displacement and dynamic stability constraints were transformed into one subjected to static stress, displacement and stability constraints. The optimization procedures include two levels, i.e., the topology optimization and the shape optimization. In each level, the comprehensive algorithm was used and the relative difference quotients of two kinds of variables were used to search the optimum solution. A comparison between the optimum results of model with stability constraints and the optimum results of model without stability constraint was given. And that shows the stability constraints have a great effect on the optimum solutions.     

具有动应力和动位移约束的离散变量结构形状优化设计方法

讨论了动应力、动位移约束下离散变量状优化设计问题。首先用拟静力算法,将结构惯性力极值作为静载荷施加到结构上,求得结构的动位移和动内力,然后将考虑动应力约束和动作移约束的离散变量结构优化设计问题化为静应力和静位移约束的优化问题。在求解过程中,将单元内力作了一阶近似,并将多约束问题转化为单约束问题,然后利用两类变量统一考虑的离散变量结构形状优化设计的综合算法进行求解。     

A numerical investigation into the solids phase chromatography using a combined continuous and discrete approach

Solids phase chromatography for particle classification is based on different retention times of particles with different properties when they are elutriated through a confined geometry.This work aims at a fundamental understanding of such a technology by using the combined continuous and discrete method.A packed bed is employed as the model confined geometry.The numerical method is compared first with experimental observations,followed by a parametric analysis of the effects on the flow hydrodynamics and solids behaviour of various parameters including the number of injected particles,the superficial gas velocity,the contact stiffness and the diameter ratio of the packed column to the packed particles.The results show that the modelling captures some important features of the flow of an injected pulse of fine particles in a packed bed. An increase in the number of injected particles or the superficial gas velocity reduces the retention time,whereas the contact stiffness does not show much effect over the range of 5×102 to5×104 N/m.It is also found that the effect on the retention time of the diameter ratio of the packed column to the packed particles seems complex showing a non-monotonous dependence.     

A numerical investigation into the solids phase chromatography using a combined continuous and discrete approach

Solids phase chromatography for particle classification is based on different retention times of particles with different properties when they are elutriated through a confined geometry. This work aims at a fundamental understanding of such a technology by using the combined continuous and discrete method. A packed bed is employed as the model confined geometry. The numerical method is compared first with experimental observations, followed by a parametric analysis of the effects on the flow hydrodynamics and solids behaviour of various parameters including the number of injected particles, the superficial gas velocity, the contact stiffness and the diameter ratio of the packed column to the packed particles. The results show that the modelling captures some important features of the flow of an injected pulse of fine particles in a packed bed. An increase in the number of injected particles or the superficial gas velocity reduces the retention time, whereas the contact stiffness does not show much effect over the range of 5 × 10^2 to 5× 10^4 N/m. It is also found that the effect on the retention time of the diameter ratio of the packed column to the packed particles seems complex showing a non-monotonous dependence.     

The activation method for discretized conservative nonlinear stability problems with multiple parameter and state variables

For nonlinear stability problems of discretized conservative systems with multiple parameter variables and multiple state variables,the activation method is put forward,by which activated potential functions and activated equilibrium equations are derived.The activation method is the improvement and enhancement of Liapunov-Schmidt method in elastic stability theory.It is more generalized and more normalized than conventional perturbation methods.The activated potential functions may be transformed into normalized catastrophe potential functions.The activated equilibrium equations may be treated as bifurcation equations.The researches in this paper will motivate the combination of elastic stability theory with catastrophe theory and bifurcation theory.     

Unsupervised neural network model optimized with evolutionary computations for solving variants of nonlinear MHD Jeffery-Hamel problem

A heuristic technique is developed for a nonlinear magnetohydrodynamics(MHD) Jeffery-Hamel problem with the help of the feed-forward artificial neural network(ANN) optimized with the genetic algorithm(GA) and the sequential quadratic programming(SQP) method. The two-dimensional(2D) MHD Jeffery-Hamel problem is transformed into a higher order boundary value problem(BVP) of ordinary differential equations(ODEs). The mathematical model of the transformed BVP is formulated with the ANN in an unsupervised manner. The training of the weights of the ANN is carried out with the evolutionary calculation based on the GA hybridized with the SQP method for the rapid local convergence. The proposed scheme is evaluated on the variants of the Jeffery-Hamel flow by varying the Reynold number, the Hartmann number, and the angles of the walls. A large number of simulations are performed with an extensive analysis to validate the accuracy, convergence, and effectiveness of the scheme. The comparison of the standard numerical solution and the analytic solution establishes the correctness of the proposed designed methodologies.     

A semi‐discrete central scheme for scalar hyperbolic conservation laws with heterogeneous storage coefficient and its application to porous media flow

In this paper, we develop a new Godunov‐type semi‐discrete central scheme for a scalar conservation law on the basis of a generalization of the Kurganov and Tadmor scheme, which allows for spatial variability of the storage coefficient (e.g. porosity in multiphase flow in porous media) approximated by piecewise constant interpolation. We construct a generalized numerical flux at element edges on the basis of a nonstaggered inhomogeneous dual mesh, which reproduces the one postulated by Kurganov and Tadmor under the assumption of homogeneous storage coefficient. Numerical simulations of two‐phase flow in strongly heterogeneous porous media illustrate the performance of the proposed scheme and highlight the important rule of the permeability–porosity correlation on finger growth and breakthrough curves. Copyright © 2013 John Wiley & Sons, Ltd.     

含液颗粒材料液固耦合分析的离散颗粒模型及特征线SPH法

对含液颗粒材料流固耦合分析建议了一个基于离散颗粒模型与特征线SPH法的显式拉格朗日-欧拉无网格方案。在已有的用以模拟固体颗粒集合体的离散颗粒模型[1]基础上,将颗粒间间隙内的流体模型化为连续介质,对其提出并推导了基于特征线的SPH法。数值例题显示了所建议方案在模拟颗粒材料与间隙流相互作用的能力和性能以及间隙流体对颗粒结构承载能力及变形的影响。     

Developments of numerical methods for linear and nonlinear fluid-solid interaction dynamics with applications

本文综述了线性与非线性流固耦合问题数值方法的进展及工程应用. 讨论了四种数值分析方法: (1) 混合有限元-子结构-子区域数值模型, 以求解有限域线性流固耦合问题, 如流体晃动, 声腔-结构耦合, 流体中的压力波, 化工容器的地震响应,坝水耦合等; (2) 混合有限元-边界元数值模型, 以求解涉及无限域的线性流固耦合问题, 如大型浮体承受飞机降落冲击, 船舰的炮击回应等; (3) 混合有限元-有限差分(体积) 数值模型, 以求解不涉及破浪和两相分离的非线性流固耦合问题; (4) 混合有限元-光滑粒子数值模型, 以求解涉及破浪和两相分离的非线性流固耦合问题. 文中推荐分区迭代求解过程, 以便应用现有的固体及流体求解器, 于毎一时间步长分别求解固体及流体的方程, 通过耦合迭代收敛, 向前推进以达问题求解. 文中选用的工程应用例子包含气-液-壳三相耦合, 液化天然气船水晃动, 人体步行冲击引起的声腔-建筑结构耦合, 大型浮体承受飞机降落冲击的瞬态动力回应, 涉及破浪和两相分离的气-翼耦合及结构于水上降落的冲击. 数值分析结果与可用的实验或计算结果作了比较, 以说明所述方法的精度及工程应用价值. 文中列出了基于流固耦合的波能采积装置模型, 以应用线性系统的共振及非线性系统的周期解原理, 有效地采积波能. 本文列出了231 篇参考文献, 以便读者进一步研讨所感兴趣方法.