超静定型钢桁架优化设计的面积比法

满应力准则是对超静定型钢桁架进行优化设计的有效方法．但这种方法的主要缺点在于收敛速度很慢甚至不收敛,这给设计工作带来很大的不便．对问题进行了研究,在“型钢压杆稳定设计直接法”的基础上,提出了满应力优化设计的一种新方法——面积比法,有效地提高了设计过程的收敛速度,降低了设计成本,供有关结构设计人员参考．     

Optimal Transitions of a Spacecraft with an Energy Storage and a Low-Power Thruster

A solution is found to the problem on optimal transitions of a spacecraft with a low-power thruster and an energy storage between two close noncoplanar circular orbits. The maximum payload is chosen to be the optimality criterion. The optimal time-dependences of controls and optimal relationships among the mass parameters of the propulsion system are presented. Ranges of these parameters are found within which an energy storage would be appropriate for use. The results are compared with those for a constant-power thruster. The effect of the radial increment and the increment in the orbit inclination angle on the efficiency of the energy storage is studied     

建筑结构最优阻尼及最优配置研究

利用阻尼来抗震是建筑物最简单的抗震方法,当在阻尼数目少于楼层数时,为使所布置的阻尼达到最优的抗震效果,本文开发了两种最优阻尼配置方法。第一种方法是根据临界激励法确定计算所有可能布置位置中的临界阻尼,选择最小的临界阻尼位置作为最优配置。第二种方法则是根据给定阻尼,计算最优控制效果以确定最优阻尼配置。然后根据实代码遗传算法,在结构抗震效果基本保证的前提下,寻找最优阻尼以降低结构总的阻尼增量。最后给出了一个计算实例。     

Minimization of the Wing Airfoil Drag Coefficient Using the Optimal Control Method

The problem of designing a wing airfoil starting from the surface velocity (or pressure) distribution, given in multi-parameter form, is considered. In the diffuser region, the velocity decrease law is determined from the conditions of minimum drag and separationless flow for a given Reynolds number. The case of boundary layer suction for the purpose of improving the aerodynamic characteristics of the airfoil is studied. A solution is obtained using optimal control theory.     

Optimal reinsurance under risk and uncertainty

This paper deals with the optimal reinsurance problem if both insurer and reinsurer are facing risk and uncertainty, though the classical uncertainty free case is also included. The insurer and reinsurer degrees of uncertainty do not have to be identical. The decision variable is not the retained (or ceded) risk, but its sensitivity with respect to the total claims. Thus, if one imposes strictly positive lower bounds for this variable, the reinsurer moral hazard is totally eliminated.Three main contributions seem to be reached. Firstly, necessary and sufficient optimality conditions are given in a very general setting. Secondly, the optimal contract is often a bang–bang solution, i.e., the sensitivity between the retained risk and the total claims saturates the imposed constraints. Thirdly, the optimal reinsurance problem is equivalent to other linear programming problem, despite the fact that risk, uncertainty, and many premium principles are not linear. This may be important because linear problems may be easily solved in practice, since there are very efficient algorithms.     

A stochastic control model of investment,production, and consumption on a finite horizon

In this paper, we consider a stochastic control problem on a finite time horizon. The unit price of capital obeys a logarithmic Brownian motion, and the income from production is also subject to the random Brownian fluctuations. The goal is to choose optimal investment and consumption policies to maximize the finite horizon expected discounted hyperbolic absolute risk aversion utility of consumption. A dynamic programming principle is used to derive a time‐dependent Hamilton–Jacobi–Bellman equation. The Leray–Schauder fixed point theorem is used to obtain existence of solution of the HJB equation. At last, we derive the optimal investment and consumption policies by the verification theorem. The main contribution in this paper is the use of PDE technique to the finite time problem for obtaining optimal polices. Copyright © 2014 John Wiley & Sons, Ltd.     

Optimal and approximate boundary controls of an elastic body with quasistatic evolution of damage

In this paper, we study an optimal control problem for the mixed boundary value problem for an elastic body with quasistatic evolution of an internal damage variable. We suppose that the evolution of microscopic cracks and cavities responsible for the damage is described by a nonlinear parabolic equation. A density of surface traction p acting on a part of boundary of an elastic body Ω is taken as a boundary control. Because the initial boundary value problem of this type can exhibit the Lavrentieff phenomenon and non‐uniqueness of weak solutions, we deal with the solvability of this problem in the class of weak variational solutions. Using the convergence concept in variable spaces and following the direct method in calculus of variations, we prove the existence of optimal and approximate solutions to the optimal control problem under rather general assumptions on the quasistatic evolution of damage. Copyright © 2014 John Wiley & Sons, Ltd.     

矩阵方程AX=B的中心对称定秩解及其最佳逼近

本文研究了矩阵方程AX=B的中心对称解.利用矩阵对的广义奇异值分解和广义逆矩阵,获得了该方程有中心对称解的充要条件以及有解时,最大秩解、最小秩解的一般表达式,并讨论了中心对称最小秩解集合中与给定矩阵的最佳逼近解.     

生态平衡制约下离散尺度结构种群的最优收获

研究基于扩展Leslie投影矩阵的离散尺度结构种群模型的最优收获问题,约束条件包括生态平衡和开发成本等.运用凸优化理论证明了最优收获策略的存在性,导出了最优收获模式,应用模型参数给出了收获比率.结论显示:最优策略具有两阶段结构.     

ECONOMICALLY OPTIMAL MARINE RESERVES WITHOUT SPATIAL HETEROGENEITY IN A SIMPLE TWO‐PATCH MODEL

Bioeconomic analyses of spatial fishery models have established that marine reserves can be economically optimal (i.e., maximize sustainable profit) when there is some type of spatial heterogeneity in the system. Analyses of spatially continuous models and models with more than two discrete patches have also demonstrated that marine reserves can be economically optimal even when the system is spatially homogeneous. In this note we analyze a spatially homogeneous two‐patch model and show that marine reserves can be economically optimal in this case as well. The model we study includes the possibility that fishing can damage habitat. In this model, marine reserves are necessary to maximize sustainable profit when dispersal between the patches is sufficiently high and habitat is especially vulnerable to damage.