离散变量优化设计的方向差商法

本文根据离散变量的特点，提出了方向差商的概念，并且针对一类目标函数、约束函数具有单调性的优化设计问题，发展了一种在可行集外由目标函数最小的点出发，沿目标函数增加最小、约束函数降低最多的方向逐步搜索，逐步靠近可行集边界的方向差商法。并将此方法应用于离散变量结构优化设计中。     

Vibration reduction in a flexible-link mechanism through synthesis of an optimal controller

In this paper, reduction of vibration of a flexible planar mechanism is achieved through synthesis of an optimal controller. A finite element model, based on the equivalent rigid-link system theory, is used to accurately describe the dynamic behavior of the system. The model, which accounts for geometric and inertial nonlinearities of the mechanism, has been fully validated through experimental tests. In order to be able to employ the classical optimal control theory, a suitable linear model has been derived from the original one by means of a suitable linearization procedure. Vibration reduction can then be obtained by first defining an adequate performance index, which accounts for vibration amplitude, then by solving Riccati’s equation in order to find the controller that minimizes the performance index, i.e. the optimal controller. The results of several tests that have been carried out are also reported, to show the effectiveness of the synthesized control system.     

Strength calculations and optimal weight design of multilayer shell-shaped composite products under a set of loads

The stress-strain state of axisymmetric multilayer shells is analyzed using kinematic and static hypotheses that allow for the transverse shear stresses satisfying the necessary equations of state, continuity conditions at the boundaries between the layers and given boundary conditions. A numerical solution of the problem of the stress-strain state for a multilayer bar is compared with the Lekhnitskii solution (for a cantilever beam loaded by a concentrated force and moment) to asses the applicability of the employed bending equations of multilayer shells. It is shown that these solutions are in good agreement. The problem of the initial fracture of the shells considered is formulated using phenomenological strength criteria for each layer. A coordinate-wise descent method in the unit interval is proposed to solve weight optimization problems for multilayer shells of composite materials under combined loading. Regions of safe operating loads and the optimal weight distribution of layer thicknesses are determined for a multilayer bar acted upon by a uniformly distributed load and concentrated force.     

Non-probabilistic reliability method and reliability-based optimal LQR design for vibration control of structures with uncertain-but-bounded parameters

Uncertainty is inherent and unavoidable in almost all engineering systems. It is of essential significance to deal with uncertainties by means of reliability approach and to achieve a reasonable balance between reliability against uncertainties and system performance in the control design of uncertain systems. Nevertheless, reliability methods which can be used directly for analysis and synthesis of active control of structures in the presence of uncertainties remain to be developed, especially in non-probabilistic uncertainty situations. In the present paper, the issue of vibration con- trol of uncertain structures using linear quadratic regulator （LQR） approach is studied from the viewpoint of reliabil- ity. An efficient non-probabilistic robust reliability method for LQR-based static output feedback robust control of un- certain structures is presented by treating bounded uncertain parameters as interval variables. The optimal vibration con- troller design for uncertain structures is carried out by solv- ing a robust reliability-based optimization problem with the objective to minimize the quadratic performance index. The controller obtained may possess optimum performance un- der the condition that the controlled structure is robustly re- liable with respect to admissible uncertainties. The proposed method provides an essential basis for achieving a balance between robustness and performance in controller design ot uncertain structures. The presented formulations are in the framework of linear matrix inequality and can be carried out conveniently. Two numerical examples are provided to illustrate the effectiveness and feasibility of the present method.     

On the comparative optimal analysis and synthesis of four-bar function generating mechanism using different heuristic methods

In this research, optimal synthesis of function generation of four-bar linkages is investigated using different heuristic optimization methods. The novelty of this study is that we considered the five precision point’s distribution and both stroke angles of the follower and crank links as the optimization variables. Therefore, a non-linear optimization was done with seven variables. Different optimization techniques, including heuristic and gradient based methods were used for optimization and were completely compared. Finally, general solutions were found and distribution of precision points for some desired functions was rationalized. GA-Hybrid seems to be the best method in finding global optimums in cases that the problem is sorely nonlinear, and also it is fast. Even it seems that distribution of precision points is independent of stroke angles of the follower and crank links. Some precision points are out of the design domain, and they are sorted in a way that they can describe the behavior of desired function better.     

Exact bounds for the static response set of structures with uncertain-but-bounded parameters

The numerical estimation of the static displacement bounds of structures with uncertain-but-bounded parameters is considered in this paper. By representing each uncertain-but-bounded parameter as an interval number or vector, a static response analysis problem for the structure can be expressed in the form of a system of linear interval equations, in which the coefficient matrix and the right-hand side term are, respectively, the interval matrix and the interval vector. In this study, we present two new simple mathematical proofs of the vertex solution theorem using Cramer’s rule for solving linear interval equations, different from the other proof methods, to find the upper and lower bounds on the set of solutions. The first takes advantage of optimization theory, while the second is based on interval extension. By means of a typical example considered first by Hansen, it can be seen that the result calculated by the vertex solution theorem is the same as one predicted by the Oettli–Prager criterion. Examples of a three-stepped beam and a 10-bar truss are presented to illustrate the computational aspects of the vertex solution theorem in comparison with the interval perturbation method.     

Reduction of a model of a mechanical system with variable reduced parameters

S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 31, No. 8, pp. 81–87, August, 1995.     

Isoclinic parameters for biaxial creep of celluloid under variable stresses

The behavior of isoclinic parameters for biaxial creep under variable stresses was investigated by creep tests with cyclic stress reversal or stepwise changes in stress including unloading for thin-walled tubes of softened celluloid under combinations of axial and torsional stresses. Paper was presented at the 1985 SEM Spring Conference on Experimental Mechanics held in Las Vegas, NV on June 9–14.     

On the stability of systems with stochastically variable parameters

The paper analyzes questions related to the construction of dynamic stability boundaries of elastic systems subjected to stochastic parametric excitation. It is supposed that the parametric action is a combination of a deterministic static component and a stochastic fluctuating component. The fluctuating component is taken to be a stationary ergodic process. The stability boundaries are built in the region of combination resonance using the stochastic averaging method and a probabilistic approach due to Khasminskii. In this connection, the stochastic averaging method based on the Stratonovich-Khasminskii theory is used. The probabilistic approach consists in using explicit asymptotic expressions for the largest Lyapunov exponent, from which the asymptotic stability boundaries are determined. As an application, the stability of a simply supported thin-walled bar subjected to a stochastically varying longitudinal load is investigated Published in Prikladnaya Mekhanika, Vol. 41, No. 12, pp. 128–138, December 2005.     

Dynamic stability of a nonlinear oscillatory liquid-gas system with variable parameters

Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 24, No. 3, pp. 111–116, March, 1988.     

Localisation of optimal perturbations in variable viscosity channel flow

We discuss how a variable fluid viscosity affects the nonmodal stability characteristics of the pressure driven flow between two parallel walls maintained at different temperatures. In this work, we specify the fluid viscosity to be a function of the fluid temperature. We employ an Arrhenius model to model the viscosity of water, and Sutherland’s law to model the viscosity of air. We impose a stable density stratification, and find that strong density stratification can suppress optimal transient growth regardless of how strong the viscosity variation is. Some studies have been inclined to neglect viscosity stratification, since the changes in levels of optimal growth, when compared to the uniform viscosity case, are often not too significant. In this article, we show significant localisation of optimal perturbation energy in the less viscous region, a feature that is not observed in uniform viscosity flows. This can have a bearing on the route to turbulence in these systems.     

基于参数化水平集方法的微结构拓扑优化设计

相比于单一材料,复合材料具有轻质高强等优点,拓扑优化方法是设计复合材料的方法之一.本文采用改进的参数化水平集方法,更新了水平集迭代格式,并应用水平集带方法在优化过程中引入中间密度,使水平集方法与变密度法无缝结合以改善水平集方法的拓扑寻优能力,降低其初始设计依赖性.本文以最大化体积模量、剪切模量和负泊松比作为材料设计目标...     

On the determination of material parameters for internal variable thermoelastic–viscoplastic constitutive models

The work presented in this paper deals with the determination of material parameters used in internal variable constitutive models. In order to determine the best suited material parameter set, in the less computationally expensive way, two optimization approaches are used: (i) a gradient-based method and (ii) a continuous evolutionary algorithm (EA) method. The first approach uses a combination of the steepest descent gradient and the Levenberg–Marquardt techniques. The performance of this method is known to be highly dependent on the starting set of parameters and its results are often inconsistent. The EA-based technique provides a better way to determine an optimized set of parameters (the overall minimum). Thus, the difficulty of choosing a starting set of parameters for this process is minor. The main application in this work is a 16 parameter thermoelastic–viscoplastic constitutive model. Experimental data was obtained from tensile and shear tests at different temperatures and used to compare with numerical results and to determine the correct set of material parameters. Numerical constraints were introduced to enforce physical requirements on the material parameters. Both methods are used to determine the 12 material parameters needed for an AA1050-O aluminium alloy. Although the EA-based method achieved a slightly better result, it proved to be computationally more expensive than the gradient-based method.     

Extensions of the Prager-Shield theory of optimal plastic design

The Prager-Shield associated displacement field method for optimal plastic design is extended to multi-component specific cost functions and multiple load conditions, and a lower bound theorem based on kinematic requirements only is introduced. Since any statically admissible stress field results in an upper bound, the proposed theorem provides a simple method for establishing bounds on the optimal cost. By a simple substitution of parameters into the general equations presented, the optimality criteria can be obtained for particular design problems. Examples of optimal fibre-reinforced plates are given.     

An optimal type II fuzzy sliding mode control design for a class of nonlinear systems

This study deals with the problem of controlling a class of uncertain nonlinear systems in the presence of external disturbances. To achieve this goal, a new Optimal Type-2 Fuzzy Sliding Mode Controller (OT2FSMC) is introduced. In the proposed controller, a novel heuristic algorithm, namely particle swarm optimization with random inertia weight (RNW–PSO), is employed. To achieve an optimal performance, the parameters of the proposed controller as well as the input and output membership functions are optimized simultaneously by RNW–PSO. The globally asymptotic stability of the closed-loop system is mathematically proved. Finally, this method of control is applied to the inverted pendulum system as a case study. Simulation results show the system performance is desirable.