机械结构的可靠性优化设计-外文文献
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英文原文Optimize the reliability of mechanical structure designIt is now generally recognized that structural and mechanical problems are nondeterministic and, consequently, engineering optimum design must cope with un-certainties,Reliability technology provides tools for formal assessment and analysis of such uncertainties,Thus, the combination of reliability-based design procedure sand optimization promises to provide a practical optimum design solution, i,e ,, a de-sign having an optimum balance between cost and risk, However, reliabilty-based structural optimization programs have not enjoyed the name popularity as their deterministic counterparts, Some reasons for this are suggested, First, reliability analysis can be complicated even for simple systems, There are various methods for handling the uncertainty in similar situations (e, g,, first order second moment methods, full distribution methods), Lacking a single method, individuals are likely to adopt separate strategies for handling the uncertainty in their particular problems, This suggests the possibility of different reliability predictions in similar structural design situations, Then, there are diverging opinions on many basic issues, from the very definition of reliability-based optimization, including the definition of the optimum solution, the objective function and the constraints, to its application in structural design practice, There is a need to formally consider these itess in the merger of present structural optimization research with reliability-based design philosophy。In general, an optimization problem can be stated as follows,Minimizesubject to the constraintswhere X is an-dimensional vector called the design vector, f(X) is called the objective function and, k(X) and i(X) are, respectively, the inequality and equality constraints, The number of variables n and the number of constraints, L need not be related in any way, Thus, L could be less than, equal to or greater than n in a given mathematical programming problem, In some problems, the value of L might be zero which means there are no constraints on the problem, Such type of problems are called unconstrained optimization problems, Those problems for which L is not equal to zero are known as constrained optimization problems。 Traditionally the designer assumes the loading on an element and the strength of that element to be a single valued characteristic or design value, Perhaps it is equal to some maximum (or minimum) anticipated or nominal value, Safety is assured by introducing a factor of safety, greater than one, usually applied as a reduction factor to strength。Probabilistic design is propose: as an alternative to the conventional approach with the promise of producing better engineered systems, each factor in the design process can be defined and treated as a random variable, Using method-ology from probabilistic theory, the designer defines the appropriate limit state and computes the probability of failure P of the element, The basic design requirement is that, where p f is the maximum allowable probability of failure。Advantages of adopting the probabilistic design approach are well documented (Wu, 1984), Basically the arguments for probabilistic design center around the fact that, relative to the conventional approach, a) risk is a more meaningful index of structural performance, and b) a reliability approach to design of a sys-tom can tend to produce an optimum design by ensuring a uniform risk in all components。 Optimization, which may be considered a component of operations research, is the process of obtaining the best result by finding conditions that produce the maximum or minimum value of a function, Table 1,1 illustrates area of operations research。Mathematical programming techniques, also known as optimization methods, are useful in finding the minimum (or maximum) of a function of several variables under a prescribed set of constraints, Rao (1979) presented a definition and description of some of the various methods of mathematical programming, Stochas-tic process techniques can be used to analyze problems which are described by a set of random variables, Statistical methods enable one to analyze the experimental data and build empirical models to obtain the most accurate representations of physical behavior。 Origins of optimization theory can be traced to the days of Newton, La-grange and Cauchy in the 1800x, The application of differential calculus to optimization was possible because of the contributions of Newton and Leibnitz, The foundations of calculus of variations were laid by Bernoulli, Euler, Lagrange and Weirstrass, The method of optimization for constrained problems, which involves the addition of unknown multipliers became known by the name its inventor, La-grange, Cauchy presented the first application of the steepest descent method to solve minimization problems。In spite of these early contributions, very little progress was made until the middle of the twentieth Gentry, when high-speed digital computers made the implementation of optimization procedures possible and stimulate, d further research on new methods, Spectacular advances followed, producing a m;sssive literature on optimization techniques, This advancement also resulted in the emergence of several well-defined new areas in optimization theory。It is interesting to note that major developments in the area of numerical methods of unconstrained optimization have been made in the TTnited Kingdom only in the 1960x, The development of the simplex method by Dantzig (1947) for linear programming and the annunciation of the principle of optimality by Bellman (195?) for dynamic programming problems paved the wa,; f= development of the methods of constrained optimization, The work by Kuhn and Tucker (1951) on necessary and xuflicient conditions for the optimal xolution of programming problems laid foundations for later research in nonlinear programming, the optimization area of this thesis。Although no single technique has been found to be universally applicable for nonlinear programming, the works by Cacrol (1961)and Fiacco and McCormic (1968) suggested practical solutions by employing well-known techniques of uncon xtrained optimization, Geometric programming was developed by Dufhn, Zener and Peterson (1960), Gomory (1963) pioneered work in integer programming, which is at this time an exciting and rapidly developing area of optimization research, Many real-world applications can be cast in this category of problem, Dantzig (1955) and Charnel and Cooper (1959) developed stochastic programming techniques and solved problems by assuming design parameters to be independent and normally distributed。Techniques of nonlinear programming, employed in this study, can be categorized 1, one-dimensional minimization method2, unconstrained multivariable minimizationA, gradient based methodB, nongradient based method3, constrained multivariable minimizationA, gradient based methodB,gradient based methodThe gradient based methods require function and derivative evaluations while the non gradient based methods require function evaluations only, In general, one would expect the gradient methods to be more effecti;re, due to the added information provided, However, if analytical derivatives are available, the question of whether a search technique should be used at all is presented, If numerical derivative approximations are utilized, the efficiency of the gradient based methods should be approximately the same as that of nongradient based methods, Gradient based methods incorporating numerical derivatives would be expected to present some numerical problems in the vicinity of the optimum, i,e,, approximations to slopes would become small, Fig, 1,1 shows the $ow chart of general iterative scheme of optimization (Rao, 1979), No claim is made that some methods are better than any others, A method works well on one problem may perform very poorly on another problem of the same general type, Only after much experience using all the methods can one judge which method would be better for a particular problem (Kuester snd Mize, 1973).First attempts to apply probabilistic and statistical concepts in structural analysis date back to the beginning of this century, However, the subject aid not receive much attention until after the World War II, In October 1945, a historic paper written by A, M, Freudenthal entitled The Safety of Structures appeared in the proceedings of the American Society of Civil Engineers, The publicationof this paper marked the genesis of structural reliability in the U,S ,A, , Professor F:eudenthal continued for many years to be in the forefront of structural reliability and risk analysis,During the 1960s there was rapid growth of academic interest in struc-total reliability theory, Classical theory became well developed and widely known through a few influential publications such as that of Freudenthal, Garrelts, and Shi-nouzuka (1966), Pugsley (1966), Kececioglu and Cormier (1964), Ferry-Borges and Castenheta (1971, and Haugen (1968), However, professional acceptance was low for several reasons, Probabilistic design seemed cumbersome, the theory, particularly system analysis, seemed mathematically intractible, Little data were available, and modeling error was an issue which needed to be addressed,But there were early efforts to circumvent these limitations, Turkstra(l070) Yrnted structural design as a problem of decision making under uncertainty and risk, Lind, Turkstra, and Wright (1965) defined the problem of rational design of a code as finding a set of best values of the load and resistance factors, Cornell (1967) suggested the use of a second moment format, and subsequently it was demonstrated that Cornells safety index requirement could be used to derive a set of safety factors on loads and resistances, This approach related reliability analysis to practically accepted methods of design The Cornell approach has been refined and employed in many structural standards,Difficulties with the second moment format were uncovered 1969 when Ditlevsen and Lind independently discovered the problem of invariance, Cornells index was not constant when certain simple problems were reformulated in a mechanically equivalent way, But the lack of invariance dilemma was overcome when Hasofer and Lind (1974) defined a generalized safety index which was invariant to mechanical formulation, This landmark paper represented a turning point in structural reliability theory, More sophisticated extensions of the Hasofer-Lind approach proposed in recent years by Rackwitz and Fiessler (1978), Chen and Lind (1982), and Wu (1984) provide accurate probability of failure estimates for complicated limit state functions,There are many modes of failure in structural systems, depending on the configuration of the system, shapes and materials of the members, the loading conditions, etc, Lz order to perform a system reliability assessment the failure modes must be defined, However, for a large system with a high degree of redundancy it is difficult in practice to determine a priori which failure modes are probabilistically significant, The following methods have been proposed to produce approximate solutions: (a) automatic generation of safety margins, (b) the p-unzipping method, and (c) branch-and-bound method (Thoft-Christensen and Murotsu, 1986), The state of the art in sysiems structural reliability analysis is comprehended in the works vi Bennett (1983), Ang and Tang (1984), Guenard (1984), Ditlevsen (1986), Madsen, Krenk, and Lind (1986), and Thoft-Christensen and Murotsu (1986), Butat this time there no general me hon for obtaining practical solutions to the system reliability problem。- 配套讲稿:
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