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本文以单工况桁架最轻设计为例,研究了一些力学准则的确切含义和它们的有效性问题。从本质来说,力学准则只能给出桁架的一种位移状态(可称为“准则性态”),但在同一准则性态情况下,可以有多种不同的设计方案。由于力学准则缺乏明确的目标函数和使其极小化的手段,因而所得设计方案甚至可能不是准则性态下的最轻解(可称为“准则最优解”),当然就更不是真正的最轻解(可称为准则的第一类失效情况)。而且力学准则也无法保证所得的准则性态就是与真正最轻解相应的“最优性态”,这时准则最优解也不是其正的(?)轻解(可称为准则的第二类失效情况),另外,对单工况桁架优化设计,本文给出了力学准则有效的条件和指明了克服准则失效以寻求最优解的方法。
This paper takes the lightest design of single-stage truss as an example to study the exact meaning of some mechanical criteria and their effectiveness. Essentially speaking, the mechanics criterion can only give a kind of displacement state of the truss (which can be called “standard behavior”), but in the same standard behavior, there can be many different design schemes. Because the mechanics criterion lacks a clear objective function and a means to minimize it, the resulting design may not even be the lightest solution to the normative behavior (which may be called the “optimal criterion solution”), and certainly not the real one. The lightest solution (can be called the first type of failure of the criteria). Moreover, the mechanics criterion cannot guarantee that the resulting normative behavior is the “optimal behavior” corresponding to the truest lightest solution. At this time, the norm optimal solution is not its positive (?) light solution (which can be called the second criterion). In addition, for the single-case truss optimization design, this paper gives the conditions for effective mechanical criteria and indicates the method to overcome the failure of the criterion to find the optimal solution.