基于可靠性的结构优化设计方法

Reliability-Based Optimization of Structures

本文研究在满足可靠性要求时的结构优化设计方法。首先分析结构的主要破坏模式,对每一个主要破坏模式用可靠性指标表示结构的可靠度。可靠性指标是设计变量的函数,将其线性化,在各主要破坏模式的可靠性指标均满足要求的条件下,使结构重量最小,形成一个线性规划问题。由此解出结构满足可靠性要求的优化设计变量。进而考虑各主要破坏模式的相关性,检查结构的可靠度能否满足要求,并对优化设计变量进行修正。通过算例证实本文提供的方法是在满足可靠性要求时结构优化设计的有效的工程方法。

Reliability-based optimization of structures is a new research subject in engineering structural design.It seems that the reported methods are suitable to the structures with minor design variables and become time-consuming for the complex structures.This paper attempts to present a procedure to eli- minate this deficiency and is,therefore,more efficient for practical use.The main failure modes of the structure are analyzed.The structural reliability for each main failure mode is indicated by its reliability index which is the function of the design variables.The optimization problem can be stated as minimizing the structural weight and at the same time satisfying the reliability index requirement for every main failure mode.Linearizing the reliability index,it becomes a typical Linear Programming problem.By means of the well-known Simplex Method it is easy to obtain the optimal structural design variables satisfying the reliability requirement.The correlation of the main failure modes is considered to further check the reliability of structure and modify the design variables if necessary.The illustrative example gives quite satisfactory result and confirms the efficiency of the proposed procedure.