随机载荷和边界条件下线性结构可靠性优化设计的单元荷载方法

Q2 Engineering
Designs Pub Date : 2023-08-02 DOI:10.3390/designs7040096
Robert James Haupin, G. Hou
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引用次数: 0

摘要

本研究采用低阶泰勒级数展开来估计线性静态结构在随机载荷和边界条件下基于可靠性的设计优化的失效准则的可靠性指标。通过利用线性叠加原理,在整个优化过程中,只需要对承受单位载荷的结构进行少量分析,即可得出可接受的结果。本文通过两个结构实例说明了所提出的基于可靠性的设计优化方法的有效性:一个是处理受随机多点约束的特拉斯结构,另一个是对受随机点载荷的平面应力问题进行形状设计优化。这两个例子都是公式化的,并用有限元方法求解。第一个例子使用惩罚方法将多点约束重新表述为外部载荷,而第二个例子引入了一种方法,将不确定性从节点位移矢量线性传播到节点von Mises应力矢量。通过蒙特卡洛模拟验证了基于可靠性的设计优化得到的最终设计。该验证过程完成时,第一个示例仅进行了四次机组负荷分析,第二个示例进行了两次。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A Unit-Load Approach for Reliability-Based Design Optimization of Linear Structures under Random Loads and Boundary Conditions
The low order Taylor’s series expansion was employed in this study to estimate the reliability indices of the failure criteria for reliability-based design optimization of a linear static structure subjected to random loads and boundary conditions. By taking the advantage of the linear superposition principle, only a few analyses of the structure subjected to unit-loads are needed through the entire optimization process to produce acceptable results. Two structural examples are presented in this study to illustrate the effectiveness of the proposed approach for reliability-based design optimization: one deals with a truss structure subjected to random multiple point constraints, and the other conducts shape design optimization of a plane stress problem subjected to random point loads. Both examples were formulated and solved by the finite element method. The first example used the penalty method to reformulate the multiple point constraints as external loads, while the second example introduced an approach to propagate the uncertainty linearly from the nodal displacement vector to the nodal von Mises stress vector. The final designs obtained from the reliability-based design optimization were validated through Monte Carlo simulation. This validation process was completed with only four unit-load analyses for the first example and two for the second example.
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来源期刊
Designs
Designs Engineering-Engineering (miscellaneous)
CiteScore
3.90
自引率
0.00%
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审稿时长
11 weeks
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