局部有限寿命疲劳约束条件下的结构拓扑优化方法

拓扑优化方法为工程结构抗疲劳性能的改善提供了有效的设计策略,为了减少大规模局部疲劳约束引起的计算代价,往往采用P范数方法将其凝聚成全局约束,但是,满足这类弱约束的最优解与原问题的最优解存在间隙。为了精确满足局部疲劳约束和降低约束数量,采用增广拉格朗日方法将原问题处理为无约束问题,提出局部有限寿命疲劳约束条件下的结构拓扑优化方法。考虑变幅值的比例载荷作用,采用Palmgren-Miner线性损伤假设和Sines疲劳准则评价材料点的疲劳强度,以局部疲劳性能为约束条件,建立结构的轻量化设计模型,采用全局收敛移动渐近线算法求解局部疲劳约束下的结构拓扑优化问题。另外,将非结构化多边形网格技术融入到拓扑优化模型,实现复杂几何边界结构的抗疲劳轻量化设计。数值算例结果表明,与P范数方法的优化结果相比,局部疲劳约束条件下的优化结构具有更优的抗疲劳性能和更少的材料用量,因而考虑局部疲劳约束有益于材料的充分利用和结构抗疲劳性能的改善。

基于多性能约束的连续体结构拓扑优化设计

为了满足多性能指标要求,提出一种考虑静强度和疲劳约束的连续体结构拓扑优化设计方法。以带符号的von Mises应力的幅值和均值绝对值之和评定结构静强度,采用修正的Goodman疲劳准则评价结构疲劳强度,将结构静强度和疲劳约束分别转化为不同的应力约束,再采用P范数对单元应力进行近似最大处理,将局部约束转化全局约束。采用材料属性有理近似模型,以结构体积最小化作为优化目标,建立考虑静强度和疲劳约束的结构拓扑优化模型;采用移动渐近线算法求解基于多性能约束的拓扑优化问题。数值算例结果表明,所提设计方法获得的拓扑结构能够同时满足静强度和疲劳性能要求。

Fatigue Analysis of Steel Catenary Risers Based on a Plasticity Model

The most critical issue in the steel catenary riser design is to evaluate the fatigue damage in the touchdown zone accurately. Appropriate modeling of the riser-soil resistance in the touchdown zone can lead to significant cost reduction by optimizing design. This paper presents a plasticity model that can be applied to numerically simulate riser-soil interaction and evaluate dynamic responses and the fatigue damage of a steel catenary riser in the touchdown zone. Utilizing the model, numerous riser-soil elements are attached to the steel catenary riser finite elements, in which each simulates local foundation restraint along the riser touchdown zone. The riser-soil interaction plasticity model accounts for the behavior within an allowable combined loading surface. The model will be represented in this paper, allowing simple numerical implementation. More importantly, it can be incorporated within the structural analysis of a steel catenary riser with the finite element method. The applicability of the model is interpreted theoretically and the results are shown through application to an offshore 8.625 steel catenary riser example. The fatigue analysis results of the liner elastic riser-soil model are also shown. According to the comparison results of the two models, the fatigue life analysis results of the plasticity framework are reasonable and the horizontal effects of the riser-soil interaction can be included.

A generalized plane strain theory for transversely isotropic piezoelectric plates

Study of generalized plane strain has so far been limited to elasticity. The present is aimed at parallel development of transversely isotropic piezoelasticity. By assuming that the along depth distribution of electric potential is linear, and that com- monly used Kane-Mindlin kinematical assumption is valid, two dimensional solution systems were deduced, for which, explicit solutions of the out-of-plane constraint factor, as well as the stress resultant concentration factor around a circular hole in a transversely isotropic piezoelectric plate subjected to remote biaxial tension are obtained. Comparisons of these formulas with their counterparts for elastic case yielded suggestions that whether the piezoelectric effect exacerbates or mitigates the stress resultant concentration greatly depends on material properties, particularly, the piezoelectric coefficients; the effect of plate thickness was extensively investigated.

考虑疲劳性能的柔顺机构拓扑优化设计

柔顺机构需要承受多次往复运动,交变应力导致机构容易发生疲劳损伤及失效。为了满足疲劳性能要求,提出一种考虑疲劳性能的柔顺机构拓扑优化设计方法。考虑恒定振幅的比例载荷作用,采用修正的Goodman疲劳准则评定柔顺机构的疲劳强度,以柔顺机构的输出位移最大化为目标函数,以疲劳性能和结构体积作为约束,采用改进的P范数方法进行疲劳约束凝聚,建立基于疲劳性能约束的柔顺机构拓扑优化模型,利用映射过滤方法避免数值不稳定性现象,采用移动渐近优化算法求解柔顺机构疲劳约束拓扑优化的多约束优化问题。数值算例结果表明基于疲劳约束拓扑优化获得的柔顺机构能够满足疲劳要求,机构的von Mises等效应力分布更加均匀;并且分析不同的作用载荷条件对柔顺机构构型及其性能的影响规律。