【作者】 赵磊；

【导师】 闫云聚； 徐斌；

【作者基本信息】 西北工业大学 ， 力学， 2020， 博士

【摘要】 航空航天等关键性结构越来越朝精密化、轻质化方向发展,其受到的振动环境日趋严苛。涉及动力学的传统结构设计大多关注于结构在动荷载下的位移、柔顺度等刚度问题,关注于强度的结构设计相对较少,这严重制约了结构拓扑优化方法在航空航天等领域的工程应用。为解决工程应用中结构轻质化设计的强度需求的问题,本文针对随机激励下的典型结构涉及动应力需求的拓扑优化方法进行了研究,主要工作及研究成果如下:(1)建立了以动应力响应可靠性指标最大化的多相材料的连续体结构优化设计方法。基于多相材料插值模型,构建了以动应力可靠性指标最大化为目标且满足多相材料体积约束的优化模型。为求解上述优化问题,对动应力可靠性指标关于设计变量的灵敏度进行了推导。接着基于双向渐进优化算法(BESO)求解该优化问题的优化解。最后,通过几个典型二维和三维结构的数值算例来说明所提出方法的可行性;(2)提出了随机激励作用下连续体结构满足动应力约束的拓扑优化方法。基于RAMP插值模型,建立了满足动应力约束的以结构轻质化为目标的优化模型。为了减少动应力约束数目,选取动应力约束的P范数凝聚函数作为整体动应力约束来减少约束数目,以提升计算效率。为求解上述定义的优化问题,对动应力约束关于设计变量倒数的灵敏度进行推导以形成约束函数关于设计变量的显式线性表达式,并在优化过程中采用变动应力约束限的方法度优化模型进行等效转化。再基于对偶理论,引入设计变量置信区间的非线性优化算法以得到该优化问题的优化解。最后,通过一些典型结构的数值算例来说明所提出优化算法的有效性与可行性;(3)构建了在周期性随机激励作用下满足高周动疲劳约束的拓扑优化方法。基于RAMP插值模型,建立以结构轻质化为目标且满足动疲劳约束要求的优化模型。根据Crossland疲劳准则,结构的动疲劳约束可以表示为周期性动应力的峰值不超过阈值的类似于应力约束的形式。基于此概念,选取动疲劳约束的KS凝聚函数来减少优化模型中约束的数目,并在目标函数中引入动疲劳约束的P范数凝聚函数作为惩罚项以消除应力集中现象。同时,在优化过程中采用一种新的不同惩罚函数法以解决中间密度的应力奇异现象,并结合变动疲劳约束限的方法获得稳定的优化解。然后,对优化模型中动疲劳约束函数关于设计变量的灵敏度进行推导,以形成约束函数的显式线性表达式。再基于对偶理论和灵敏度信息,求解上述定义的优化问题。最后,通过几个典型结构的数值算例来说明所提出优化设计方法的可行性;(4)研究了随机激励作用下考虑动应力的结构的宏观多孔材料分布与周期性微结构一体化设计的优化方法。建立了以宏观结构动应力最小化为目标,且满足宏观多孔材料和微观相材料体积约束的优化模型。为确保在优化过程中结构的安全性,采用一种新的放缩方法,以建立动应力约束限与微结构力学性能之间的联系。为了得到宏微观结构的并行优化设计,分别推导了结构动应力关于宏观设计变量和微观设计变量的灵敏度。再基于双向渐进优化方法求解上述优化问题。最后,通过典型结构的数值算例来说明所提出宏观多孔材料分布与周期性微观结构并行设计的拓扑优化方法的有效性与可行性。更多还原

【Abstract】 The structures in aerospace engineering are developing toward the characteristics of precise and lightening,and subjected to increasingly harsh vibration environments.Traditionally,most works were focused on the stiffness problems under dynamic loads,such as displacement and complaisance.While few works has been devoted to the strength design problems,leading to the restriction of the topology optimization in the application of engineering design.In order to solve the strength requirement of lightweight design in engineering application,the topology optimization methods for typical structures considering dynamic stress requirements under random excitations are studied in this paper.The main achievements and contributions of this paper are as follows:(1)A methodology for maximizing dynamic stress response reliability of continuum structures involving multi-phase materials is established.The topology optimization model is built based on a material interpolation scheme with multiple materials.The objective function is to maximize the dynamic stress response reliability index subject to volume constraints on multi-phase materials.To solve the defined topology optimization problems,the sensitivity of the dynamic stress response reliability with respect to the design variables is derived for updating the structural topology.Subsequently,an optimization procedure based on the bi-directional evolutionary structural optimization(BESO)method is developed.Finally,several numerical examples are presented to demonstrate the effectiveness of the proposed approach.(2)A methodology for the topology optimization of continuum structures subject to dynamic stress response constraints under random excitations is proposed.The topology optimization model is built based on the rational approximation for material properties(RAMP),with the structural weight as the objective function,and structural dynamic stress response constraints.In order to greatly reduce the computational cost of dynamic stress responses,the P-norm aggregation function is adopted to replace the dynamic stress response constraints.To solve the defined topology optimization problem,a method with varying dynamic stress response limits is presented,and the sensitivity of the equivalent dynamic stress response constraints with respect to the reciprocal design variables is derived so as to form the explicit approximate functions for structural equivalent dynamic stress response constraints.Then,based on dual theory,an algorithm by using nonlinear programming method with simple trust regions is introduced to solve the optimization problem.Finally,the results of several numerical examples are given to demonstrate the validity and effectiveness of the proposed approach.(3)A new layout optimization method is proposed to consider high-cycle dynamic fatigue constraints which are caused by periodic random dynamic loads.Being incorporated with the rational approximation for material properties(RAMP),the optimization model is built,where the objective function is the structural weight,and the dynamic fatigue failure constraints are applied in the structure.According to the Crossland’s criterion,the dynamic fatigue constraints can be formulated by the peak value of the period fluctuating dynamic stress that never exceed the threshold.Then,the Kreisselmeier–Steinhauser(KS)aggregation function is introduced to reduce the number of dynamic fatigue failure constraints.Moreover,a constraint-limit-variant method is adopted to obtain stable convergent topologies.The sensitivity of the dynamic fatigue constraints with respect to the design variables is derived so as to form the approximate functions for the dynamic fatigue constraint functions.Finally,based on the sensitivity and dual theory,the defined optimization problem is solved.The results of several numerical examples are given to demonstrate the validity and effectiveness of the proposed approach.(4)A concurrent topology optimization method of macrostructural material distribution and periodic microstructure considering dynamic stress response under random excitations is proposed.The optimization model is built to minimize the dynamic stress response of the macro structure subject to volume constraints in both macrostructure and microstructure.To ensure the safety of the macrostructure,a new relaxation method is put forward to establish a relationship between the dynamic stress limit and the mechanical properties of microstructure.The sensitivities of the dynamic stress response with respect to the design variables in two scales,i.e.,macro and micro scales,are derived.Then,the aforementioned optimization problem is solved by the BESO method.Finally,several numerical examples are presented to demonstrate the feasibility and effectiveness of the proposed method.更多还原