冲击荷载下结构优化设计研究

发布时间：2018-06-30 16:47

本文选题：冲击荷载 + 结构优化设计　；参考：《大连理工大学》2016年博士论文

【摘要】：冲击荷载下结构优化设计受到学者与工程师的广泛关注。这是因为,对于许多结构,冲击荷载下的结构响应将直接影响其性能,而结构优化设计可以有效的改善冲击荷载下的结构性能。然而,相较于其他类型的结构优化设计问题,冲击荷载下的结构优化设计的研究较少。这是因为,冲击荷载下的结构优化设计问题需考虑时间因素,有时还需考虑材料非线性与几何非线性等非线性效应。这一方面增加了结构分析的困难,使得结构分析耗时增加,另一方面也使得计算结构响应关于设计变量的灵敏度难以解析的实现。这些困难促使冲击荷载下的结构优化设计成为最具挑战的结构优化设计问题之一。本文致力于研究冲击荷载下的结构优化设计问题,提出了一系列的方法用于克服前文中提到的冲击荷载下结构优化设计问题面临的困难。本文重点关注了两类有代表性的冲击荷载下的结构优化设计问题,分别为残余振动最小化结构优化设计问题和结构耐撞性拓扑优化设计问题。残余振动最小化结构优化设计问题中,本研究采用二次型积分形式的性能指标衡量结构的残余振动大小。该结构性能指标可以总体的衡量结构的残余振动,但需要通过耗时的时程响应分析计算。基于李雅普诺夫方法,研究中首先将上述性能指标的表达式大幅简化,从而避免了时程响应分析。对于上述的性能指标,若残余振动阶段的初始激励与设计变量无关,计算其关于设计变量的灵敏度将更为方便。因此,本文在研究中把残余振动响应最小化结构优化设计问题分为：初始激励作用结构的残余振动最小化结构优化设计问题；冲击荷载作用结构的残余振动最小化结构优化设计问题。对于初始激励作用结构的残余振动最小化结构优化设计问题,本研究提出了残余振动响应的二次型积分形式性能指标关于设计变量的灵敏度分析的伴随法。无论优化问题中包含多少个设计变量,提出的伴随法均仅需求解两个李雅普诺夫方程便可以获得全部的灵敏度结果。这不仅实现了解析的计算灵敏度还大幅的减少了灵敏度分析过程的计算耗时。基于提出的伴随法,研究中采用拓扑优化方法,分别研究了以残余振动最小化为目标的阻尼器／阻尼弹簧和有阻尼材料的最优分布问题。数值算例显示,基于提出的方法获得的优化设计有效的改善了结构性能。对于冲击荷载作用结构的残余振动最小化结构优化设计问题,残余振动阶段的初始激励是与设计变量相关的。为了在灵敏度计算中考虑初始激励与设计变量的相关性,本文提出了第二种计算衡量残余振动的二次型积分形式的性能指标关于设计变量的灵敏度的伴随法,从而极大的拓宽了本文工作的适用范围。本文中基于提出的第二种灵敏度计算方法,研究了以残余振动最小化为目标受冲击荷载作用板结构中的阻尼材料最优分布问题。数值算例结果显示,本节提出的方法是高效且可靠的。之后,本文考虑了约束不完全结构中的残余弹性振动最小化结构优化设计问题。李雅普诺夫方法无法直接应用于约束不完全结构的残余振动优化设计问题。这是因为,约束不完全结构的总体刚度阵奇异,导致李雅普诺夫方程无法求得唯一解。研究中提出了两种分别基于刚体运动模态与弹性变形模态的模型降阶法,提出的方法即实现了消除结构刚体位移而又不影响结构弹性变形。基于上述方法,研究中考虑了将单谐振器微结构系统用于减小结构的残余振动的最优参数与最优分布问题。所关注的单谐振器微结构系统,在特定的参数取值下可以等效为一个具有负的质量系数的质量块。最后,本文研究了较高冲击荷载下结构耐撞性拓扑优化设计问题。耐撞性问题需要考虑多种非线性效应,这使得考虑耐撞性的结构优化设计变得十分困难,而采用拓扑优化方法获得耐撞性概念设计则更困难。针对耐撞性拓扑优化设计,本文提出了一种新的混合优化法。新的混合法基于修改的惯性释放法构造的等效静力荷载,并基于该等效荷载可以构造等效静力分析,从而将非线性瞬态动力分析和优化问题转化为非线性静力优化问题。对于该非线性静力优化问题,研究中采用混合元胞自动机法求解。新的混合法采用双层迭代的优化流程,其中,内层迭代采用混合元胞自动机法求解构造的非线性静力优化问题,而外层迭代则基于非线性动力分析校核优化设计的结构响应并构造基于改进的惯性释放法的等效静力荷载。研究中,通过数值算例比较了混合法与混合元胞自动机的优化结果与计算效率。结果显示,混合法与混合元胞自动机法得到了相似的优化设计,但前者的计算效率远高于后者。最后,研究中考虑了一个简化的整车模型的耐撞性拓扑优化设计问题,其优化结果说明了提出的混合法的有效性。
[Abstract]:Structural optimization design under impact loads is widely concerned by scholars and engineers. This is because, for many structures, structural responses under impact loads will directly affect their performance, and structural optimization design can effectively improve the structural performance under impact loads. However, the impact load is compared to other types of structural optimization problems. There are few studies on the structural optimization design under the load. This is because the time factors should be taken into consideration in the structural optimization design under the impact load, and the nonlinear effects of material nonlinearity and geometric nonlinearity should be considered. This increases the difficulty of structural analysis, increases the time-consuming of structural analysis, and also makes the calculation structure on the other. The sensitivity of the response to the design variables is difficult to be resolved. These difficulties have prompted the structural optimization design under the impact load to become one of the most challenging structural optimization problems. This paper is devoted to the study of structural optimization design under impact loads, and a series of square methods are proposed to overcome the impact load mentioned in the previous article. This paper focuses on two types of representative structural optimization problems under impact loads, which are the optimization design problem of residual vibration minimization and structural optimization design of structural crashworthiness. In the optimization design of residual vibration minimization, this study adopts two times. The performance index of the integral form measures the residual vibration size of the structure. The structural performance index can generally measure the residual vibration of the structure, but it needs to be calculated by time-consuming response analysis. Based on Lyapunov method, the expression of the above performance index is greatly simplified in the study, thus avoiding the time history response analysis. For the above performance indicators, if the initial excitation of the residual vibration stage is independent of the design variables, it is more convenient to calculate the sensitivity of the design variables. Therefore, in this paper, the optimal design problem of the minimization of the residual vibration response is divided into the optimization design of the residual vibration minimization of the initial excitation structure. The problem of structural optimization design for the minimization of residual vibration of the impact loading structure. For the optimization design problem of the residual vibration minimization of the initial excitation structure, this study puts forward the adjoint method of the sensitivity analysis of the two type integral form of the residual vibration response on the design variables. Many design variables are included, and the proposed adjoint method only needs two Lyapunov equations to obtain all the sensitivity results. This not only realizes the analytical calculation sensitivity but also greatly reduces the time-consuming of the sensitivity analysis process. Based on the proposed adjoint method, the topology optimization method is used in the study, respectively. The optimal distribution problem of dampers, damped springs and damping materials with the objective of minimizing the residual vibration is investigated. Numerical examples show that the optimized design based on the proposed method improves the structural performance effectively. The residual vibration phase of the residual vibration is the optimal design for the minimization of the residual vibration of the impact load structure. The initial excitation is related to the design variables. In order to consider the correlation between the initial excitation and the design variables in the sensitivity calculation, this paper presents second methods to calculate the performance index of the two type integral form of the residual vibration on the sensitivity of the design variables, which greatly widens the scope of application of this work. Based on the second sensitivity methods proposed in this paper, the optimal distribution of damping materials in the impacted loading plate structure with the objective of minimizing the residual vibration is studied. The numerical example shows that the method proposed in this section is efficient and reliable. After that, the maximum residual elastic vibration in the constrained structure is considered. The Lyapunov method can not be applied directly to the problem of optimal design for residual vibration of incomplete structures. This is because two kinds of rigid body motion modes and elasticity are proposed in this paper, which can not obtain the unique solution of the Lyapunov equation. Based on the above method, the single resonator microstructural system is used to reduce the optimal parameters and optimal distribution of the residual vibration of the structure. The fixed parameters can be equivalent to a mass block with negative mass coefficient. Finally, this paper studies the problem of topological optimization design for structural crashworthiness under high impact load. The problem of Crashworthiness needs to consider a variety of nonlinear effects, which makes it very difficult to consider the structural optimization design with the consideration of crashworthiness, and the topology optimization side is adopted. It is more difficult to obtain the conceptual design of crashworthiness. For the design of Crashworthiness topology optimization, a new mixed optimization method is proposed in this paper. The new hybrid method is based on the modified inertial release method to construct the equivalent static load, and based on the equivalent load, the equivalent static analysis can be constructed, and the nonlinear transient dynamic analysis and optimization problem are made. The hybrid cellular automaton method is used to solve the nonlinear static optimization problem. The new hybrid method uses the two-layer iterative optimization process, in which the inner iteration adopts the hybrid cellular automaton to solve the nonlinear static optimization problem, while the outer iteration is based on the nonlinear dynamic. The structural response of the optimized design is checked and the equivalent static load based on the improved inertial release method is constructed. In the study, the optimization results and calculation efficiency of the hybrid method and the hybrid cellular automata are compared by numerical examples. The results show that the hybrid method and the hybrid cellular automaton method are similar to the optimal design, but the former is calculated. The calculation efficiency is much higher than that of the latter. Finally, the problem of a simplified vehicle model's crashworthiness topology optimization design is considered. The optimization results show the effectiveness of the proposed hybrid method.
【学位授予单位】：大连理工大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TB12

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