【作者】 肖曼玉； 马骏；

【Author】 Xiao Manyu;Ma Jun;Northwestern Polytechnical University;

【机构】 西北工业大学；

【摘要】 振动特性是影响机械性能、使用寿命、抗疲劳性能和安全性的关键因素。随着现代精密的数值计算方法和先进制造技术的发展,航空航天工业对机械部件的性能要求越来越高,此时需要一个高精度模型来精确地模拟机械性能。这种高度精细的有限元模型模拟通常会导致一系列自由度从数千万到数十亿不等的大规模问题,这些问题的主要难点在于求解每次迭代的有限元分析产生的大规模动力平衡方程,以及灵敏度分析产生的伴随方程,近年来已有研究将模型缩减技术融入整体拓扑优化过程中,静态问题的拓扑优化已经得到了广泛的研究。然而,大量物理现象是瞬态的。针对瞬态问题的拓扑优化问题的研究还很少。基于此,本文提出了一套缩减模型与拓扑优化相耦合的新方法,针对大规模时变结构优化问题,通过对有限元分析中的高维动力学平衡方程,以及基于积分格式的连续伴随法的动力学灵敏度分析方法得到的伴随方程构建双POD缩减模型,并通过优化过程收敛准则动态更新缩减基,2维和3维的数值算例表明该套方法缩减性好,可行性高。更多还原

【Abstract】 Vibration Characteristics is a critical factor that affects performance,service life,fatigue resistance and safety of structural components,and is inarguably an important design criterion.With modern-day sophisticated numerical methods and the recent development of advanced manufacturing technologies,the performance requirements for mechanical parts in the aerospace industry have become increasingly demanding.This would then entail a very fine model to simulate the mechanical performance accurately.This simulation modelling with highly refined finite element models typically results in a series of large-scale problems with degrees of freedom ranging from tens of millions to even billions.The main hindrances are the solutions of both the large-scale dynamical equilibrium equations resulting from the FEA analysis in each iteration,as well as the adjoint equations from the sensitivity analysis.Recent research papers have opened promising pathways for integrating model reduction techniques within the overall topology optimization process.It has been well studied on topology optimization for static problems.However,many physical phenomena are transient.Topology optimization for transient problems has been far less studied.In this paper,a new method of coupling the reduction model with the topology optimization is proposed.For large-scale time-dependent structural optimization problems,the double-POD reduction model is constructed from the high-dimensional dynamic balance equation in the finite element analysis and the adjoint equation obtained by the dynamic sensitivity analysis method of the continuous adjoint method based on the integral scheme,and the reduction basis is updated dynamically by the convergence criterion of the optimization process.2D and 3D numerical examples show that the proposed method has good reduction performance and high feasibility.更多还原