基于均匀化的周期性梁板结构降阶及拓扑优化

发布时间：2018-03-22 13:17

本文选题：周期性梁板　切入点：渐近均匀化　出处：《大连理工大学》2015年博士论文　论文类型：学位论文

【摘要】：梁板结构是工程中广泛应用的两大类结构,在近代商用飞机、卫星、运载火箭、高速列车结构中具有广阔的应用前景。随着工程技术的高速发展,人们对工程结构的高比刚／强度,轻质及多功能等性能提出了更高的要求,出现了越来越多的新型复合梁板结构,对于先进复合梁板结构的优化设计需求也越来越强烈。本论文针对周期性复合板结构和梁结构,利用渐近均匀化方法,拓扑优化技术以及多尺度分析技术等多种方法,对周期性梁结构的等效性能预测,指定或极值刚度的微结构优化设计以及周期性板的宏微观一体化优化设计等进行了深入的研究,并将商用有限元软件作为黑箱,实现基于商用软件高性能计算的复合梁板结构均匀化降阶及优化设计。本文研究的主要内容包括：(1)基于一维周期性渐近均匀化理论,发展了一维周期性梁结构渐近均匀化方法的有限元列式,并将基于商业软件的均匀化理论求解新方法扩展到一维周期性梁结构中,将具有复杂微结构单胞的一维周期性梁结构等效为宏观欧拉伯努利梁,实现了对其等效刚度的快速预测。新方法将商业软件作为一个黑箱,从而充分利用软件中的各种单元类型和建模技术,减小编程工作量及单胞模型规模,提高求解效率。上述方法的建立,使得对三维(二维)周期性材料,二维周期性板壳结构和一维周期性梁结构的均匀化求解都可以统一在相同数值求解和软件实现的框架内完成。将一维周期性梁的求解新方法与弯曲能量近似方法和基于三维周期性均匀化的近似方法进行了比较,并讨论了沿厚度方向的尺度效应。结果表明,基于直法线假定的弯曲能量法忽视了复合梁结构内的三维应力状态,过高地估计了梁的等效性质。而基于三维周期性均匀化的方法引入了截面内的周期性假设,在梁截面内单胞数量较少时,与一维均匀化新方法的结果差别较大,当截面内单胞数量足够多时,二者的结果趋于一致。(2)作为微结构优化设计的基础性研究,对使用体积守恒的Heaviside函数密度过滤进行优化过程中,迭代后期目标函数发生严重振荡的原因进行了研究。推导了体积守恒的非线性密度过滤的精确灵敏度表达式,通过有限差分法验证了新公式的正确性,并通过算例比较了采用不同灵敏度求解公式的结果差别。结果发现,当非线性参数增大时,原灵敏度公式的结果与差分结果严重背离,而精确灵敏度公式的结果与差分结果保持一致,进而验证了精确灵敏度公式的正确性。此外,当固化可调参数时,原灵敏度公式仍然是正确的灵敏度公式。这项工作为后期优化中得到清晰的微结构拓扑提供了有力的支持。(3)在一维周期性梁均匀化新方法的基础上,研究了在一定材料体积约束下的一维周期性梁结构指定刚度或极值刚度优化问题。提出了基于均匀化新方法的解析灵敏度求解方法,通过构造复合位移场并提取相应的应变能项,实现了基于商业软件对等效刚度及其灵敏度的求解,从而降低了优化的门槛,提高了优化的效率。将该优化方法推广到了一维周期性桁架梁结构,并实现了对拉扭耦合刚度的优化。讨论了单胞数量较少的短梁的优化方法,说明基于变量连接的短梁优化可以考虑到横向剪切的影响。(4)研究了蜂窝板结构的刚度设计问题,通过沿法线方向单元的变量连接来模拟蜂窝单胞,并将基于均匀化新方法的解析灵敏度求解方法推广到了周期性板壳结构。将此方法与基于直法线假设的二维均匀化和沿法线方向积分的求解方法进行比较,发现蜂窝单胞的长高比对于优化的最终结果是有影响的,而基于直法线假设的求解方法不能区分这一影响。在此基础上,研究了以宏观结构的最小柔顺性为目标、同时考虑宏观板结构与微观单胞构型的双尺度优化方法,给出了基于商业软件计算的目标函数及宏微观设计变量的灵敏度求解方法,从而实现了对双尺度拓扑优化问题的高效求解。(5)作为梁板模型降阶方法在工程中的实际应用,研究了MSC.SimXpert软件平台面向ProE的多层次多精度弹体结构分析模板的开发方法。提出了基于特征命名的CAD与CAE之间的信息传递方式,并通过外部XML文件数据库对属性自动识别和创建,实现了MSC.SimXpert模板对于ProE模型的精确识别和有限元模型的一键式快速转换。通过均匀化方法等模型降阶技术,将复杂精细实体模型替换为简化模型或一维梁模型,并通过模板平台进行多级弹体结构部件的自由替换与组装,从而建立多层次的有限元分析模型,有效的降低了全弹结构的计算规模。此外,通过模板能自动生成单元质量检查和结果文件,提高产品的研发速度。
[Abstract]:The beam slab structure is two kinds of structures are widely used in engineering, in the modern commercial aircraft, satellites, launch vehicles, and has wide application prospect of high speed train structure. With the rapid development of engineering technology, high specific strength and people of engineering structure, put forward higher requirements of lightweight and multifunctional properties. A new composite beam slab structure more and more, for the optimization design of advanced composite beam slab structure is also more and more strong. This thesis focuses on the periodic composite plate and beam structures, using the asymptotic homogenization method, topology optimization technology and multi-scale analysis methods, prediction of the equivalent properties of periodic beam structure the specified or extreme stiffness of micro structure optimization design and periodic plate optimization integration of macro and micro design are studied, and the finite element software as a black box, realize Composite beam slab structure calculation software of high performance reduction and homogenization based optimization design. The main contents of this paper include: (1) the one-dimensional periodic asymptotic homogenization theory based on finite element formulation developed one-dimensional periodic beam asymptotic homogenization method, and a new method of homogenization theory for business the software based on extended to one-dimensional periodic structure, with complex microstructure cell of the one-dimensional periodic beam structure is equivalent to macro Euler Bernoulli beam, to achieve a rapid prediction of the equivalent stiffness. The new method will be commercial software as a black box, so as to make full use of software in a variety of cell types and modeling technology, reduce the workload of programming and the cell model scale, improve the efficiency of the algorithm. The establishment of the above methods, the three dimensional (2D) periodic material, two-dimensional periodic one-dimensional periodic beam and plate structure. The homogenization solution can be unified in the framework of the same numerical solution and software. The new method for solving the one-dimensional periodic beam and bending energy approximation method and the approximate method of three-dimensional periodic homogenization based on the comparison, the scale effect along the thickness direction are discussed. The results show that the three-dimensional stress the state of the composite beam structure in bending energy method based on the assumption of normal straight neglect, overestimate the equivalent properties of the beam. The three-dimensional periodic homogenization method is introduced based on the hypothesis of periodicity in the cross section, in the section in the number of single cell is small, and the new method of one-dimensional uniform results vary greatly in the section, when the number of single cell is big enough, the two results are consistent. (2) as the basic research on the design of micro structure optimization, Heaviside function of density filtering using volume conservation optimize. In the process, the reason later iterations objective function serious oscillation is studied. The accurate sensitivity expression of nonlinear density filter of volume conservation is deduced and verified the correctness of the new formula by finite difference method, the sensitivity of different solution formula and compare the difference between the results by examples. The results showed that when the nonlinear parameters with the increase of the original sensitivity formula results and the difference results seriously, and accurate results and the sensitivity formula of difference was consistent, and then verify the correctness of the accurate sensitivity formula. In addition, when the solid of adjustable parameters, the sensitivity formula is still the sensitivity formula correct. This work provides a strong the support of micro structure topology obtained for later optimization. (3) based on the new method of homogeneous one-dimensional periodic beam, in the study of the materials under a certain volume constraint Dimensional periodic beam structure specified stiffness or extreme stiffness optimization problem is proposed. The analytic sensitivity method for solving the new method based on homogenization, by constructing a composite displacement field and extract the corresponding strain energy, the solution of the equivalent stiffness and the commercial software based on sensitivity, thus reducing the optimization threshold, improve the efficiency of optimization. The optimization method is applied to one-dimensional periodic truss beam structure, and realize the optimization of the tension torsion coupling stiffness is discussed. The optimization method of short beam cell number, indicating the short beam connection based on the optimization variables can take into account the effect of transverse shear. (4) study stiffness design problem of honeycomb board, through the unit along the normal direction of variables connected to analog cellular cell, and the analytic sensitivity method for solving the new method of homogenization is extended to periodic structure based on the shell. Compare this method with two-dimensional uniform based on the assumption of straight normal and integral along the normal direction of solving method, single celled cellular found taller than the final results for the optimization is influential, but not solving method based on the assumption of straight normal distinguish this effect. On this basis, to study the minimum compliance the macro structure as the goal, considering the two scale optimization method of macro and micro structure in single cell configuration, given the sensitivity calculation method based on the commercial software of objective function and macro design variables, so as to realize the efficient solution of the topology optimization problem of two scale. (5) as a practical application of beam plate model order method in engineering, research the multi precision structure of MSC.SimXpert software platform for ProE analysis of the development method of template. Based on CAD and CAE features named between The transmission of information, and through the external XML file to automatically identify and create database attributes, to achieve the MSC.SimXpert template for a type of accurate identification of ProE model and finite element model of the rapid conversion. Through the model of homogenization method and reduction technique, the complex solid model is replaced with simplified model or one-dimensional beam model, and the multilevel structure of parts through the template free replacement and assembly platform, so as to establish a multilevel finite element analysis model, effectively reduces the computational scale of missile structure. In addition, the template can automatically generate unit quality inspection and result file, improve the speed of product development.

【学位授予单位】：大连理工大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：TB12

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