【作者】 刘岭；

【导师】 程耿东；

【作者基本信息】 大连理工大学 ， 工程力学， 2006， 硕士

【摘要】 随着科学技术的发展,传统的实体金属材料已远不能满足工程需要,人们对新材料提出了更高的要求:轻质、强韧且兼具多功能性。为实现这一目标,力学家们通过控制材料微结构实现了多种构型新颖的结构化材料,如蜂窝、泡沫、类桁架材料等。这些材料由于其卓越的比力学性能,能够在保证力学性能的前提下有效降低结构重量,并且易于实现多功能要求,因而受到了科学界和工程界的广泛关注和青睐。 本文的研究对象是具有周期性微结构的超轻质材料。微结构的周期性给这类材料的性能预测带来了很大方便,其中有代表性的方法包括均匀化理论和代表体元法,但如果考虑到材料在制造和使用过程中可能产生的随机缺陷,等效性能的求解往往非常耗时,如何高效预测其等效性能是一个亟待解决的问题:微结构的存在同时也增加了由这类材料所构成结构的弹塑性分析难度,复杂的内部构形需要投入更多的分析时间和计算资源,因此发展快速等效求解方法是非常必要的,尤其当作为优化/可靠度求解的分析工具时,这一需求显得尤为突出;另一方面,现有的结构/材料协同优化方法得到的微结构结果在宏观上往往点点相异,这给实际制造带来了一定困难,有必要发展考虑制造性的协同优化方法。针对以上这些问题,本文将主要讨论以下三部分内容: 1.对于随机性材料等效性能预测问题,本文采用蒙特卡洛模拟方法,从数值的角度比较了不同的边界条件对预测结果的影响,讨论了其中的尺度效应和对胞元选择的依赖性。为了提高Dirichlet边界条件下的计算效率和改善结果精度,本文提出了考虑内部胞元能量等效的代表体元法。该方法能够有效削弱边界条件和胞元选择的影响,实现了采用较小代表体元得到更好结果的目的。 2.对于由类桁架材料构成结构的弹塑性分析,本文考虑到材料单胞近似为桁架的特点,基于数值均匀化理论,建立了宏微观两级求解格式。原问题转化为宏观上一个非线性弹性连续体计算问题和微观上多个小规模桁架系统的弹塑性计算问题,从而在保证精度的前提下有效提高了计算效率。 3.对于结构/材料一体化设计,针对现有结果给制造带来的困难,本文提出了以均一微结构为前提的多孔材料与结构的协同优化方案。采用拓扑优化技术,微结构不再局限为特定构形;在两个尺度上独立定义单元密度为设计变量,分别引入了SIMP和PAMP方法对密度进行惩罚,并集成到一个优化模型中进行协同设计。以此为极限值,我们还提出了基于子结构的两级协同优化方案,并讨论了其在制造上的优势及尺度效应。更多还原

【Abstract】 As the rapid development of science and technology, conventional solid metals have become inadequate to satisfy the needs of practical applications. People are constantly seeking new materials with some fascinating properties: light, stiff and multifunctional. To achieve this goal, mechanics researchers have developed several innovative structured materials by controlling the configuration of material microstructures, including honeycomb, foam and truss-like material. These materials are very promising for their superior mechanical properties and multifunctional capabilities.The ultra-light materials investigated herein all have periodic microstructures. The existence of microstructure on one hand makes it very convenient to predict material properties, for which, Homogenization theory and Representative Volume Element (RVE) method are two mainstream methods. But if we take into account random imperfections induced during manufacturing process and subsequent practical applications, the prediction of equivalent properties could become very time-consuming. For this reason, there is interest in finding a new methodology which exhibits more efficiency over traditional ones. On the other hand, however, the existence of microstructure also increase the difficulty of elasto-plastic analysis of structures constructed of ultra-light materials, since complex internal configuration requires much more time and computing resources. So it is of great importance to develop a more efficient analytical algorithm, especially in the case that this analysis is for optimization / reliability solution. In the aspect of structure / material concurrent optimization, existing methods always lead to non-uniform microstructures in the macro-scale, which poses insurmountable manufacturing difficulties. Thus it is desirable to have a concurrent optimization scheme considering manufacturing factors. Addressing these problems, the study of this thesis can be divided into three main parts:1. In predicting equivalent properties of materials with imperfections, Monte Carlo simulation is adopted based on the Homogenization theory and the Representative Volume Element method. We have compared different boundary conditions, and discussed the size effect and the influence of different cell selections. To improve the efficiency of computation and refine the results under Dirichlet boundary condition, it is proposed a Representative Volume Element computation based on energy equivalence of inner cells, and therefore better results could be achieved with relatively smaller RVE.2. For the elasto-plastic analysis of structures composed of truss-like materials, we first simplify the unit cell as a truss model, and then present a two-scale analysis based on the numerical homogenization. The original problem is thereby transformed to two interrelated problems in two scales: a nonlinear elastic continuum computation in macro-scale and several elasto-plastic analyses of small-scale truss systems in micro-scale. The proposed method is verified to have the same precision but less used time.3. To address the manufacturing difficulty in existing structure / material optimization, this thesis presents a new concurrent topology optimization scheme to simultaneously achieve the optimum structure and optimum material microstructure. Microstructure is assumed to be uniform in macro-scale to meet manufacturing requirements. Design variables in both scales are independently defined and then integrated into one system with the help of homogenization theory. Penalization approaches are adopted in both scales to ensure clear topologies, i.e. SIMP (Solid Isotropic Material with Penalization) in micro-scale and PAMP (Porous Anisotropic Material with Penalization) in macro-scale. Further, it is proposed another concurrent optimization scheme based on substructure. The size effect and advantages for manufacturing are discussed.更多还原