基于拓展多尺度有限元的点阵材料结构最小柔顺性设计  

MINIMUM COMPLIANCE DESIGN OF LATTICE MATERIALS BASED ON EXTENDED MULTISCALE FINITE ELEMENT METHOD

作　　者：阎军[1] 胡文波[1] 段尊义[1] 

机构地区：[1]大连理工大学工业装备结构分析国家重点实验室,运载程与力学学部,工程力学系,大连116024

出　　处：《固体力学学报》2013年第1期47-54,共8页Chinese Journal of Solid Mechanics

基　　金：国家自然科学基金项目(90816025,10902018);科技重大专项基金(2011ZX02403-002);973项目(2011CB610304);大连理工大学学科研究基金(DUT11LK05)资助

摘　　要：论文应用拓展的多尺度有限元法(Extended Multiscale Finite Element Method),以微观构件的截面积为设计变量,研究了体积约束下点阵材料构成结构的最小柔顺性设计问题.建立了适应具有复杂几何形状和载荷边界的点阵材料结构的优化模型,应用序列二次规划算法对悬臂梁和L形梁算例在线性边界条件和周期性边界条件下进行了优化设计,讨论了点阵材料微结构尺寸效应对优化结果的影响,验证了优化模型和求解算法的可靠性,为点阵材料应用于复杂实际工程结构的优化设计提供了新的技术手段.Extended Multiscale Finite Element Method （EMFEM） is employed to deal with the mini- mum compliance design of structures composed of periodic lattice materials with the sectional area of micro components as design variables under volume constraints. For unit cells with finite size, an optimization model which adapts to the structure with complex geometry and loading conditions has been established. The size effect of micro-structure of the lattice materials is discussed. Cantilever and L-shaped beams under linear boundary condition and periodic boundary condition are optimized with sequential quadratic programming algorithm. The reliability of the optimization model and algorithm are verified by the numerical exam- ples. The paper presents a new approach for optimization of lattice materials to compose engineering con- structions.

关 键 词：拓展多尺度有限元 点阵材料 结构优化 尺寸效应 

分 类 号：V250[一般工业技术—材料科学与工程]