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阎军, 刘岭, 程耿东, 刘书田. 点阵材料微极连续介质模型的应力优化设计[J]. 力学学报, 2006, 38(3): 356-363. DOI: 10.6052/0459-1879-2006-3-2005-518
引用本文: 阎军, 刘岭, 程耿东, 刘书田. 点阵材料微极连续介质模型的应力优化设计[J]. 力学学报, 2006, 38(3): 356-363. DOI: 10.6052/0459-1879-2006-3-2005-518
Stress optimization for truss-like materials based on micropolar continuum representation[J]. Chinese Journal of Theoretical and Applied Mechanics, 2006, 38(3): 356-363. DOI: 10.6052/0459-1879-2006-3-2005-518
Citation: Stress optimization for truss-like materials based on micropolar continuum representation[J]. Chinese Journal of Theoretical and Applied Mechanics, 2006, 38(3): 356-363. DOI: 10.6052/0459-1879-2006-3-2005-518

点阵材料微极连续介质模型的应力优化设计

Stress optimization for truss-like materials based on micropolar continuum representation

  • 摘要: 在将二维周期性点阵类材料等效为具有非局部化本构的微极连续介质的基础上,运用优化技术,探讨了基于材料相对密度和微单胞特征尺度两类变量的优化结构应力的方法,给出了针对最小化结构关键部位应力、结构最大应力最小化、最大化结构关键部位安全储备三类特定目标的结构与材料一体化协同优化结果. 利用圆板小孔应力集中的数值算例验证了方法的有效性.

     

    Abstract: In this paper, the optimum stress distribution around a holeis investigated for LCMs materials with micropolar continuum representationto reduce the computational cost. Two classes of design variables, relativedensity and cell size distribution of the truss-like materials, are to bedetermined by optimization under the given total material volume constraint.The concurrent designs of materials and structures are obtained for threedifferent optimization formulations. In the first formulation, oneminimizes the stress around the hole; in the second formulation, oneminimizes the highest stress within the whole structure. Since the yieldstrength of truss-like materials depends on the relative materialdensity, we minimize the ratio of stress over the corresponding effectiveyield strength along the hole boundary in our third formulation, whichmaximizes the strength reserve, which seems more rational. Numerical resultsfor the three objectives validate the method proposed in this paper. Theinfluence of the ply angle (angle between the principle direction of materialand the axes of system's coordinate) on the optimum result is discussed.The dependence of the optimum design on finite element meshes is alsoinvestigated.

     

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