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刘华雩, 郑永彤, 彭海峰, 高效伟, 杨恺. 基于径向积分边界元法的周期性复合材料面内等效热弹性参数分析方法. 力学学报, 2024, 54(8): 1-10. DOI: 10.6052/0459-1879-24-044
引用本文: 刘华雩, 郑永彤, 彭海峰, 高效伟, 杨恺. 基于径向积分边界元法的周期性复合材料面内等效热弹性参数分析方法. 力学学报, 2024, 54(8): 1-10. DOI: 10.6052/0459-1879-24-044
Liu Huayu, Zheng Yongtong, Peng Haifeng, Gao Xiaowei, Yang Kai. A method for computing the effective in-plan thermoelastic properties of periodic composites based on the radial integration boundary element method. Chinese Journal of Theoretical and Applied Mechanics, 2024, 54(8): 1-10. DOI: 10.6052/0459-1879-24-044
Citation: Liu Huayu, Zheng Yongtong, Peng Haifeng, Gao Xiaowei, Yang Kai. A method for computing the effective in-plan thermoelastic properties of periodic composites based on the radial integration boundary element method. Chinese Journal of Theoretical and Applied Mechanics, 2024, 54(8): 1-10. DOI: 10.6052/0459-1879-24-044

基于径向积分边界元法的周期性复合材料面内等效热弹性参数分析方法

A METHOD FOR COMPUTING THE EFFECTIVE IN-PLAN THERMOELASTIC PROPERTIES OF PERIODIC COMPOSITES BASED ON THE RADIAL INTEGRATION BOUNDARY ELEMENT METHOD

  • 摘要: 具有人工设计结构的多材料夹杂的复合材料不仅具有可编辑的弹性模量和泊松比, 还可以实现热膨胀系数的调控. 这些复合材料的等效热弹性参数与其微观结构和材料分布密切相关. 文章提出了一种基于径向积分边界元法的周期性复合材料的均匀化热弹性参数的计算方法. 该方法基于代表性体积元均匀化方法建立材料的微观结构应力、应变与宏观等效热弹性参数之间的关联. 同时, 采用径向积分边界元法计算周期变形条件下代表性体积元的应力和应变场. 该方法无需内部网格和域积分, 仅依赖于边界的位移和面力等信息即可获得材料的等效热弹性参数, 具有容易实现参数化建模、容易考虑细小结构特征等优势. 另外, 在角点处采用非连续元处理, 大大简化了周期性边界条件的施加. 针对复合材料梁的弯曲问题, 通过与直接有限元模拟的结果进行对比, 验证了该方法的有效性. 然后, 还采用该方法对网状复合超材料的热膨胀系数进行了分析. 结果表明, 通过调整结构的尺寸, 可实现结构在热载荷下从正膨胀到负膨胀的转变.

     

    Abstract: One can program not only the elastic modulus and Poisson’s ratio but also the thermal expansion coefficients of the composites which consist of artificial microstructures and multiple materials. The macro effective thermoelastic properties of the composites are determined by their microstructures. In this paper, the authors proposed a novel method to evaluate the homogenized in-plan thermoelastic properties of the composites made of the periodic microstructures, which is based on the radial integration boundary element method. The proposed method employs the representative volume elements homogenized approach to calculate the effective properties based on the displacements and stresses of the micro unit cells, while utilizing the radial integral boundary element method for solving the displacements and stresses. The proposed method does not require internal grid and domain integration, and it only relies on the displacements and surface tractions on the boundary to obtain the effective thermoelastic parameters of materials, such as elastic modulus and thermal expansion coefficients. This method has advantages such as easy implementation of parameterized modeling, which leads to priorities in structure optimization. Besides, using the boundary element method makes it easy to analyze accurately the cells with tiny structural features. What’s more, the discontinuous elements are employed at the conners of structures in this paper to simplify the implementation of the periodic boundary conditions of the representative volume elements. The authors simulated the banding problem of a composite beam using both the homogenized thermoelastic properties and the direct finite element simulation. The results of the homogenized model coincide the direct simulation well, which indicates the effectiveness of the proposed method. Using the proposed method, the authors also conducted the parametric analysis of the coefficients of thermal expansion of a cellular microstructure. The results show that one can achieve the negative thermal expansion by changing the sizes of the cellular structure’s components.

     

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