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考虑内部热传导,研究了格栅夹层梁一侧受热后的弯曲变形。认为变形后夹层结构中间腹板无弯曲。利用格栅夹层梁结构上的周期性,通过胞元结构的内力平衡方程和变形协调关系,得到了胞元两端内力和位移的关系。引入传递矩阵,建立了夹层梁内力和变形随温度变化的表达式。应用所建立的模型计算了悬臂格栅夹层梁在其上表面受热后的变形。在格栅夹层梁包含的胞元数量较多、腹板高度较小且厚度与表板厚度相近的情况下,由本文模型计算得到的挠度结果与有限元结果吻合较好。
Considering the internal heat conduction, the bending deformation after heating on one side of grille sandwich beam was studied. It is considered that there is no bending in the middle web of sandwich structure after deformation. Based on the periodicity of the structure of grillage mezzanine beam, the relationship between the internal forces and displacements at both ends of the cell was obtained by the internal force balance equation of cell structure and the deformation coordination. The transfer matrix is introduced to establish the expression of internal force and deformation of the sandwich beam with temperature. The deformation of the cantilever grid beam was calculated after the upper surface of the cantilever was heated by the established model. The results of deflection calculated by this model are in good agreement with the finite element results when there are many cells in the grid sandwich beam and the web height is small and the thickness is close to the thickness of the panel.