非均匀温度影响下格栅夹芯结构微极梁等效方法

An Equivalent Micropolar Beam Method for Grid Sandwich Structures Under Inhomogeneous Temperature Conditions

通过胞元能量等效的方法,将格栅夹芯结构等效为连续的微极弹性材料,得到了等效微极弹性材料的本构关系.利用几何关系与平衡条件建立了微极梁受热变形的控制方程组,给出了微极梁位移随温度载荷变化的表达式.通过对比等效微极梁模型、夹层梁模型和ANSYS有限元软件计算的非均匀温度影响下悬臂格栅夹层梁受热弯曲变形的数值结果,验证了微极弹性等效的有效性.结果表明,将不连续的格栅夹芯结构等效为连续介质构成的模型时,由于约束的增加、自由度的减少,需要更多的应力、应变参量来描述其非局部的特性.

The grid sandwich structure was equivalent to a continuous micropolar elastic material with the method of cell energy equivalence,and the constitutive relation of the equivalent micropolar elastic material was obtained. Based on the geometrical relation and the equilibrium condition,the governing equations for the micropolar beam with thermal deformation were established,and the expression of the variation of the micropolar beam displacement under temperature load was given. By means of a grid sandwich cantilever beam under inhomogeneous temperature conditions,the effectiveness of the micropolar elastic equivalent was verified through comparison of the thermal bending deformation results calculated with the equivalent micropolar beam model,the sandwich beam model and the ANSYS finite element software,respectively. The results also show that,more stress and strain parameters are needed to describe the nonlocality due to the increase of constraints and the decrease of degrees of freedom when the discontinuous grid sandwich structure is equivalent to a continuous medium model.