含初应力复合材料柱壳结构的双稳态特性

Bi-stability behaviors of initially stressed composite cylindrical shell structure

为分析初应力对复合材料圆柱壳结构双稳态特性的影响,采用经典板壳理论建立复合材料圆柱壳力学模型,基于层合结构本构关系推导用双参数表达的系统应变能公式;根据最小势能原理得到双稳态产生的条件和稳态时的曲率表达式。利用Abaqus软件构建圆柱壳的有限元模型,通过附加边界弯矩对柱壳稳态跃迁过程进行模拟。理论计算结果与有限元结果的对比验证理论模型的正确性。分析结果表明:当初应力满足一定条件时,复合材料柱壳结构在其变形过程中有2个稳定平衡位置,并且在稳定平衡位置结构都不产生扭转变形;2个稳定平衡位置的曲率方向可以相同或相反,这与无初应力时反对称复合材料柱壳双稳态曲率方向只能相同的情况有区别。

To analyze the influence of initial stress on the bi-stability behaviors of composite cylindrical shell structure,the mechanical model of composite cylindrical shell is established using classical plate and shell theory.Based on the constitutive relation of laminated structure,the system strain energy formula with two parameters is derived.According to the principle of minimum potential energy,the condition of bi-stability and the expression of curvature in steady state are obtained.The finite element model of cylindrical shell structure is established by Abaqus software,and the stability transition process is simulated using additional boundary bending moment.The correctness of the theoretical model is verified by the comparison between the theoretical calculation results and the finite element results.The analysis results show that,when the initial stress satisfies certain conditions,there are two stability equilibrium points in the deformation process of composite cylindrical shell structure,and there is no torsion deformation at the two points.The curvature directions at the two stability equilibrium points can be same or opposite,which is different from the case that the bi-stability curvature of anti-symmetric composite cylindrical shell can only be the same without initial stress.