双层壳的双稳态力学特性理论分析和数值模拟

Bi-stable Mechanical Behaviors of Double-layered Isotropic Shell Structure

双稳态结构一般均由复合材料制作而成,然而复合材料有其固有的缺陷,即采用正对称铺层的层合板在弯曲过程中会产生扭转变形,而采用反对称铺层的层合板容易受到温度影响。对于各向同性材料结构,在变形过程中既没有拉弯耦合效应也没有弯扭耦合效应。本文据此建立了存在预应力的各向同性材料圆柱壳的双稳态力学模型,给出了其变形过程中的弯曲应变能和拉伸应变能的表达式。结果表明,预应力柱壳总应变能有两个极小值,故柱壳存在两个稳定状态,通过计算得到了结构卷曲半径的大小。同时,对双层壳的双稳态过程进行了有限元数值模拟。数值结果与理论模型解吻合很好。

Bi-stable structures are usually made of laminated composite materials. However, composite materials have inherent shortcomings, e.g. , laminated plates of symmetrical lay-up can twist when bending; laminated plates of anti-symmetrical lay-up are easily liable to temperature. In contrast, isotropic structures have no bending-stretching and twisting-bending coupling. A pre-stressed double-layered isotropic cylindrical shell model is proposed in this paper. Expressions for the bending and stretching strain energies are presented. Calculations show that total strain energy has two local minimum values, which reveals that the cylinder shell structure has its bi-stability. The corresponding rolled-up radius is thus determined. Meanwhile, FEM simulation on the bi-stable processes has been performed, and numerical data coincide with well the predicted results by the proposed model.