承压叠层圆柱的弹性分析

Elasticity analysis of laminated cylinders with compressive load

基于弹性理论,对轴向压力作用下的、由不同材料于径向方向上叠合而成的叠层圆柱的受力全过程进行力学分析,以研究轴向荷载作用下圆柱任意位置的应力值和应变值.考虑了三向应力的作用,分别求得每一叠层的弹性力学解,然后通过层间变形协调关系,建立了叠层圆柱从内叠层内边界到外叠层外边界间的递推关系,最后通过内外边界条件可对叠层圆柱内任意点的应力和应变进行求解.以3种不同形式的叠层承压圆柱为例,运用上述理论,对其弹性阶段的承载力进行了分析,该理论由于考虑了不同叠层泊松比所引起的叠层间挤压应力的影响,因而理论计算与有限元吻合很好.

Based on elasticity theory, the stress and the strain of certain part of laminated cylinders with different materials laminated at radical direction were analyzed under axial pressure. With the considera- tion of three-dimensional stress influence, the elastic solution of each layer was obtained respectively. The recursive relationship from laminated cylinder inner boundary to outer boundary was established based on the deformation coordination relationship among layers. The stress and the strain at any point within laminated cylinder were achieved according to the boundary conditions. Taking three different la- minated columns as examples, the elastic stress and strain were analyzed. Because the influence of extru- sion force caused by different Poisson＇s ratio in each layer is considered in the proposed theory, the theo- retical results are well consistent with those from finite element software.