斜向缠绕复合材料悬臂管混合应力场及其剪力效应

Mixed stress field for inclined winding composite cantilever tube as well as its shear force effect

提出一种求解一般斜向缠绕复合材料悬壁管的混合应力场,包括正比于轴线坐标的比例应力部分和不随轴线 变化的应力部分.各分量中的比例应力部分可以利用纯弯曲公式由比例弯矩计算,而不变应力部分可以结合所获得 应力的梯度确定其环向三角函数形式,根据这些三角函数刚好和比例应力部分的环向三角函数相反,可得横截面上 混合应力场的对称轴绕原点产生了转动,这是一般斜绕复合材料悬壁管中剪力所引起的特殊效应.数值算例对5根 简单复合材料悬壁管进行了数值模拟,结果验证了上述特殊剪力效应.

A mixed-stress field is introduced for the inclined winding composite cantilever tube,including a proportional stress part in direct ratio to the axis coordinate and an invariant stress part along the axis.The proportional stress part in every component can be obtained by the proportional moment using the pure bending formulae.Furthermore,with the gradient of obtained stresses,the trigonometric function in circumferential direction for the invariant stress part can be determined.Since these trigonometric functions are opposite to those for the proportional stress part,the axis of symmetry of the mixed stress field in the cross section rotates around the origin.This special effect results from the shear force in the inclined winding composite cantilever tubes.Five simple composite cantilever tubes are simulated in numerical examples and results obtained in this study demonstrate the above shear force effect.