单层厚壁圆筒弹性动应力的简化计算方法

A SIMPLIFIED METHOD FOR CALCULATING ELASTODYNAMIC STRESSES OF MONOBLOC THICK-WALLED CYLINDER

厚壁圆筒在爆炸领域被广泛应用,经典厚壁圆筒弹性动应力公式计算十分复杂,不利于工程直接应用。为了得到有效的精度较高的单层厚壁圆筒弹性动应力的简化计算公式,从经典动应力公式出发,通过求取频率特征方程的特征值,再将其代入动应力公式中进行简化计算,结合对动应力公式的级数表达式的讨论,最后得到了简化的厚壁圆筒内壁和外壁处动应力计算公式。数值计算结果表明,在圆筒外直径和内直径之比K不超过2时,简化计算结果和精确解的相对误差不大于6%。

Thick-walled cylinders are widely used to contain the effects of internal explosion events such as demilitarization of munitions and explosive manufacture. Formulae for calculating elastodynamic stresses of monobloc thick-walled cylinder under transient loading, which contain roots of frequency eigen-equation of thick-walled cylinder, are very complex, and it is difficult to find the analytical roots. Simplified formulae for prediction of stress at the inner surface and outer surface of a thick-walled cylinder were obtained by finding the positive roots of frequency eigen-equation of thick-walled cylinder. Numerical results indicate that the relative error between the simplified formulae and the exact solution is less than 6% when the ratio of outer radius to inner radius is no more than 2.