刚性空腔内弹性衬壳热屈曲温度数值解法

Numerical analysis of the liners encased in a rigid cavity

研究了刚性空腔内弹性圆柱形两端固支钢衬壳由于温度变化引起的屈曲问题。应用非线性理论导出衬壳热屈曲问题的大挠度控制方程，用渐进分析法将其线性化。假设满足边界条件和刚性空腔约束条件的屈曲模态，分别采用伽辽金（Ｇａｌｅｒｋｉｎ）法和配点法解出屈曲温度。计算了一个模型，两种方法得出的结果十分接近。给出衬壳的长度和厚度对屈曲温度的影响曲线。文中结果可应用于核反应堆安全壳和化学工业中厚壁高压反应塔中内衬壳设计。

This paper deals with the thermal buckling of the cylindrical shells encased in arigid cavity such as the thin steel liner of prestressed concrete pressure vessels of nuclearreactors and the liner of pressure vessels in chemical industry etc. The governing equationfor the thermal buckling was developed based on nonlinear theory of thin shells. Then a trigonometry series was assumed as the buckling model to satisfy the boundary condition andthe condition limited by the rigity cavity. Two numerical methods (the Galerkin method andthe collocation method) were used to obtain the critical temperature of buckling for considered shells. The relations between the critical temperature and length or thickness of cylindrical shells were investigated. The corresponding results obtained will be valuble for engineering design. The results obtained by the two numerical methods show that the collocation method will give the same precision as the Galerkin method.