基于伽辽金法的圆柱形衬壳限制失稳研究

A study on buckling of the cylindrical liner by using the Galerkin method

研究了圆柱形衬壳的限制失稳问题.应用最小势能原理导出了圆柱形衬壳在均匀外压作用下屈曲的控制方程;通过伽辽金法对圆柱形衬壳的临界屈曲问题进行了求解;引入波长缩短比例因子,研究了衬壳与外围设备壁面之间的接触对衬壳屈曲临界压力的影响.研究结果表明,在不考虑衬壳与外围设备壁面的接触而只是将衬壳的屈曲位移限制在外围设备空腔内部的情况下,相比于衬壳自由失稳其限制失稳的临界压力在所选模型尺寸范围内提高了36%左右;边界接触可使衬壳失稳的临界压力有很大提高,当衬壳屈曲环向波长缩短至其自由失稳的一半时,衬壳限制失稳临界压力可达其自由失稳临界压力的3倍.

This paper deals with the confined buckling of the cylindrical liner. The control equation for the buekling of the cylindrical liner under uniform external pressure was derived using the principle of minimum potential energy. The critical buckling problem of the cylindrical liner was solved by using the Galerkin method. The shortened scaling factor of the wavelength was introduced, and the impact of the contact between the cylindrical liner and the wall of the outer equipment on the critical buckling pressure of the cylindrical liner was studied. The results show that, if the contact between the cylindri- cal liner and the wall of the outer equipment is not considered and the displacement is confined in the cavity of the outer equipment, the critical buckling pressure of the confined cylindrical liner increased about by 36% than that of the non - confined cylindrical liner in the range of the model size the paper selected. The contact between the cylindrical liner and the wall of the outer equipment increased the critical buckling pressure of the cylindrical liner much. When the circumferential buckling wavelength of the cylindrical liner is reduced to half of the non - confined cylindrical liner, its critical buckling pressure is over three times than that of the non - confined cylindrical liner.