组合圆筒管的优化设计

OPTIMUM DESIGN OF THE CIRCULAR CYLINDRICAL PIPES COMBINED WITH GFRP/STEEL

用外缠绕玻璃纤维增强复壁钢管来代替油气田内部承高压的高强度钢管,既可节省大量的优质钢材,又能对场内集输管道起到良好的外防腐效果。本文着重研究由玻璃钢/钢组合而成的厚壁圆筒管在管内高压作用下的优化设计问题。首先利用组合管的边界条件,由弹性理论导出了平面应变状态下组合管壁内三个主应力的计算公式;然后建立了以组合管总壁厚、玻璃钢外套管壁厚和玻璃纤维缠绕角为设计变量,单位长度组合管的材料成本为目标函数以及钢管的强度约束和玻璃钢的变形限制为约束条件的优化设计数学模型,采用复形法对本问题求得了最优解。作者还用所编的电算程序计算了各种管内径,各种内压及各种钢管强度等级所对应的设计变量最佳取值,从而讨论了管内径、内压及钢管强度等级变化对优化设计变量的影响,计算实例表明,在承受相同内压作用的情况下,组合管的材料成本较单纯钢管低,组合管的重量减轻尤为明显。主题词:组合圆筒管;内压;平面应变状态;优化设计;复形法。

This paper puts the emphasis on studying the optimum design of the thick-walled circular cylindrical pipes combined with GFRP/steel (shortly called, combined pipe, below) subjected to the internal high pressure. Firstly, considering a few of boundary conditions, the formulas of three principal stresses in the wall of the combined pipe in the state for plane strain are derived by elastic theories. Next, the mathematical model for the optimization of the combined pipe is set up, in which the total wall thickness of the combined pipe, tile wall thickness of GFRP out-sleeve and the wound angle of the glass fibre are chosen as design variables, the materials cost of the combined pipe per unit length is taken as an objective function, and the strength requirement of steel pipe and the deformation limitation of GFRP are considered as constraints as well. Finally, the model for the optimization is solved by using the Complex-Methol. Also, the author discusses the influence, caused by the changes of the inner diameter of the combined pipe, the internal pressure as well as the strength class of steel pipe, on the optimum values of design variables. A numerical example shows that, under the same pressure, the materials cost of the combined pipe is less than that of a pure steel pipe, and the weight evidently lighter.