CAJ | 학술논문

假定衬砌与围岩为光滑接触，在满足隧洞净空尺寸和衬砌厚度的前提下，以使衬砌内边界上的切向应力最小为优化准则，寻求最优的支护断面形状。寻优过程是解决一类几何反问题的过程，相应的正问题运用平面弹性复变函数中的保角变换方法进行求解。寻优时，衬砌内边界的切向应力即为优化的目标函数，映射函数系数为设计变量。运用混合罚函数优化方法寻找目标函数的极小值，可以获得能满足给定约束条件的最优支护断面形状。优化后的衬砌断面形状可以最大限度地改善隧洞衬砌的应力状态，保证衬砌内边界获得最小的应力集中。
가정츤체여위암위광활접촉，재만족수동정공척촌화츤체후도적전제하，이사츤체내변계상적절향응력최소위우화준칙，심구최우적지호단면형상。심우과정시해결일류궤하반문제적과정，상응적정문제운용평면탄성복변함수중적보각변환방법진행구해。심우시，츤체내변계적절향응력즉위우화적목표함수，영사함수계수위설계변량。운용혼합벌함수우화방법심조목표함수적겁소치，가이획득능만족급정약속조건적최우지호단면형상。우화후적츤체단면형상가이최대한도지개선수동츤체적응력상태，보증츤체내변계획득최소적응력집중。
Under the assumption of pure slip contact along the lining-rock interface and the requirements of the net size and the lining thickness,derivation of shape optimization of a tunnel support was carried out with the objective of the greatest tangential stress along the inner edge of the support being minimized. The optimizing process is to solve a class of inverse geometry problems,and the corresponding forward problem can be solved with the method of conformal mapping of complex variable function in plane elasticity. During the process,the tangential stress along the inner edge of the support was selected as the objective function and coefficients of the mapping function were taken as the design variables. The method of mixed penalty function was used to minimize the objective function. As the objective function reached the minimum value,the optimal shape of support can be obtained.With the optimal shape,stress state in tunnel support was improved most effectively and the tangential stress concentration along the inner edge of support was minimized.