連續보의 最適設計에 關한 硏究

Abstract

本 論文은 斷面이 연속적으로 變하는 要素들로 된 連續보의 最適設計를 爲한 한 Optimality Criteria 方法을 提示한다. 이 方法은 처음 Taig가 提案하였으며 以後 著者에 依하여 많은 部分이 修正되었다. 처짐 勾配를 求할때 흔히 하는 것처럼 假想일의 方法을 利用하여 應力勾配를 近似的으로 表現하였고 이 近似的 表現이 效率的일 뿐 아니라 最適設計를 求하는데 充分히 正確함을 알 수 있었다. 各 要素의 斷面이 연속的으로 變하므로 要素의 어떤 斷面의 높이 대신 節點에서의 斷面의 높이를 設計變數로 擇하여 正確性을 期하였으며 例題를 풀어 이 方法의 效率性과 正確性을 立證하였다.

This paper presents an Optimality Criteria method, which is first proposed by Taig and then modified by the author, to obtain the optimum design of continuous beams with tapered elements. An approximation to stress gradients is made using the method of virtual work, as is often the case with deflection gradients, and proves not only efficient but also accurate enough to find the optimum design. The depth of sections at nodal points is preferably chosen for the design variable since the depth of the tapered elements is continuously varying. Worked examples demonstrate the efficiency and accuracy of the method.

This paper presents an Optimality Criteria method, which is first proposed by Taig and then modified by the author, to obtain the optimum design of continuous beams with tapered elements. An approximation to stress gradients is made using the method of virtual work, as is often the case with deflection gradients, and proves not only efficient but also accurate enough to find the optimum design. The depth of sections at nodal points is preferably chosen for the design variable since the depth of the tapered elements is continuously varying. Worked examples demonstrate the efficiency and accuracy of the method.