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題名 | 用最小平方配點法解各向同性材料規則形狀等截面實心桿之彈性扭轉問題=Numerical Analysis of the Elastic Torsion Problem of Isotropic Prismatic Bars with Solid Regular Cross Sections by the Least-Squares Point-Matching Method |
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作者 | 涂建祥; | 書刊名 | 國立虎尾技術學院學報 |
卷期 | 3 2000.03[民89.03] |
頁次 | 頁159-166 |
分類號 | 446.12 |
關鍵詞 | 應力函數; 加權殘值法; 最小平方配點法; 抗扭剛度; Stress function; Method of weighted residuals; Least-squares point-matching method; Torsional rigidity; |
語文 | 中文(Chinese) |
中文摘要 | 關於均質各向同性材料規則形狀等截面實心直桿彈性扭轉問題之分析,已有許多解法,然而受扭轉之機械元件及結構組件剖面形狀繁多,絕大多數的解法必須對個別形狀分別建構解題之關鍵函數,如翹曲函數、共軛函數、保角轉換函數及應力函數等,如此,對於簡單形狀,已然不便,對剖面形狀較複雜的桿件求解,更為困難。對前述問題之分析,本文採用一種較系統化且應用較廣的解法,選擇適當的應力試函數,用加權殘值法中之最小平方配點法求問題的近似解;並以正三角形、正方形、橢圓形、四對稱軸曲線所圍成形狀等的實心直桿之扭轉為例,解得最大剪應力及抗扭剛度之估算值與應用已知文獻中精確解所得之值比較,結果發現估算值與精確值極為吻合。 |
英文摘要 | There are many analytical method of elastic torsion problems of uniform isotropic prismatic bars with solid regular cross sections have been presented. However, a multitude of solid cross sections of torsion mechanical elements and structure elements are used. Consequently, most analytical method must derived on of the key functions of solution for each cross section, such as warping function, conjugate function, conformal mapping function and stress function, etc. it is not only inconvenient for simple cross sections, but also difficult for complicated sections. In this presents study, a general trial stress function and a systematic numerical method of analysis based on the least-squares point-matching method are proposed to determind the shearing stress and torsional rigidity in elastic torsion problems of arbitrarily solid regular cross sections. Computations of the maximum shearing stress and torsional rigidity are carried out for elastic torsion problems of various sections such as equilateral triangle, square, ellipses, and shapes constituted by four curves having 4-axis of symmetry, Excellent agreements were found for the computational results from the present method with the classical solutions. |
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