古典線彈性力學中，楔形體內部應力之表達式在臨界角度下會變得不合理，此奇異性引人困惑，以往有許多人加以研討，試圖消除此奇異性。本文以狀態空間法解析楔形體問題，不引入應力函數解析。狀態空間法以實際物理量當作狀態向量，配合轉換矩陣處理楔形體問題，文獻中奇異性之產生乃因為傳統方法未能考慮特徵值為重根所造成數學解析不正確之結果。本文中發現臨界角度所對應之特徵值為重根，且發現此奇異現象不只發生在臨界角度，與特徵值有密切關係，本文並以數值方法對特徵值方程式之根進行計算，驗證在楔形體角度與外力特殊組合下，特徵值確為重根，若未考慮重根，應力表達式不完整，會導致奇異性問題，若對特徵值重根情況考慮週詳，則沒有應力奇異性的問題。

In the classical linear elasticity, the expression for the stress distribution in a wedge becomes unreasonable at those critical angles. This confused singularity had been often investigated, and many efforts for the elimination of the singularity had been made. In this article the wedge problem is studied using the state space formalism which is greatly different to the formulation using analytic stress function. In this formalism, the state vectors are taken from those physical quantities. In corporation to the process of transfer matrix, the wedge problem is then solved. The existences of the singularity in those literatures are all due to the incomplete results of the classical analysis in which the effect of the repeated eigenvlaues had been neglected. We found that the eigenvlaues for the critical angles are all repeated. And the singularity exists not only at those critical angles, but it is also related to the eigenvlaues. We have used several numerical methods for calculating the roots of the characteristic equation and verified that the eigenvlaues are really repeated under the special cases of wedge at some specified angles and subjected to some specified forms of external force. If the effect of the repeated roots is neglected, the singularity exists due to the incomplete expressions for the stress fields. Under the complete consideration for the repeated eigenvlaues, there is no such singularity.

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