本文由三維彈性力學出發，在圓柱座標系統下，建立柱體側表面荷重沿軸向成多項式分布作用下之狀態空間法解析模式。相較於傳統的理論架構，狀態空間解析模式將所處理之力學問題視為一線性系統，針對問題審慎選擇狀態向量，對場量變數適當的分類，透過有系統的矩陣運算與推導，得到形式簡單優美的狀態方程式。將此一理論套用至單層軸對稱正向性圓柱中，其中圓柱承受與軸向無關之外力作用，驗証由本文所得之解和參考文獻相同。進而探求單層軸對稱正向性圓柱和多層軸對稱正向性圓柱受與z軸有關之外力作用下之位移和應力。

　On the basis of three-dimensional basic equations of elasticity in the cylindrical coordinate, a state space formalism of a circular cylindrical elastic body subjected to surface tractions varying in the axial direction is established. Herein the surface tractions are prescribed in power functions of the axial coordinate. In the state space formalism the physical problems are dealt with in a linear system in comparison with the conventional formalisms. By grouping the field variables properly using matrix notations and partitioning the constitutive matrices accordingly, the basic equations of elasticity are formulated into a concise state equation in terms of the state vector. The formalism is examined through the analysis of an axisymmetric homogeneous orthotropic cylinder subjected to surface loadings independent of the axial direction. Further investigations in the axisymmetric problems of both single-layered and multi-layered orthotropic cylinders subjected to surface tractions varying in the z-axis are analyzed.

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