摘 要 本文探討Blatz-Ko 圓柱運動方程所得到的不變解，並且將非線性偏微分方程轉換至非線性常微分方程，使得求解過程得以簡化。本論文專注於兩個特別的案例作討論，並透過其常微分方程的相位平面分析兩個特別的案例的解之宏觀行為和奇異性和對稱性。且對那些可能碰到奇異解的區域，來對Blatz-Ko圓柱體的應變和應力做數值分析，了解材料可能的變化情況，並針對這些變化情況所代表的物理意義來做個解釋和說明，可以去更深入的了解Blatz-Ko 圓柱體的性質。 Abstract This thesis studies two solutions of the equation of motion for Blatz-Ko cylinders. The nonlinear partial differential equation governing the cylinders is transformed into nonlinear ordinary differential equations and thus the whole solving process is simplified. The two solutions studied through analyzes of their phase plane of ordinary equations. We analyze the stresses and strains of Blatz-Ko cylinders for the cases where the solutions are singular.
