The aim of this paper is to determine the buckling shapes and loads of an isotropic cylinders subjected to temperature and/or mechanical loads. First, the governing differential equations for buckling are derived. Second, their solution is presented. The buckling shapes are found to be trigonometrical functions in a skew coordinate system. With the aid of these functions, closed form solutions are developed for calculating the buckling loads. The paper presents some examples which illustrate unexpected results, e.g., unconstrained cylinders subjected to a change in temperature may buckle at a critical temperature, and may buckle either with increasing or with decreasing temperature.
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