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Abstract
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In this study, an efficient finite element model with two degrees of freedom per node is developed for buckling analysis of axially functionally graded (AFG) tapered Timoshenko beams resting on Winkler elastic foundation. The material properties are assumed to vary continuously along the beam axis according to the power-law model. The shape functions are exactly acquired through solving the system of equilibrium equations of Timoshenko beam by means of the power series expansions of displacement components. It is also demonstrated that the resulting shape func-tions, in comparison with Hermitian cubic interpolation functions, are proportional to the me-chanical features of beam element including the geometrical properties, material characteristics, as well as the critical axial load. Then the element stiffness matrix is formulated by applying the developed shape functions to the total potential energy along the element axis. An exhaustive nu-merical example is implemented to clarify the efficiency and simplicity of the proposed mathe-matical methodology. Furthermore, effects of end conditions, material gradient, Winkler parame-ter, tapering ratio, and aspect ratio on the critical buckling load of AFG tapered Timoshenko beam are studied in detail. The numerical outcomes reveal that the elastic foundation enhances the sta-bility characteristics of axially non-homogeneous and homogeneous beams with constant or vari-able cross-section.
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