Critical load of beam with linear and quadratic axial gradation rested on rotational spring hinge

Abstract— The buckling analysis of Euler beam made up of functionally graded material with linear and quadratic variations of elasticity modulus in axial direction is studied. The simply supported beam is rested on a rotational spring hinge at right end. The beam is ideal without initial curvature and it is subjected to axial compression without eccentricity. The linearelastic material behavior and engineering axial strain are considered. The analytical formulas of linearized buckling characteristic equations are calculated for linear and quadratic material gradation in the axial direction of the beam. The buckling behaviors of these kinds of elements is a basic theory for more complex structural analyses. By approaching rotational stiffness of the rotational spring hinge to zero or infinity, the critical load of simply supported or pinned-clamped axially graded beam is calculated, respectively. The numerical examples are conducted and critical load diagrams are depicted.

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