Fractal continuum approach for self-similar beam bending
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Bending of beams with fractal structure is studied. A formulation of self-similar beam bending applying Euller–Bernoulli principle in the fractal continuum is defined. The generalization of standard Euler–Bernoulli beam equation is obtained using local fractional differential operators, and the corresponding mapping of a bending problem for a self-similar beam is defined. The formulation obtained allowed us to calculate the exact values of spatial distribution of beam response along its length based on the estimated displacements, rotations, bending moments and shear forces as functions of fractal parameters of the beam. To study the influence of the fractal nature and scale effects of a beam on its mechanical properties, structural behavior of a cantilever beam with a load at the free end is considered.
