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Analytical bending solution of functionally graded cantilever-beam. (Chinese. English summary) Zbl 1222.74029
Summary: Based on the semi-inverse method, an analytical solution is obtained for a functionally graded cantilever-beam that is clamped at one end and subjected to a concentrated force and a couple at another end. The problem is treated as a plane stress case of an orthotropic (elastic) body. The mechanical properties of the material have been assumed to have the same dependence on the height-coordinate. This solution is valid for arbitrary gradient functions and it can play as a benchmark result for assessing other approximate methodologies or as a basis for establishing simplified functionally graded beam theories. Degenerate results for the isotropic homogeneous elastic case coincide well with existing analytical solutions. Some numerical examples are also given by assuming an exponential gradient function.

MSC:
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74G99 Equilibrium (steady-state) problems in solid mechanics
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