Axisymmetric elasticity solutions for a uniformly loaded annular plate of transversely isotropic functionally graded materials. (English) Zbl 1142.74024
Summary: We consider the axisymmetric problem of a functionally graded transversely isotropic annular plate subject to a uniform transverse load. A direct displacement method is developed in which non-zero displacement components are expressed in terms of suitable combinations of power and logarithmic functions of \(r\), the radial coordinate, with coefficients being undetermined functions of \(z\), the axial coordinate. The governing equations as well as the corresponding boundary conditions for the undetermined functions are deduced from equilibrium equations and boundary conditions for the annular plate, respectively. Through a step-by-step integration scheme along with the consideration of boundary conditions at the upper and lower surfaces, the \(z\)-dependent functions are determined in explicit form, and certain integral constants are then determined completely from the remaining boundary conditions. Thus, analytical elasticity solutions for the plate with different cylindrical boundary conditions are presented. As a promising feature, the developed method is applicable when the five material constants of a transversely isotropic material vary along the thickness arbitrarily and independently. A numerical example is finally given to show the effect of material inhomogeneity on the elastic field in the annular plate.
MSC:
| 74K20 | Plates |
| 74E10 | Anisotropy in solid mechanics |
| 74E05 | Inhomogeneity in solid mechanics |
| 74G05 | Explicit solutions of equilibrium problems in solid mechanics |
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