Axis-symmetrical solutions for n-plies functionally graded material cylinders under strain no-decaying conditions

作者：Fraldi M^*; Nunziante L; Carannante F

来源：Mechanics of Advanced Materials and Structures, 2007, 14(3): 151-174.

DOI：10.1080/15376490600719220

• functionally graded materials
• exact solutions
• decaying conditions

The proposal of the present work is to furnish a general approach to construct exact elastic solutions for FGM cylinders, made of a central core and n arbitrary cylindrical hollow homogeneous and isotropic phases. The hypothesis of axis-symmetrical boundary conditions is here assumed in order to analyze a class of elastic problems which present no-decaying of selected mechanical quantities and in particular of the axial strains epsilon(33) in the radial direction, being x(3) the axis of the laminated cylinder. To construct a robust mathematical procedure for obtaining exact elastic solutions for axis-symmetrical n-plies-Functionally Graded Material Cylinders (n-FGMCs), a theorem is first given for qualifying the space of the solutions and then their mathematical form is identified, when the object exhibits no-decaying of the axial strain. By starting from the classical Boussinesq-Somigliana-Galerkin vector and specializing it to torsionless composite cylinders characterized by no-decaying of the axial strain, a special form of the bi-harmonic Love's function chi((i))(r, x(3)) is finally obtained. It is then demonstrated that the differential boundary value problem (BVP) always can be translated in an equivalent linear algebraic one, first solving an in cascade one-dimensional Euler-like differential system (field equations) and then writing the boundary conditions by means an algebraic system ruled by a (6n + 4)-order square matrix P. At the end, constructive and existence theorems are formulated and proved, showing examples in comparison with literature data.

• 出版日期2007-4