Keywords: finite length cylinder, functionally graded materials, laminated composites, piezoelectricity, boundary value problem, elasticity theory.

A mixed semi-analytical formulation is presented which accounts for the coupled mechanical and electrical response of piezoelectric, functionally graded (FG) and layered composite finitely long hollow circular cylinders. The exact theory of elasticity is used to define the behaviour of such cylinders as a boundary value problem(BVP). Under axisymmetric mechanical and electrical loadings, the three-dimensional problem problem is reduced to a two-dimensional plane strain problem of elasticity. The two-dimensional problem is reduced to a one-dimensional one by assuming an analytical solution in the longitudinal direction in terms of a Fourier series expansion which satisfies the simply (diaphragm) supported boundary conditions exactly at the two ends z=0, l. The fundamental (basic) dependent variables are chosen in the radial direction (thickness coordinate) of the cylinder. The resulting mathematical model is cast in the form of first order simultaneous ordinary differential equations which are integrated through an effective numerical integration technique by first transforming the BVP into a set of initial value problems (IVPs). The cylinder is subjected to internal/external pressurized mechanical and an electrical loading. Finally, numerical results are obtained which govern the active and sensory response of piezoelectric and FG cylinders. Numerical results are compared for their accuracy with available results. New results of finite length cylinders are generated and presented for future reference.

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