Influence of coupling effects on analytical solutions of functionally graded (FG) spherical shells of revolution

Due to the lack of commercially available finite elements packages allowing us to analyse the behaviour of porous functionally graded (FG) structures in this paper, axisymmetric deformations of coupled FG spherical shells are studied. The analytical solution is presented by using complex hypergeometric polynomial series. The results presented agree closely with the reference results for isotropic spherical shells of revolution. The influence of the effects of material properties is characterized by a multiplier characterizing an unsymmetric shell wall construction (stiffness coupling). The results can be easily adopted in design procedures. The present results can be treated as the benchmark for finite element investigations.

ASYMPTOTICS OF A 3F2 POLYNOMIAL ASSOCIATED WITH THE CATALAN–LARCOMBE–FRENCH SEQUENCE

The large n behavior of the hypergeometric polynomial [Formula: see text] is considered by using integral representations of this polynomial. This 3F2 polynomial is associated with the Catalan–Larcombe–French sequence. Several other representations are mentioned, with references to the literature, and another asymptotic method is described by using a generating function of the sequence. The results are similar to those obtained by Clark (2004) who used a binomial sum for obtaining an asymptotic expansion.

Some results on generalized hypergeometric polynomials

In this paper, using a generalized hypergeometric polynomial defined bywhere Δ(m, − n) denotes the set of m-parameters:and m, n are positive integers, we have established some infinite series, transformations, integrals and expansion formulae for generalized hypergeometric polynomials. The polynomial is in a generalized form which yields many known polynomials with proper choice of parameters. Special cases have also been given.

Some infinite integrals involving Whittaker functions and generalized hypergeometric polynomials, with their applications

We have defined the generalized hypergeometric polynomial ((6), eqn. (2·1), p. 79) by means ofwhere δ and n are positive integers and the symbol Δ(δ, − n) represents the set of δ-parametersThe polynomial is in a generalized form which yields many known polynomials with proper choice of parameters and therefore the results are of general character.

On some results involving generalized hypergeometric polynomials

The generalized hypergeometric polynomial ((7), equation (2·1)) has been defined bywhere the symbol Δ(δ, −n) represents the set of δ-parameters:and δ, n are positive integers. The polynomial is in a generalized form which yields many known polynomials on specializing the parameters.