Enrichment of a rational polynomial family of shape functions with regularity C^k₀, k=0,2,4…

Abstract

PurposeThe purpose of this paper is to investigate the approximation performance of a family of piecewise rational polynomial shape functions, which are enriched by a set of monomials of order p to obtain high order approximations. To numerically demonstrate the features of the enriched approximation some examples on the mechanical elastic response and free‐vibration of axisymmetric plates and shells are carried out.Design/methodology/approachThe global approximation is based on a particular family of weight function, which is defined on the parametric domain of the element, ξ∈[−1,1], resulting in shape functions with compact support, which have regularity C0k,k=0,2,4… in the global domain Σ. The PU shape functions are enriched by a set of monomials of order p to obtain high order approximation spaces.FindingsBased on the numerical results of elastic axisymmetric plates and shells, it is demonstrated that the proposed methodology produces satisfactory results in terms of keeping the ill‐conditioning of the system of equations under accepted levels. Comparisons are established between linear and Hermitian shape functions showing similar results. The observed results for the free‐vibration problem of plates and shells show the potential of the proposed approximation space.Research limitations/implicationsIn this paper the formulation is limited to the modeling of axisymmetric plate and shell problems. However, it can be applied to model other problems where the high regularity of the approximation is required.Originality/valueThe paper presents an alternative approach to construct partition of unity shape functions based on a particular family of weight function.