Use of axiomatic/asymptotic approach to evaluate various refined theories for sandwich shells

• Published in: Composite structures 2014-03, Vol.109, p.139-149
• Main Authors: Mashat, Daoud S., Carrera, Erasmo, Zenkour, Ashraf M., Al Khateeb, Sadah A.
• Format: Article
• Language: English
• Subjects: Best shell theories; Higher order theories; Layer-wise theories; Sandwich structures; Shell theories; Zig-zag theories
• ISSN: 0263-8223; 1879-1085
• DOI: 10.1016/j.compstruct.2013.10.046

This paper evaluates refined theories for sandwich shells. Layer-wise and equivalent single-layer models (including zig-zag theories) are used with linear and higher order expansion in the thickness layer/shell direction for the displacement variables. So called asymptotic/axiomatic approach is employed to establish the effectiveness of each displacements terms for a given problems: that is the initial axiomatic expansion with all the terms related to the assigned order N is asymptotically reduced to a ‘best’ displacement models which has the same accuracy of the full model but with less terms. The various sandwich theories are conveniently formulated by using the unified formulation by Carrera (CUF) that leads to governing equations which forms are formally the same for the different sandwich shell theories. Accuracy of a given theory is established by fixing the sandwich shell in term of geometry, boundary conditions, lay-out of the face/core layers (including very soft-core cases) as well as by choosing a criteria to measure the errors. Two error criteria have been adopted which are related to a fixed point and to the maximum values of displacement/stress variables in the thickness shell direction. A number of problems have been treated and the related ‘best’ displacement model have been obtained. The effectiveness of the asymptotic/axiamotic problems is proved by comparing with available reference solutions. It has been found that the resulting reduced ‘best’ theories are very much subordinated to the considered problems. These changes by changing geometrically parameters as well as by adopting a different error criteria.