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Investigation of the stress‐strain state of the laminated shallow shells by R‐functions method combined with spline‐approximation
Author(s) -
Awrejcewicz J.,
Kurpa L.,
Osetrov A.
Publication year - 2011
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201000164
Subject(s) - spline (mechanical) , curvature , boundary value problem , structural engineering , maple , boundary (topology) , geometry , stress–strain curve , mathematics , shear stress , bending , mathematical analysis , materials science , deformation (meteorology) , engineering , composite material , botany , biology
Abstract The bending behavior of the laminated shallow shells under static loading has been studied using the R‐functions theory together with the spline‐approximation. Formulation is based on the first order shear deformation theory. Due to usage of the R‐functions theory the laminated shallow shells with complex shape and different types of the boundary conditions can be investigated. Application of the spline‐approximation allows getting reliable and validated results for non concave domains and domains with holes. The proposed method is implemented in the appropriate software in framework of the mathematical package MAPLE. The analysis of influence of certain factors (curvature, packing of layers, geometrical parameters, boundary conditions) on a stress‐strain state is carried out for shallow shells with cut‐outs. The comparison of obtained results with those already known from literature and results obtained by using ANSYS are also presented.