Nonlinear static isogeometric analysis of arbitrarily curved Kirchhoff-Love shells. (15th February 2021)

• Record Type: Journal Article
• Authors: Radenković, G.; Borković, A.; Marussig, B.
• Is Part Of: International journal of mechanical sciences. Volume 192(2021)
• Publication Date: 2021-02-15
• Subjects: Strongly curved Kirchhoff-Love shell -- Nonlinear analysis -- Reciprocal shift tensor -- Analytical constitutive relation; Mechanical engineering -- Periodicals; Génie mécanique -- Périodiques; Mechanical engineering; Maschinenbau; Mechanik; Zeitschrift; Periodicals; 621.05
• DOI: 10.1016/j.ijmecsci.2020.106143
• Languages: English
• ISSNs: 0020-7403

Abstract

Highlights: A rigorous geometric nonlinear static IGA shell formulation is developed and implemented. The complete analytic elastic constitutive relation between energetically conjugated pairs for Kirchhoff-Love shells is derived. The three reduced models are considered and one of them is suggested for the analysis of strongly curved shells. The nonlinear distribution of strain throughout the thickness is significant for a strongly curved shell. The curviness of a shell at each configuration determines the appropriate shell formulation. Graphical abstract: Abstract: The geometrically rigorous nonlinear analysis of elastic shells is considered in the context of finite, but small, strain theory. The research is focused on the introduction of the full shell metric and examination of its influence on the nonlinear structural response. The exact relation between the reference and equidistant strains is employed and the complete analytic elastic constitutive relation between energetically conjugated forces and strains is derived. Utilizing these strict relations, the geometric stiffness matrix is derived explicitly by the variation of the unknown metric. Moreover, a compact form of this matrix is presented. Despite the linear displacement distribution due to the Kirchhoff-Love hypothesis, a nonlinear strain distribution arises along the shell thickness. This fact is sometimes disregarded for the nonlinear analysis of thin shells based on the initial geometry, thereby ignoring the strong curviness of a shell at some subsequent configuration. We show that the curviness of a shell at each configuration determines the appropriate shell formulation. For shells that become strongly curved at some configurations during deformation, the nonlinear distribution of strain throughout the thickness must be considered in order to obtain accurate results. We investigate four computational models: one based on the full analytical constitutive relation, and three simplified ones. Robustness, accuracy and relative efficiency of the presented formulation are examined via selected numerical experiments. Our main finding is that the employment of the full metric is often required when the complete response of the shells is sought, even for the initially thin shells. Finally, the simplified model that provided the best balance between efficiency and accuracy is suggested for the nonlinear analysis of strongly curved shells.