Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonlinear static isogeometric analysis of arbitrarily curved
  Kirchhoff-Love shells   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 via the
reciprocal shift tensor. 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,
efficiency and accuracy 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.

25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio