‘Best’ transverse shearing and stretching shell theory for nonlinear finite element simulations

Abstract Convinced of the powerful capability of modern computational techniques the question of ‘best’ physical shell models is re-raised. In the present paper, ‘best’ interior shell equations are derived by mapping a 3-dimensional body, described as a multi-director-continuum, on a Cosserat-surface kinematics. The derived shell equations hold for arbitrarily large deformations and material laws in rate-description, incorporating shear distortions and thickness changes. The optimal character of the developed model — proven by tensor norm bounding techniques — is finally demonstrated by results of numerical simulations of nonlinear shell responses.

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