An energy–momentum conserving scheme for geometrically exact shells with drilling DOFs

• Published in: Computational mechanics Vol. 67; no. 1; pp. 341 - 364
• Main Authors: Zhang, Run, Stanciulescu, Ilinca, Yao, Xiaohu, Zhong, Hongzhi
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 2021; Springer; Springer Nature B.V
• Subjects: Analysis; Classical and Continuum Physics; Computational Science and Engineering; Conservation laws; Derivatives; Drilling; Drilling and boring; Engineering; Environmental law; Laws, regulations and rules; Locking; Mathematical analysis; Momentum; Original Paper; Orthogonality; Quadratures; Shells (structural forms); Theoretical and Applied Mechanics; Mixed discrete derivatives; Energy–momentum conserving scheme; Weak form quadrature element method; Drilling degrees of freedom; Geometrically exact shell
• ISSN: 0178-7675; 1432-0924
• DOI: 10.1007/s00466-020-01936-9

An energy–momentum conserving temporal integration scheme is presented for a recently proposed geometrically exact shell formulation with drilling degrees of freedom. The scheme is based on a novel idea of defining mixed discrete derivatives for holonomic constraint functions with displacements and rotations. By defining general discrete derivative expressions with unknown terms, the mixed discrete derivatives with second-order accuracy are constructed according to deformation modes to satisfy directionality and orthogonality properties simultaneously, thus preserving conservation laws of total energy and momenta. The analysis of shell structures is conducted using the weak form quadrature elements to ensure exact incorporation of constraints and conservation of total energy after discretization, as well as circumvent shear and membrane locking phenomena. Benchmark numerical examples are presented to demonstrate the validity of the present scheme.