On the static analysis of nonlinear beam and shell structures with singular stiffness matrices due to redundant coordinates

作者：Christian Hente^*; Cristian Guillermo Gebhardt; Raimund Rolfes

来源：THIN-WALLED STRUCTURES, 2021, 161: 107496.

DOI：10.1016/j.tws.2021.107496

• Static analysis
• Singular stiffness matrices due to redundant coordinates
• Variational-consistent null-space method
• Geometrically exact beams and solid-degenerate shells
• Efficient implementation

The static analysis of nonlinear slender structures represented by a director-based formulation requires to deal with singular stiffness matrices. Classical linear buckling analysis produces eigenvalues and eigenvectors that are not physically assignable. Moreover, the linearized system in saddle-point form is very prone to ill-conditioning, which leads to a reduced robustness of the path-following nonlinear analysis. Here, we present the extension of a variational-consistent null-space method, previously developed by the authors, that reduces linear and nonlinear static equilibrium problems to their minimal representation, remedying at once both critical aspects without sacrificing the objectivity and path independence of the underlying formulation. Its validity is successfully tested by several examples.