TY - JOUR

T1 - On the static analysis of nonlinear beam and shell structures with singular stiffness matrices due to redundant coordinates

AU - Hente, Christian

AU - Gebhardt, Cristian Guillermo

AU - Rolfes, Raimund

N1 - Funding Information: This study has been carried out within the ForWind joint research project “ventus efficiens - joint research for the efficiency of wind energy converters within the energy supply system” (FKZ ZN3024), financially supported by the Ministry for Science and Culture in Lower Saxony, Germany and within the research project ”PreciWind - Precise measuring system for contact-less recording and analysis of the dynamic flow behavior of wind turbine rotor blades”. (FKZ 03EE3013B), financially supported by Federal Ministry for Economic Affairs and Energy, Germany

PY - 2021/4

Y1 - 2021/4

N2 - 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.

AB - 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.

KW - Efficient implementation

KW - Geometrically exact beams and solid-degenerate shells

KW - Singular stiffness matrices due to redundant coordinates

KW - Static analysis

KW - Variational-consistent null-space method

UR - http://www.scopus.com/inward/record.url?scp=85101035297&partnerID=8YFLogxK

U2 - 10.1016/j.tws.2021.107496

DO - 10.1016/j.tws.2021.107496

M3 - Article

AN - SCOPUS:85101035297

VL - 161

JO - Thin-Walled Structures

JF - Thin-Walled Structures

SN - 0263-8231

M1 - 107496

ER -