Abstract
The quasi-static explicit finite element method (FEM) and element free Galerkin (EFG) method are applied to trace the post-buckling equilibrium path of thin-walled members in this paper. The factors that primarily control the explicit buckling solutions, such as the computation time, loading function and dynamic relaxation, are investigated and suggested for the buckling analysis of thin-walled members. Three examples of different buckling modes, namely snap-through, overall and local buckling, are studied based on the implicit FEM, quasi-static explicit FEM and EFG method via the commercial software LS-DYNA. The convergence rate and accuracy of the explicit methods are compared with the conventional implicit arc-length method. It is drawn that EFG quasi-static explicit buckling analysis presents the same accurate results as implicit finite element solution, but is without convergence problem and of less-consumption of computing time than FEM.
Highlights
Thin-walled members of various shapes have been widely used in civil and mechanical engineering
It is drawn that element free Galerkin (EFG) quasi-static explicit buckling analysis presents the same accurate results as implicit finite element solution, but is without convergence problem and of less-consumption of computing time than finite element method (FEM)
The loading-displacement curves solved by explicit quasi-static FEM, implicit FEM and explicit quasi-static EFG method are compared and the reliability of explicit quasi-static buckling analysis with the suggested computation time, loading function and dynamic relaxation is demonstrated
Summary
Thin-walled members of various shapes have been widely used in civil and mechanical engineering. Compared with the finite element method, the mesh-free method possesses the same accuracy and can save some computing time as well as work out the problems that can’t be solved by the traditional FEM. The FEM and EFG quasi-static explicit methodologies are applied to trace the post-buckling path of thin-walled members in this paper. The key factors that control the convergence rate and dynamic responses, such as the computation time, loading function and damping relaxation, are discussed and suggested in the numerical buckling analysis. Three examples of thin-walled members occurred snap-through, overall and locally buckling are studied in detail by quasi-static explicit FEM and EFG method, and the efficiency and accuracy of the applied methods are demonstrated through the comparison with the conventional solution of implicit arc-length method
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