Finite element analysis of post-buckling dynamics in plates-Part I: An asymptotic approach

By Hui Chen, Lawrence N. Virgin. 2006

51 citations recorded by the source corpus.

Abstract Various static and dynamic aspects of post-buckled thin plates, including the transition of buckled patterns, post-buckling dynamics, secondary bifurcation, and dynamic snapping (mode jumping phenomenon), are investigated systematically using asymptotical and non-stationary finite element methods. In part I, the secondary dynamic instability and the local post-secondary buckling behavior of thin rectangular plates under generalized (mechanical and thermal) loading is investigated using an asymptotic numerical method which combines Koiter’s nonlinear instability theory with the finite element technique. A dynamic multi-mode reduction method—similar to its static single-mode counterpart: Liapunov–Schmidt reduction—is developed in this perturbation approach. Post-secondary buckling equilibrium branches are obtained by solving the reduced low-dimensional parametric equations and their stability properties are determined directly by checking the eigenvalues of the resulting Jacobian matrix. Typical post-secondary buckling forms—transcritical, supercritical and subcritical bifurcations are observed according to different combinations of boundary conditions and load types. Geometric imperfection analysis shows that not only the secondary bifurcation load but also changes in the fundamental post-secondary buckling behavior are affected. The post-buckling dynamics and the global analysis of mode jumping of the plates are addressed in part II.

Subfields: Computational Mechanics, Control and Systems Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/ba7d100bb34aa1444e364fe1ac30fd62caa89514

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In Computational Mechanics

In Control and Systems Engineering

In Mechanics of Materials

Citations in the corpus

An efficient mixed variational reduced‐order model formulation for nonlinear analyses of elastic shells (2018, methodology): “Consideration of the orthogonality constraints (8) to (10) allows to express Equations 12 to 14 in terms of 2 augmented systems of linear equations: [ K −F −FT 0 ] [ uα lα ] = [ 0 − eα ]”