On a generalization of the lower bound theorem for elastic rods and plates subjected to compressive follower forces

DOI10.1016/0045-7825(81)90170-5zbMath0506.73049OpenAlexW2016361389MaRDI QIDQ1837018

H. H. E. Leipholz

Publication date: 1981

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0045-7825(81)90170-5

zbMATH Keywords

follower forcesSobolev's embedding theorembuckling load bound to stabilityinternal energy bounded below in timenonconservative problemsSobolev norm of deflection

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Plates (74K20) Stability of dynamical problems in solid mechanics (74H55) Bifurcation and buckling (74G60) Stability of solutions to ordinary differential equations (34D20)

Related Items

On the stability of elastic structures subjected to follower forces, Nonlinear finite element analysis of elastic systems under nonconservative loading - natural formulation. Part I. Quasistatic problems, On the stability of rectangular, completely supported plates with uncoupling boundary conditions subjected to uniformly distributed follower forces, The Lyapunov-Movchan method in problems of the stability of flows and deformation processes

Cites Work

• On a special case of Friedrich's inequality
• On a lower bound theorem for the buckling load of elastic beams subjected to nonconservative, compressive follower loads
• On Movchan's theorems for stability of continuous systems
• On a stability theory of non-selfadjoint mechanical systems
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