On the dual formulation of boundary value problems in nonlinear elastostatics

DOI10.1016/0020-7225(82)90048-9zbMath0489.73016OpenAlexW1971501893MaRDI QIDQ1166957

Franz K. Labisch

Publication date: 1982

Published in: International Journal of Engineering Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0020-7225(82)90048-9

zbMATH Keywords

energy methodboundary value problemsnonlinear elastostaticsequivalent normseminormboundary conditions independent of deformationcase of body forcescase of locally convex displacement energydual description in terms of displacement gradientelastic statesenergy-normlike estimatesfirst Piola-Kirchhoff stress tensorlocally nonconvex displacement energy

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Dynamical problems in solid mechanics (74H99) Elastic materials (74B99) Miscellaneous applications of functional analysis (46N99)

Cites Work

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• On stability and uniqueness in finite elasticity
• Error bounds in nonlinear elastostatics
• On the failure of ellipticity of the equations for finite elastostatic plane strain
• Convexity conditions and existence theorems in nonlinear elasticity
• Dual extremum principles and error bounds in nonlinear elasticity theory
• Theorems on existence, uniqueness, and stability of the solution of the place boundary-value problem, in statics, for hyperelastic materials
• Structure of the set of stationary solutions of the navier‐stokes equations
• Inequalities associated with the inversion of elastic stress-deformation relations and their implications
• Equivalent Norms for Sobolev Spaces

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