Finite Elements for Mindlin and Kirchhoff Plates Based on a Mixed Variational Principle

2021 ◽  
Author(s):  
Ziad M. Elias
Keyword(s):  
Variational Principle ◽  
Finite Elements ◽  
Kirchhoff Plates ◽  
Mixed Variational Principle

Modified Mixed Variational Principle and the State-Vector Equation for Elastic Bodies and Shells of Revolution

1992 ◽  
Vol 59 (3) ◽  
pp. 587-595 ◽  
Author(s):  
Charles R. Steele ◽  
Yoon Young Kim
Keyword(s):  
Variational Principle ◽  
Equations Of State ◽  
Classical Mechanics ◽  
Three Dimensional ◽  
Shells Of Revolution ◽  
Elastic Bodies ◽  
Mixed Variational Principle ◽  
Stress Components ◽  
Independent Variable ◽  
Nonsymmetric Deformation

A modified mixed variational principle is established for a class of problems with one spatial variable as the independent variable. The specific applications are on the three-dimensional deformation of elastic bodies and the nonsymmetric deformation of shells of revolution. The possibly novel feature is the elimination in the variational formulation of the stress components which cannot be prescribed on the boundaries. The result is a form exactly analogous to classical mechanics of a dynamic system, with the equations of state exactly in the form of the canonical equations of Hamilton. With the present approach, the correct scale factors of the field variables to make the system self-adjoint are readily identified, and anisotropic materials including composites can be handled effectively. The analysis for shells of revolution is given with and without the transverse shear deformation considered.

A mixed variational principle for the Föppl–von Kármán equations

2020 ◽  
Vol 79 ◽  
pp. 381-391 ◽  
Author(s):  
Matteo Brunetti ◽  
Antonino Favata ◽  
Achille Paolone ◽  
Stefano Vidoli
Keyword(s):  
Variational Principle ◽  
Mixed Variational Principle ◽  
Von Karman ◽  
Von Kármán Equations ◽  
Von Kármán
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