Variational principles for nonlinear Kirchhoff rods
Sign Up to like & getrecommendations! Published in 2019 at "Acta Mechanica"
DOI: 10.1007/s00707-019-02562-0
Abstract: The present article studies variational principles for the formulation of static and dynamic problems involving Kirchhoff rods in a fully nonlinear setting. These results, some of them new, others scattered in the literature, are presented… read more here.
Keywords: variational principles; principles nonlinear; geometry; kirchhoff rods ... See more keywords
Generalized variational principles for buckling analysis of circular cylinders
Sign Up to like & getrecommendations! Published in 2019 at "Acta Mechanica"
DOI: 10.1007/s00707-019-02569-7
Abstract: A generalized variational principle and a parameterized generalized variational principle are obtained for large deformation analysis of circular cylinders by the semi-inverse method; all known variational principles in the literature are special cases of the… read more here.
Keywords: variational principles; generalized variational; variational principle; circular cylinders ... See more keywords
Variational principles for conformal geodesics
Sign Up to like & getrecommendations! Published in 2021 at "Letters in Mathematical Physics"
DOI: 10.1007/s11005-021-01469-z
Abstract: Conformal geodesics are solutions to a system of third-order equations, which makes a Lagrangian formulation problematic. We show how enlarging the class of allowed variations leads to a variational formulation for this system with a… read more here.
Keywords: conformal geodesics; order; system; variational principles ... See more keywords
Variational principles on topological spaces
Sign Up to like & getrecommendations! Published in 2019 at "Optimization"
DOI: 10.1080/02331934.2019.1671384
Abstract: To the best of our knowledge, all the existing variational principles were established in the framework of a complete metric space or a Banach space. In this paper, we consider variational principles in topological spaces.… read more here.
Keywords: topological spaces; principles topological; space; variational principles ... See more keywords
A review of the variational methods for solving DC circuits
Sign Up to like & getrecommendations! Published in 2019 at "European Journal of Physics"
DOI: 10.1088/1361-6404/ab0525
Abstract: Direct current (DC) circuits are usually taught in upper-level physics curricula, and Kirchhoff's laws are stated and used to solve the steady-state currents. However, students are not often introduced to alternative techniques, such as variational… read more here.
Keywords: review variational; variational principles; thermodynamics; variational methods ... See more keywords
Variational principles for ideal MHD of steady incompressible flows via Lie-point symmetries with application to the magnetic structures of bipolar sunspots
Sign Up to like & getrecommendations! Published in 2020 at "European Physical Journal Plus"
DOI: 10.1140/epjp/s13360-020-00598-z
Abstract: In this paper, Lie-point symmetries and conservation laws for the generalized Grad–Shafranov equation (GGSE) for symmetric magnetohydrodynamic (MHD) fluids with steady, inhomogeneous, incompressible flows are derived. The adjointness of that equation is discussed via a… read more here.
Keywords: variational principles; via lie; incompressible flows; point symmetries ... See more keywords
On variational principles in coupled strain-gradient elasticity
Sign Up to like & getrecommendations! Published in 2022 at "Mathematics and Mechanics of Solids"
DOI: 10.1177/10812865221081854
Abstract: Strain-gradient elasticity is a special case of high-gradient theories in which the potential energy density depends on the first and second gradient of the displacement field. The presence of a coupling term in the material… read more here.
Keywords: coupled strain; elasticity; strain gradient; energy ... See more keywords