Open AccessAnalytical methods of theoretical physics in the modeling of building structures
Author(s) -
Aleksandr Gulkanov,
Konstantin Modestov
Publication year - 2019
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1425/1/012180
Subject(s) - mathematics , calculus of variations , lagrange multiplier , classical mechanics , formalism (music) , partial differential equation , differential equation , deflection (physics) , timoshenko beam theory , variational principle , mathematical analysis , physics , beam (structure) , mathematical optimization , art , musical , optics , visual arts
In this paper, on the basis of the variational principle of the least Hamilton action, the field-theoretic Lagrange equations of the 2nd kind are derived in the presence of a dependence of the density of the Lagrange function on the higher derivatives. On the basis of the obtained equations, written in terms of variables that most fully reflect hypotheses and used assumptions, the equations of continuum mechanics are obtained and the Timoshenko, Rayleigh and Euler-Bernoulli beam models are calculated. It is shown that the method used leads to a more efficient method of obtaining partial differential equations describing the dynamics of deflection of beams. The possibility of taking into account the distributed load and the elastic base in the Lagrangian formalism is noted. The possibility of further development of analytical and theoretical-physical methods in application to mathematical modeling of building structures is analyzed.