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Beam element matrices derived from Vlasov's theory of open thin‐walled elastic beams
Author(s) -
Friberg P. O.
Publication year - 1985
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620210704
Subject(s) - stiffness matrix , eigenvalues and eigenvectors , mathematical analysis , direct stiffness method , mathematics , stiffness , image warping , finite element method , mass matrix , beam (structure) , algebraic equation , matrix (chemical analysis) , classical mechanics , physics , nonlinear system , computer science , materials science , optics , quantum mechanics , artificial intelligence , nuclear physics , neutrino , composite material , thermodynamics
A uniform beam element of open thin‐walled cross‐section is studied under stationary harmonic end excitation. An exact dynamic (transcendentally frequency‐dependent) 14 × 14 element stiffness matrix is derived from Vlasov's coupled differential equations. Special attention is paid to the computational problems arising when coefficients vanish in these equations because of symmetric cross‐section, zero warping stiffness, etc. The dynamic element stiffness matrix is established via a generalized linear eigenvalue problem and a system of linear algebraic equations with complex matrices. A static stiffness matrix is also derived and the associated consistent mass and geometric stiffness matrices are given. Modal masses are evaluated. A FORTRAN program and a numerical example are included.