
Accession Number : AD0748086
Title : Application of the Finite Element Method to Nonconservative Stability Problems with Damping.
Descriptive Note : Technical rept.,
Corporate Author : WATERVLIET ARSENAL N Y
Personal Author(s) : Wu,Julian J.
Report Date : AUG 1972
Pagination or Media Count : 30
Abstract : The method of finite elements in conjunction with an adjoint variational principle is applied to nonconservative problems in the theory of elastic stability. The effects of internal and external damping are included by assuming a KelvinVoigt material and a dissipative force proportional to the velocity, respectively. Because boundary value problems in the theory of nonconservative elastic stability are nonselfadjoint, by virtue of the fact that nonconservative forces do not possess potentials, no complete functional exists for the classical form of Hamilton's principle. A boundary value problem that is the adjoint of the original problem is introduced, and in terms of the original and adjoint variables a complete functional is derived for an extended or generalized version of Hamilton's principle. This principle contains generalized expressions for the kinetic, potential, and dissipation energies that are bilinear forms in the original and adjoint variables. A CANTILEVERED BEAM SUBJECTED TO A CONCENTRATED FOLLOWER'S FORCE WITH DAMPING EFFECTS IS ANALYZED. The finite element formulation emanates from this generalized version of Hamilton's principle. The beam is divided into several segments (elements). The displacement function in each element is approximated by a cubic polynomial for both theoriginal and the adjoint problems, with the coefficinets to be determined. These approximate expressions are used in the complete functional of the generalized Hamilton's principle. When the boundary and continuity conditions are imposed on the displacement functions, this principle leads to a eigenvalue matrix equation. (Author, modifiedPL)
Descriptors : (*CANTILEVER BEAMS, VIBRATION), (*VIBRATION, EQUATIONS OF MOTION), ELASTIC PROPERTIES, STABILITY, DAMPING, NUMERICAL ANALYSIS, PARTIAL DIFFERENTIAL EQUATIONS, BOUNDARY VALUE PROBLEMS, MATRICES(MATHEMATICS)
Subject Categories : Structural Engineering and Building Technology
Mechanics
Distribution Statement : APPROVED FOR PUBLIC RELEASE