Mixed Finite Element Models for Free Vibrations of Thin-Walled Beams.

Abstract

Simple, mixed finite element models are developed for the free-vibration analysis of curved, thin-walled beams with arbitrary open cross section. The analytical formulation is based on a linear, Vlasov-type, thin-walled beam theory with the effects of flexural-torsional coupling, transverse shear deformation, and rotary inertia included. The fundamental unknowns consist of seven internal forces and seven generalized displacements of the beam. The element characteristic arrays are obtained by using a modified form of the Hellinger-Reissner mixed variational principle. Only C continuity is required for the generalized displacements. The internal forces and the Lagrange multiplier are allowed to be discontinuous at interelement boundaries. Numerical results are presented to demonstrate the high accuracy and effectiveness of the elements developed. The standard of comparison is taken to be the solutions obtained by using two-dimensional plate/shell models for the beams.

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1989
Accession Number
ADA310573

Entities

People

  • Ahmed K. Noor
  • Byung-jin Min
  • Jeanne M. Peters

Organizations

  • Langley Research Center

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Accuracy
  • Applied Mechanics
  • Boundaries
  • Boundary Value Problems
  • Cantilever Beams
  • Continuity
  • Coordinate Systems
  • Equations
  • Finite Element Analysis
  • Frequency
  • Mechanics
  • Modulus Of Elasticity
  • Shape
  • Shear Modulus
  • Shear Stresses
  • Two Dimensional
  • Variational Principles

Fields of Study

  • Engineering
  • Physics

Readers

  • Control Systems Engineering.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Mechanical Engineering/Mechanics of Materials.