Free and forced vibrations of a segmented bar by a Meshless Local Petrov-Galerkin (MLPG) formulation

R. C. Batra, M. Porfiri, D. Spinello

Research output: Contribution to journalArticlepeer-review


We use the meshless local Bubnov-Galerkin (MLPG6) formulation to analyze free and forced vibrations of a segmented bar. Three different techniques are employed to satisfy the continuity of the axial stress at the interface between two materials: Lagrange multipliers, jump functions, and modified moving least square basis functions with discontinuous derivatives. The essential boundary conditions are satisfied in all cases by the method of Lagrange multipliers. The related mixed semidiscrete formulations are shown to be stable, and optimal in the sense that the ellipticity and the inf-sup (Babuška-Brezzi) conditions are satisfied. Numerical results obtained for a bimaterial bar are compared with those from the analytical, and the finite element methods. The monotonic convergence of first two natural frequencies, first three mode shapes, and a static solution in the L 2, and H 1 norms is shown. The relative error in the numerical solution for a transient problem is also very small.

Original languageEnglish (US)
Pages (from-to)473-491
Number of pages19
JournalComputational Mechanics
Issue number4
StatePublished - Mar 2008


  • Convergence analysis
  • Inf-sup condition
  • MLPG method
  • Material discontinuities
  • Segmented bar

ASJC Scopus subject areas

  • Computational Mechanics
  • Ocean Engineering
  • Mechanical Engineering
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics


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