Title page for ETD etd-04282006-102241

Type of Document Dissertation
Author Porfiri, Maurizio
Author's Email Address mporfiri@vt.edu
URN etd-04282006-102241
Title Analysis by Meshless Local Petrov-Galerkin Method of Material Discontinuities, Pull-in Instability in MEMS, Vibrations of Cracked Beams, and Finite Deformations of Rubberlike Materials
Degree PhD
Department Engineering Science and Mechanics
Advisory Committee
Advisor Name Title
Batra, Romesh C. Committee Chair
Henneke, Edmund G. II Committee Member
Hyer, Michael W. Committee Member
Librescu, Liviu Committee Member
Lindner, Douglas K. Committee Member
  • Rubberlike Materials
  • Discontinuities
  • Vibrations
  • MEMS
  • MLPG method
Date of Defense 2006-04-27
Availability unrestricted
The Meshless Local Petrov-Galerkin (MLPG) method has been employed to analyze the following linear and nonlinear solid mechanics problems: free and forced vibrations of a segmented bar and a cracked beam, pull-in instability of an electrostatically actuated microbeam, and plane strain deformations of incompressible hyperelastic materials. The Moving Least Squares (MLS) approximation is used to generate basis functions for the trial solution, and for the test functions. Local symmetric weak formulations are derived, and the displacement boundary conditions are enforced by the method of Lagrange multipliers. Three different techniques are employed to enforce continuity conditions at the material interfaces: Lagrange multipliers, jump functions, and MLS basis functions with discontinuous derivatives. For the electromechanical problem, the pull-in voltage and the corresponding deflection are extracted by combining the MLPG method with the displacement iteration pull-in extraction algorithm. The analysis of large deformations of incompressible hyperelastic materials is performed by using a mixed pressure-displacement formulation. For every problem studied, computed results are found to compare well with those obtained either analytically or by the Finite Element Method (FEM). For the same accuracy, the MLPG method requires fewer nodes but more CPU time than the FEM.
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