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

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.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Engineering Science and Mechanics

Department dc:contributor.department

Engineering Science and Mechanics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2006

Author dc:creator

• Porfiri, Maurizio

Chair dc:contributor.committeechair

• Batra, Romesh C.

Committee members dc:contributor.committeemember

• Lindner, Douglas K.
• Librescu, Liviu
• Hyer, Michael W.
• Henneke, Edmund G. II

• Rubberlike Materials
• Discontinuities
• Vibrations
• MEMS
• MLPG method

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

etd-04282006-102241

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/27420