A point interpolation mesh free method for static and frequency analysis of two-dimensional piezoelectric structures |
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Authors: | G R Liu K Y Dai K M Lim Y T Gu |
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Affiliation: | (1) Center for Advanced Computations in Engineering Science, Department of Mechanical Engineering, The National University of Singapore, 10 Kent Ridge Crescent, Singapore, 119260 e-mail: mpeliugr@nus.edu.sg, SG |
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Abstract: | A mesh free method called point interpolation method (PIM) is presented for static and mode-frequency analysis of two-dimensional
piezoelectric structures. In the present method, the problem domain and its boundaries are represented by a set of properly
scattered nodes. The displacements and the electric potential of a point are interpolated by the values of nodes in its local
support domain using shape functions derived based on a point interpolation scheme. Techniques are discussed to surmount the
singularity of the moment matrix. Variational principle together with linear constitutive piezoelectric equations is used
to establish a set of system equations for arbitrary-shaped piezoelectric structures. These equations are assembled for all
quadrature points and solved for displacements and electric potentials. A polynomial PIM program has been developed in MATLAB
with matrix triangularization algorithm (MTA), which automatically performs a proper node enclosure and a proper basis selection.
Examples are also presented to demonstrate the accuracy and stability of the present method and their results are compared
with the conventional FEM results from ABAQUS as well as the analytical or experimental ones.
Received: 6 February 2002 / Accepted: 5 August 2002 |
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Keywords: | Mesh free methods Piezoelectric structures |
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