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Shape optimization of piezoelectric devices using an enriched meshfree method
Author(s) -
Liu C. W.,
Taciroglu E.
Publication year - 2008
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2479
Subject(s) - shape optimization , sensitivity (control systems) , kernel (algebra) , piezoelectricity , meshfree methods , mathematical optimization , sequential quadratic programming , mathematics , basis function , quadratic programming , computer science , mathematical analysis , finite element method , structural engineering , physics , engineering , acoustics , electronic engineering , combinatorics
We present an enriched reproducing kernel particle method for shape sensitivity analysis and shape optimization of two‐dimensional electromechanical domains. This meshfree method incorporates enrichment functions for better representation of discontinuous electromechanical fields across internal boundaries. We use cubic splines for delineating the geometry of internal/external domain boundaries; and the nodal coordinates and slopes of these splines at their control points become the design parameters. This approach enables smooth manipulations of bi‐material interfaces and external boundaries during the optimization process. It also enables the calculation of displacement and electric‐potential field sensitivities with respect to the design parameters through direct differentiation, for which we adopt the classical material derivative approach. We verify this implementation of sensitivity calculations against an exact solution to a variant of Lamé's problem, and also, finite‐difference approximations. We follow a sequential quadratic programming approach to minimize the cost function; and demonstrate the utility of the overall technique through a model problem that involves the shape optimization of a piezoelectric fan. Copyright © 2008 John Wiley & Sons, Ltd.