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Forward and inverse problems in piezoelectricity using isogeometric symmetric Galerkin boundary element method and level set method. (English) Zbl 07173365
Summary: This work presents the method to combine isogeometric analysis coupled to symmetric Galerkin boundary element method (IGA-SGBEM) and parametric level set (PaLS)-based optimization scheme for the analysis of linear problems in two-dimensional piezoelectric media. IGA-SGBEM is used to obtain field variables (i.e. generalized displacement and traction) in the forward analysis. Then, inverse analysis of flaw detection in piezoelectric structures is attempted by combining IGA-SGBEM with PaLS-based optimization scheme. In this proposed method, the versatility of isogeometric analysis (IGA) is proved in the inverse progress, where the iso-line of the level set function can be easily reconstructed and incorporated into the IGA framework. Numerical examples are examined to validate and to demonstrate the robustness of the proposed method in solving both forward and inverse problems in piezoelectricity.
MSC:
74S15 Boundary element methods applied to problems in solid mechanics
74F15 Electromagnetic effects in solid mechanics
65N38 Boundary element methods for boundary value problems involving PDEs
Software:
MCS
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