A meshless Hermite weighted least-square method for piezoelectric structures. (English) Zbl 1508.78015
Summary: In this paper, a meshless Hermite weighted least-square method is developed to improve the accuracy and stability of the numerical analysis for piezoelectric structures. The basic equations of the piezoelectric structures including the constitutive equation, geometric equations, equilibrium equations and boundary conditions are introduced. The approximate function of the Hermite weighted least-square method is constructed through the Hermite approximation method and weighted least-square method. The collocation method is utilized to derive the discrete equation of the Hermite weighted least-square method for the piezoelectric structures. Furthermore, the influences of the scale parameter and node number on the calculation accuracy of the present method are discussed, and the effectiveness of the present method for analyzing the piezoelectric structures is demonstrated by some numerical examples. The numerical results show that the Hermite weighted least-square method can effectively analyze the piezoelectric structures with various boundary conditions, and has excellent convergence and calculation accuracy.
MSC:
| 78M22 | Spectral, collocation and related methods applied to problems in optics and electromagnetic theory |
| 65N35 | Spectral, collocation and related methods for boundary value problems involving PDEs |
| 74F15 | Electromagnetic effects in solid mechanics |
Keywords:
meshless method; Hermite weighted least-square method; collocation method; piezoelectric structures; electromechanical coupling problemsReferences:
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