Numerical solution of a piezoelectric contact problem
Keywords:
Piezoelectricity, Electrical contact, Finite element, Penalty method, Numerical simulationsAbstract
We consider a mathematical model, which describes a contact problem between a piezoelectric body and a conductive foundation. The linear electro-elastic constitutive law is employed to model the piezoelectric material. The process is static, the contact is frictionless and described with the normal compliance condition and an electric contact condition. Our aim is to present a detailed description of the numerical modelling of the problem. To this end, we introduce a discrete scheme, based on the finite element method to approximate the spatial variable. Then we treat the contact conditions by using a penalized approach and a version of Newton's method. Finally, we provide numerical simulations in the study of a two-dimensional example and compare the regularized problem with the original one.
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