کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4632549 | 1340648 | 2009 | 14 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Solvability of a dynamic contact problem between a piezoelectric body and a conductive foundation
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کلمات کلیدی
Normal compliance - انطباق عادیMonotone operator - اپراتور مونوتونFrictionless contact - تماس بدون اصطکاکWeak solution - جواب ضعیف، راه حل ضعیفFinite element method - روش اجزاء محدودPenalization method - روش مجازاتNewton method - روش نیوتنNumerical simulations - شبیه سازی عددیPiezoelectric material - مواد پیزوالکتریکFixed point - نقطه ثابت
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Solvability of a dynamic contact problem between a piezoelectric body and a conductive foundation Solvability of a dynamic contact problem between a piezoelectric body and a conductive foundation](/preview/png/4632549.png)
چکیده انگلیسی
We consider a mathematical model which describes the dynamic process of contact between a piezoelectric body and an electrically conductive foundation. We model the material's behavior with a nonlinear electro-viscoelastic constitutive law; the contact is frictionless and is described with the normal compliance condition and a regularized electrical conductivity condition. We derive a variational formulation for the problem and then, under a smallness assumption on the data, we prove the existence of a unique weak solution to the model. We also investigate the behavior of the solution with respect the electric data on the contact surface and prove a continuous dependence result. Then, we introduce a fully discrete scheme, based on the finite element method to approximate the spatial variable and the backward Euler scheme to discretize the time derivatives. We treat the contact by using a penalized approach and a version of Newton's method. We implement this scheme in a numerical code and, in order to verify its accuracy, we present numerical simulations in the study of two-dimensional test problems. These simulations provide a numerical validation of our continuous dependence result and illustrate the effects of the conductivity of the foundation, as well.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematics and Computation - Volume 215, Issue 8, 15 December 2009, Pages 2978-2991
Journal: Applied Mathematics and Computation - Volume 215, Issue 8, 15 December 2009, Pages 2978-2991
نویسندگان
Mikael Barboteu, Mircea Sofonea,