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تسجيل مستخدم جديدنهج المجال الخيالي المبني على XFEM لنموذج الالتزام الخطي المتضخم مع الشق
XFEM based fictitious domain method for linear elasticity model with crack
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تقليل تكلفة الحلول الحسابية هو القضية الرئيسية لحل مشكلات التعرف على الشقوق أو الانتشار الشقوق. واحدة من الحلول هي تجنب إعادة الشبكة للنطاق عند تغيير موضع الشق أو عند تمديد الشق. لتجنب إعادة الشبكة، نقترح طريقة العنصر المحدد الخيالي للمحاكاة الرقمية للانقسامات التي تنتجها الشقوق داخل الوسائل المرنة. يستند الأسلوب إلى طريقة النطاق الخيالي الأصلية التي تم تطويرها لشروط ديريشلت لمشكلة بوسون ولمشكلة ستوكس، والتي تم تكيفها مع شروط الحدود النويمان لمشكلات الشقوق. يمثل الشق بواسطة وظائف المستوى. وتم إجراء اختبارات رقمية باستخدام تركيب مختلط للتأكيد على دقة الأسلوب، فضلاً عن ثباته مع الهندسة التي تفرضها تقنية الاستقرار. وتم إثبات شرط التحقق من الأقل من الأعلى لذلك نظرياً. وتم إعطاء تجربة واقعية مع شقة مضغوطة متساوية في الداخل من بركان لإظهار قابلية الأسلوب للتطبيق.
Reduction of computational cost of solutions is a key issue to crack identification or crack propagation problems. One of the solution is to avoid re-meshing the domain when the crack position changes or when the crack extends. To avoid re-meshing, we propose a new finite element approach for the numerical simulation of discontinuities of displacements generated by cracks inside elastic media. The approach is based on a fictitious domain method originally developed for Dirichlet conditions for the Poisson problem and for the Stokes problem, which is adapted to the Neumann boundary conditions of crack problems. The crack is represented by level-set functions. Numerical tests are made with a mixed formulation to emphasize the accuracy of the method, as well as its robustness with respect to the geometry enforced by a stabilization technique. In particular an inf-sup condition is theoretically proven for the latter. A realistic simulation with a uniformly pressurized fracture inside a volcano is given for illustrating the applicability of the method.
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