المشاكل الرياضية في نمذجة المواد المركبة الحقيقية
Abstract
يعتمد تشكيل النماذج الرياضية الحاسوبية على طريقة التجانس المؤلفة من أربع معادلات تفاضلية ذات معاملات دورية. يعالج القسم الأول من هذا البحث المشكلات المرتبطة بصياغة نماذج المادة المركبة الحقيقية، حيث يتم حل المسألة ذات القيم غير المؤكدة للمعاملات، بوساطة طريقة الحل الموثوقة المسماة طريقة السيناريو الأسوأ.
جدير بالذكر أن بنية المادة المركبة الحقيقية ليست دورية تماماً (أي ليست متكررة بشكل منتظم)، يدرس القسم الثاني من البحث الخطأ الناتج من افتراض الحالة الدورية في حالة لا دورية.
Numerical modelling of composite uses homogenization method developed for differential equations with periodic coefficients. The contribution deals with tow problems connected with modelling of real composite material. The problem of uncertain values of the coefficients is solved by means of method of reliable solution called also the worst scenario method. Structure of the real composite material is not exactly periodic. Error caused by assuming periodicity in non-periodic case is studied in second part
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