Etude d'un problème de contact quasistatique avec réponse normale instantanée

Abstract

یه 􀀄􀀁 مل 􀀴 ل􀀇􀀵 روس و 􀀊􀀃 ال 􀀶 لام 􀀟 ي لل 􀀸􀀐 ان 􀀸􀀐􀀃 ذج ال 􀀲􀀃􀀻 ال 􀀏􀀐􀀵􀀇􀀟 اني ل 􀀼 الأول وال 􀀨􀀐 ل􀀢 الف 􀀿􀀐􀀢􀁀 ت 􀀦 ل. ت 􀀲􀀢 ثلاثة ف 􀀨 وحة م 􀀏􀁃 ن الأ 􀀲􀀫􀀟 ت ار مع 􀁍􀀟 مع اع 􀀏􀁍􀀟 ع􀁎 ة. 􀀻 ه ساك 􀁍 اس ش 􀀃 ألة ت 􀀙 ا رسة م 􀀊 ل 􀀿􀀢􀁀 م 􀁅 ال 􀀼 ل ال 􀀢 ة. الف 􀀏 اك 􀀇 ة اللازمة في ال 􀀐 اض 􀀗􀀏 الأدوات ال 􀁋 ع􀁌 ة 􀀐 ف􀀐􀁖􀀲 ل ال 􀀐 ل􀁔􀀟 ات ال 􀀐􀀻 ام تق 􀀊􀁀􀀟 اس 􀁌 ده 􀀏 ف وتف 􀀐 د حل ضع 􀀲 ة وج 􀁒􀀐􀀟 ا على ن 􀀻 ل􀀢 ألة، ح 􀀙􀀃 ه ال 􀀇 ة له 􀁍􀀙􀀻 ال 􀁌 ة. 􀀐􀁓􀁔 ة ل 􀁎 ة عاد 􀁌 ا􀁒􀀟 اس قارب. 􀀟 ا ال 􀀇 ا ه 􀀻􀀟􀁍 ة وأث 􀀐 ائ 􀀊􀀟 الاب 􀁝 و􀀏􀀳 ال 􀀏􀀐􀀐 تغ 􀀊􀀻 ل ع 􀁔 ا تقارب ال 􀀻 ، درس 􀀏اً 􀀐 ة. أخ 􀀏􀀐 غ􀀟􀀃The aim of this memory is a variational study of a boundary problem describing the contact with friction between a deformable body and a foundation. The thesis is structured in three chapters. The first and the second chapters are devoted to reminding the mechanical model of contact studied as well as some mathematical tools necessary in the memory. The third chapter is intended for the study of a quasi-static contact problem. The contact law considered is a contact law with instantaneous normal response. For this problem, we obtained a result of existence and uniqueness of a weak solution using functional and variational analysis techniques. Finally, we study the continuous dependence of the solution with the initial data and we prove convergence results.