Metoda homogenizace pro kompozitní materiály

Abstract

This thesis deals with composite materials and their mathematical transfer to homogenic material with same nature. Is exemined, how composite material is composed, to be seen as homogenic material. Problem is transform to boundary value problem of heat conduction equation in 1D on interval $\left<0,1\right>$. Specifically is solved periodical problem, specified with second order differential equation $-\big(a(x) \cdot u'(x)\big)'=f(x)$ with appropriate boundry value. Solution is obtained by finite element method and asymptotic expansion and is compared with limit solution. There are looked for instances, when composit is seen as homogenic matherial.