1.4 Cas statique

Le cas statique pour la poutre

L’équation statique (indépendance vis-à-vis du temps) est (on considère trois types de conditions aux limites):

\[ \boxed {\begin{array}{l}\hbox{ L'équation de la poutre:}D\displaystyle \frac{\partial ^4 u}{\partial x^4}=F,0{<}x{<}L,\\ \hbox{CL1:}u(0)=\displaystyle \frac{\partial u}{\partial x}(0)=u(L)=\displaystyle \frac{\partial u}{\partial x}(L)=0,\hbox{ double encastrement},\\ \hbox{ CL2:}u(0)=\displaystyle \frac{\partial u}{\partial x}(0)=0\hbox{ et }\displaystyle \frac{\partial ^2 u}{\partial x^2}(L)=\displaystyle \frac{\partial ^3u}{\partial x^3 }(L)=0\hbox{ encastrée-libre},\\ \hbox{CL3:}u(0)=\displaystyle \frac{\partial ^2 u}{\partial x^2}(0)=u(L)=\displaystyle \frac{\partial ^2 u}{\partial x^2}(L)=0\hbox{ appuis simples}.\end{array}} \]