如何在板中创建横截面？

Question

我想在板内创建如下这样的横截面？

希望有人能帮忙。

这就是我现在所拥有的：

\documentclass[tikz]{standalone}

\begin{document}
    \begin{tikzpicture}
        
        % left part
        \draw (0,0) arc (270:90:0.5 and 1.5);% left half of the left ellipse
        \draw[dashed] (0,0) arc (-90:90:0.5 and 1.5);% half circle facing left
        
        % middle part
        \draw[dashed] (1.5,0) arc (-90:90:0.5 and 1.5);% half circle facing left
        \draw(1.5,0) arc (-90:90:-0.5 and 1.5);% 

        \draw (0,0) -- (4,0);% bottom line
        \draw (0,3) -- (4,3);% top line
        
        \draw (4,1.5) ellipse (0.5 and 1.5);% a circle / the right ellipse
        \draw (1.6,1.5) node {$A_{x}$};
        \draw (-1.25,1.5) node {$\sigma$};
        
        % x ticks
        \draw (-0.5,-0.6) -- (4.5,-0.6);% x line
        \draw (0,-1) node {$a$};
        \draw (1.6,-1) node {$x$};
        \draw (4,-1) node {$b$};
        \draw (0,-0.8) -- (0,-0.5);% connector to a
        \draw (4,-0.8) -- (4,-0.5);% connector to b
        \draw[dashed] (1.6,-0.6) -- (1.6,0);% x line
        
    \end{tikzpicture}
\end{document}

谢谢