How to make a structured mesh with a hole and extrude it

Update: New version of FEMAddOns v1.4.2 includes ExtrudeMesh

@user21 updated FEMAddOns and ExtrudeMesh is included. Now, you only need to call FEMAddOns and don't need to worry about namespace collisions with MeshTools. For completeness, here is the updated workflow to get the latest version of FEMAddOns and extend Alex's answer by two lines:

ResourceFunction["FEMAddOnsInstall"][]
Needs["FEMAddOns`"]
(* From Alex Trounev's Answer *)
Lx = 100;
Ly = 50; r[t_] := 
 Piecewise[{{Lx/Cos[t], 0 <= t <= ArcTan[Ly/Lx]}, {Ly/Sin[t], 
    ArcTan[Ly/Lx] < t <= Pi - ArcTan[Ly/Lx]}, {-Lx/Cos[t], 
    Pi - ArcTan[Ly/Lx] < t <= Pi + ArcTan[Ly/Lx]}, {-Ly/Sin[t], 
    Pi + ArcTan[Ly/Lx] < t <= 2 Pi - ArcTan[Ly/Lx]}, {Lx/Cos[t], 
    2 Pi - ArcTan[Ly/Lx] < t <= 2 Pi}}]; pts1 = 
 Table[r[θ] {Cos[θ], Sin[θ]} // N, {θ, 0, 
   2 π, 2 Pi/360}]; pts2 = 
 Table[10. {Cos[θ], Sin[θ]} // N, {θ, 0, 2 π,
    2 Pi/360}];
mesh2D = StructuredMesh[{pts1, pts2}, {96, 16}];
mesh2D["Wireframe"]
(* Extrude the mesh *)
mesh3D = ExtrudeMesh[mesh2D, 40, 6];
mesh3D["Wireframe"]

Original Answer

This is an extension of Alex Trounev's answer because I found a potential version problem with FEMAddOns package. Perhaps someone can confirm.

If you download the latest version (v1.4.0) of FEMAddOns, you will see that ExtrudeMesh appears to be missing.

ResourceFunction["FEMAddOnsInstall"][]
Needs["FEMAddOns`"]
SystemOpen["paclet:FEMAddOns/guide/FEMAddOns"]

A potential workaround is to download MeshTools directly as shown in the following:

ClearAll["Global`*"]
ResourceFunction["GitHubInstall"]["c3m-labs", "MeshTools"]
Needs["MeshTools`"]
(* From Alex Trounev's Answer *)
Lx = 100;
Ly = 50; r[t_] := 
 Piecewise[{{Lx/Cos[t], 0 <= t <= ArcTan[Ly/Lx]}, {Ly/Sin[t], 
    ArcTan[Ly/Lx] < t <= Pi - ArcTan[Ly/Lx]}, {-Lx/Cos[t], 
    Pi - ArcTan[Ly/Lx] < t <= Pi + ArcTan[Ly/Lx]}, {-Ly/Sin[t], 
    Pi + ArcTan[Ly/Lx] < t <= 2 Pi - ArcTan[Ly/Lx]}, {Lx/Cos[t], 
    2 Pi - ArcTan[Ly/Lx] < t <= 2 Pi}}]; pts1 = 
 Table[r[θ] {Cos[θ], Sin[θ]} // N, {θ, 0, 
   2 π, 2 Pi/360}]; pts2 = 
 Table[10. {Cos[θ], Sin[θ]} // N, {θ, 0, 2 π,
    2 Pi/360}];
mesh2D = StructuredMesh[{pts1, pts2}, {96, 16}];
mesh2D["Wireframe"]
(* Extrude the mesh *)
mesh3D = ExtrudeMesh[mesh2D, 40, 6];
mesh3D["Wireframe"]

We can play with numbers to get an ideal mesh. As a stating point you could use this one:

Needs["MeshTools`"](*Needs["FEMAddOns`"]*)
Lx = 100;
Ly = 50; r[t_] := 
 Piecewise[{{Lx/Cos[t], 0 <= t <= ArcTan[Ly/Lx]}, {Ly/Sin[t], 
    ArcTan[Ly/Lx] < t <= Pi - ArcTan[Ly/Lx]}, {-Lx/Cos[t], 
    Pi - ArcTan[Ly/Lx] < t <= Pi + ArcTan[Ly/Lx]}, {-Ly/Sin[t], 
    Pi + ArcTan[Ly/Lx] < t <= 2 Pi - ArcTan[Ly/Lx]}, {Lx/Cos[t], 
    2 Pi - ArcTan[Ly/Lx] < t <= 2 Pi}}]; pts1 = 
 Table[r[\[Theta]] {Cos[\[Theta]], Sin[\[Theta]]} // N, {\[Theta], 0, 
   2 \[Pi], 2 Pi/360}]; pts2 = 
 Table[10. {Cos[\[Theta]], Sin[\[Theta]]} // N, {\[Theta], 0, 2 \[Pi],
    2 Pi/360}];
mesh = StructuredMesh[{pts1, pts2}, {96, 16}];
mesh["Wireframe"] 

Thanks Tim Laska for explanation interface with MeshTools. Since I have MeshTools installed, I call directly

mesh3D = ExtrudeMesh[mesh, 42, 9];
mesh3D["Wireframe"["MeshElementStyle" -> EdgeForm[Gray]]]