# How to get the boundary terms of a physical system using variational package?

I have a mechanical system as shown in the figure. I have extracted the kinetic and potential energy of the system. Using variational package I can able to get only the governing differential equations. But I am also interested in extracting the Boundary terms. Is there any ways to get the boundary terms using the variational package. ClearAll["Global*"];
<< VariationalMethods
a = (D[u1[x1, t], {t, 1}])^2;
a = (D[v1[x1, t], {t, 1}])^2;
a = (D[w1[x1, t], {t, 1}])^2;
a = (D[\[Phi]1[x1, t], {t, 1}])^2;

a = (D[u2[x1, t], {t, 1}])^2;
a = (D[v2[x1, t], {t, 1}])^2;
a = (D[w2[x1, t], {t, 1}])^2;
a = (D[\[Phi]2[x1, t], {t, 1}])^2;

b = (D[u1[x1, t], {x1, 1}])^2;
b = (D[v1[x1, t], {x1, 2}])^2;
b = (D[w1[x1, t], {x1, 2}])^2;
b = (D[\[Phi]1[x1, t], {x1, 1}])^2;

b = (D[u2[x1, t], {x1, 1}])^2;
b = (D[v2[x1, t], {x1, 2}])^2;
b = (D[w2[x1, t], {x1, 2}])^2;
b = (D[\[Phi]2[x1, t], {x1, 1}])^2;

T = Total[Table[a[i], {i, 1, 8}]];(*Kineatic energy*)
V = Total[Table[b[i], {i, 1, 8}]];(*Potential energy*)
Lg = T - V;(*Lagrangian*)
e1 = EulerEquations[
Lg, {u1[x1, t], v1[x1, t], w1[x1, t], \[Phi]1[x1, t], u2[x1, t],
v2[x1, t], w2[x1, t], \[Phi]2[x1, t]}, {x1, t}];
e2 = FullSimplify[e1[]]
e3 = FullSimplify[e1[]]
e4 = FullSimplify[e1[]]
e5 = FullSimplify[e1[]]
e6 = FullSimplify[e1[]]
e7 = FullSimplify[e1[]]
e8 = FullSimplify[e1[]]
e9 = FullSimplify[e1[]]