Eq. of motion of elastic 2D finite element

A simple question about elasticity theory/finite element method:

Suppose I have a tetragonal 2D piece of a linear isotropic elastic material, that has Young's modulus ##E## and Poisson's ratio ##\nu##. The vertices of the tetragon are at positions ##\textbf{x}_{1}##, ##\textbf{x}_{2}##, ##\textbf{x}_{3}##, ##\textbf{x}_{4}##. In its unstrained state, the element is a square with side length ##L##.

What are the equations of motion of the nodal points (vertices of the tetragon). What is the potential energy, ##V(\textbf{x}_{1},\textbf{x}_{2},\textbf{x}_{3},\textbf{x}_{4})## of the element?

Thanks for any help