Equilibrium Equations

Structural equilibrium requires that internal forces balance external forces. For a static solid body, the governing equilibrium equation in the domain can be expressed conceptually as:

divergence(sigma) + b = 0

where sigma is the stress tensor and b is the body force per unit volume.

Boundary conditions complete the problem definition. Displacement constraints are applied on essential boundaries, while tractions or pressures are applied on natural boundaries.

After finite element discretization, the equilibrium equations become the global algebraic system:

K u = f

where K is the global stiffness matrix, u is the unknown nodal displacement vector, and f is the global force vector.