Finite element method (FEM)

The finite element method (FEM) is a numerical technique that divides a structure into small elements, each with a polynomial displacement field, then assembles their stiffness into a global system [K]{u} = {F} solved for nodal displacements and recovered stresses. In ship structures it is the engine behind direct strength analysis: the cargo-hold or full-ship model is meshed with plate (shell) and beam elements, loaded with still-water and wave bending plus local pressure, and checked for yield and buckling. Mesh density follows class rules, typically one element per stiffener spacing for coarse models and t x t fine mesh at hot spots for fatigue. Convergence and element aspect ratio govern result quality.