FEA

Finite element analysis (FEA) is a computational method for predicting how structures and components respond to physical effects such as forces, heat, vibration, and other boundary conditions. It works by subdividing a complex domain into smaller, simpler parts called finite elements that are connected at nodes. By applying variational principles, the method converts differential equations governing physical behavior into a system of algebraic equations that can be solved numerically.

In a typical FEA workflow, a model is created with a defined geometry, material properties, and boundary conditions. The domain is discretized into elements and a mesh is generated. Field variables (such as displacement or temperature) are approximated within each element using shape functions. The elemental equations are assembled into a global stiffness (and possibly mass and damping) matrix, and the boundary conditions reduce the system to solvable equations. Solving yields nodal values, from which stresses, strains, temperatures, and other quantities are derived in post-processing.

Element types include one-dimensional bars and beams, two-dimensional triangles and quadrilaterals, and three-dimensional tetrahedra and hexahedra. FEA can handle linear and nonlinear material behavior, static and dynamic loads, and both steady-state and transient problems. It is widely used across engineering and science, including structural, thermal, fluid-structure interaction, acoustics, and electromagnetics analyses.

Applications span automotive, aerospace, civil engineering, biomechanics, electronics packaging, and consumer products. While powerful, FEA results depend on mesh quality, material models, and problem formulation, and require verification and validation to ensure reliability.