What is FEM? . . .
Definition
FEM, or Finite Element Method, is a mathematical technique used to predict the response of structures and materials to environmental factors.
Finite Element Analysis (FEA) uses FEM, as a powerful engineering tool, to numerically simulate the real world without the need to test prototypes in a lab.
History
Finite Element Analysis was first developed in the early 1960's as a simulation and design tool in the aerospace and nuclear industries where the safety of structures is critical.
The process starts with the creation of a geometric model. Then, the model is subdivided (meshed) into small pieces (elements) of simple shapes connected at specific node points. Within each element, the variation of displacement is assumed to be determined by simple polynomial shape functions and nodal displacements.
Equations for the strains and stresses are developed in terms of the unknown nodal displacements. From this, the equations of equilibrium are assembled in a matrix which can be easily programmed and solved on a computer. After applying the appropriate boundary conditions, the nodal displacements are found by solving the matrix stiffness equation. Once the nodal displacements are known, element stresses and strains can be calculated.
Only within the last few years have computers become powerful enough to solve these FEA math problems in a timely fashion, and thus help improve the engineering process.
