Finite Element Analysis

Finite element analysis is a numerical method for predicting how a physical object, a beam, a bracket, an airframe, will behave under load by dividing its geometry into a mesh of small, simply shaped elements, writing approximate equations for each element, and solving the resulting large system of equations together. Mathematician Richard Courant proposed the underlying idea in 1943, extending the Ritz method to piecewise triangular approximations over a domain, but the resulting systems were too large to solve by hand and the approach was not pursued further at the time. Boeing engineer M. J. Turner presented the method's first practical structural application at a 1954 meeting, and Turner, together with Ray Clough, H. C. Martin and L. J. Topp, published Stiffness and Deflection Analysis of Complex Structures in the Journal of the Aeronautical Sciences in 1956, the paper generally credited as the method's formal founding. Clough coined the term finite element in a 1960 conference paper. The method became practical only as computing power grew through the 1960s and 1970s, and it is now standard practice across mechanical, aerospace, civil and automotive engineering, closely paired with computer-aided design.