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Finite element method in structural mechanics
The finite element method (FEM) is a powerful technique originally developed for numerical solution of complex problems in structural mechanics, and it remains the method of choice for complex systems. In the FEM, the structural system is modeled by a set of appropriate finite elements interconnected at points called nodes. Elements may have physical properties such as thickness, coefficient of thermal expansion, density, Young's modulus, shear modulus and Poisson's ratio.
== History ==
The origin of finite method can be traced to the matrix analysis of structures〔Matrix Analysis Of Framed Structures, 3rd Edition by Jr. William Weaver, James M. Gere, Springer-Verlag New York, LLC, ISBN 978-0-412-07861-3, 1966〕 where the concept of displacement or stiffness matrix approach was introduced. Finite element concepts were developed based on engineering methods in 50s. The finite element method obtained its real impetus in the 1960s and 1970s by the developments of J. H. Argyris with co-workers at the University of Stuttgart, R. W. Clough with co-workers at UC Berkeley, O. C. Zienkiewicz with co-workers Ernest Hinton, Bruce Irons and others at the University of Swansea, Philippe G. Ciarlet at the University of Paris and Richard Gallagher with co-workers at Cornell University. The original works such as those by Argyris〔Argyris, J.H and Kelsey, S. Energy theorems and Structural Analysis Butterworth Scientific publications, London〕 and Clough〔Clough, R.W, “The Finite Element in Plane Stress Analysis.” Proceedings, 2nd ASCE Conference on Electronic Computations, Pittsburgh, Sep 1960〕 became foundation for today’s finite element structural analysis methods. Earlier books such as by Zienkiewicz 〔The Finite Element Method for Solid and Structural Mechanics, Zienkiewicz O. C and Taylor R L ISBN 978-0-7506-6321-2, 1967, McGraw Hill, New York〕 and more recent books such as by Yang〔Finite Element Structural Analysis , T.Y Yang, Prentice-Hall, Inc, Englewood, NJ, 1986〕 give comprehensive summary of developments in finite-element structural analysis. Implementing the method in software is described in the classic text by Smith, Griffiths and Margetts.
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