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 discrete 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.

The origin of finite method can be traced to the matrix analysis of structures where the concept of a displacement or stiffness matrix approach was introduced. Finite element concepts were developed based on engineering methods in 1950s. The finite element method obtained its real impetus in the 1960s and 1970s by John Argyris, and co-workers; at the University of Stuttgart, by Ray W. Clough; at the University of California, Berkeley, by Olgierd Zienkiewicz, and co-workers Ernest Hinton, Bruce Irons; at the University of Swansea, by Philippe G. Ciarlet; at the University of Paris; at Cornell University, by Richard Gallagher and co-workers. The original works such as those by Argyris and Clough became the foundation for today’s finite element structural analysis methods. Earlier books such as by Zienkiewicz and more recent books such as by Yang 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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