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28 December 1992 A review of finite element analysis techniques: capabilities and limitations
Alson E. Hatheway
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Proceedings Volume 10265, Optomechanical Design: A Critical Review; 102650G (1992) https://doi.org/10.1117/12.61113
Event: San Diego '92, 1992, San Diego, CA, United States
Abstract
In its most general form the finite element method is a computational procedure used for resolving tensor states in three dimensional continua based upon the conditions at the boundary. The procedure provides approximate solutions for continua of any shape or configuration, some of which may be very difficult or impossible to solve in closed form. This facility is provided by the fact that the procedure divides a continuum into smaller units, often many units, and the shape of the units are selected to be shapes for which solutions are either known or can be solved by approximate numerical methods. The elastic equations for each of the small units are assembled for simultaneous solution by matrix methods, thereby solving for the boundary conditions (displacements) of each small unit that are consistent with the conditions at the boundary of the continuum. The final step of the analysis is to apply a modified Ritz analysis method to determine the tensor state inside each small unit based upon the boundary conditions for the unit.
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Alson E. Hatheway "A review of finite element analysis techniques: capabilities and limitations", Proc. SPIE 10265, Optomechanical Design: A Critical Review, 102650G (28 December 1992); https://doi.org/10.1117/12.61113
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KEYWORDS
Finite element methods
Numerical analysis
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