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State-of-the-art development of hybrid/mixed finite element method. (English) Zbl 0875.73310

Summary: A brief review of multifield variational principles for the formulation of finite element methods in solid mechanics and an account of the evolution of hybrid/mixed finite element methods are presented first. Discussions of recent applications of the hybrid/mixed finite element methods include: (1) formulation of Loof and semi-Loof elements, (2) special elements based on a priori satisfaction of equilibrium and compatibility conditions, (3) analysis of heterogeneous materials with randomly distributed microstructures and (4) finite element and 3-D finite strip analyses of free edge problems in laminated composites.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
74P10 Optimization of other properties in solid mechanics
74E30 Composite and mixture properties
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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