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Tessler, A.; Riggs, H. R.; Macy, S. C.

A variational method for finite element stress recovery and error estimation. (English) Zbl 0845.73074

Comput. Methods Appl. Mech. Eng. 111, No. 3-4, 369-382 (1994).
Summary: A variational method for obtaining smoothed stresses from a finite element derived non-smooth stress field is presented. The method is based on minimizing a functional involving discrete least-squares error plus a penalty constraint that ensures smoothness of the stress field. An equivalent accuracy criterion is developed for the smoothing analysis which results in a \(C^1\)-continuous smoothed stress field possessing the same order of accuracy as that found at the superconvergent optimal stress points of the original finite element analysis. Application of the smoothing analysis to residual error estimation is also demonstrated.

Cited in 9 Documents

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
74B10 Linear elasticity with initial stresses

Keywords:

non-smooth stress field; least-squares error; penalty constraint; smoothing analysis; superconvergent optimal stress points
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References:

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