Improvement of the Zienkiewicz–Zhu Error Recovery Technique Using a Patch Configuration

The Zienkiewicz–Zhu (ZZ) super-convergent patch recovery technique based on a node neighborhood patch configuration is used most widely for recovery of the stress field of a finite element analysis. In this study, an improved ZZ recovery technique using element neighborhood patch configuration is proposed. The improved recovery procedure is based on recovery of the stress field in the least-squares sense over an element patch that consists of the union of the elements surrounding the element under consideration. The proposed patch configuration provides more sampling points and improves the performance of the standard ZZ recovery technique. The effectiveness and reliability of the improved ZZ recovery approach is demonstrated through plane elastic and plastic plate problems. The problem domain is discretized with triangular and quadrilateral elements of different sizes. A comparison of the quality of error estimation using the ZZ recovery of derivative field and recovery of the displacement field using similar element neighborhood patch configurations is also presented. The numerical results show that the ZZ recovery technique and the displacement recovery technique, using a modified patch configuration, yield better results, convergence rate, and effectivity as compared with the standard ZZ super-convergent patch recovery technique. It is concluded that the improved ZZ recovery technique-based adaptive finite element analysis is very effective for converging a predefined accuracy with a significantly smaller number of degrees of freedom, especially in an elastic problem. It is also concluded that the improved ZZ recovery technique captures the plastic deformation problem solution errors more reliably than the standard ZZ recovery technique.

Download Full-text

A Posteriori Detection of Numerical Locking in hpq-Adaptive Finite Element Analysis

Applied Sciences ◽

10.3390/app10228247 ◽

2020 ◽

Vol 10 (22) ◽

pp. 8247

Author(s):

Łukasz Miazio ◽

Grzegorz Zboiński

Keyword(s):

Finite Element Analysis ◽

Sensitivity Analysis ◽

Finite Element ◽

Solid Mechanics ◽

Problem Solution ◽

Adaptive Finite Element ◽

A Posteriori ◽

Element Analysis ◽

Numerical Locking ◽

Locking Phenomena

The proposed detection algorithms are assigned for the hpq-adaptive finite element analysis of the solid mechanics problems affected by the locking phenomena. The algorithms are combined with the M- and hpq-adaptive finite element method, where M is the element model, h denotes the element size parameter, and p and q stand for the longitudinal and transverse approximation orders within an element. The applied adaptive scheme is extended with the additional step where the locking phenomena are a posteriori detected, assessed and resolved. The detection can be applied to shear, membrane, or shear–membrane locking phenomena. The removal of the undesired influence of the numerical locking on the problem solution is based on p-enrichment of the mesh. The detection algorithm is also enriched with the locking assessment algorithm which is capable of determination of the optimized value of p which is sufficient for the phenomena removal. The detection and assessment algorithms are based on a simple sensitivity analysis performed locally for the finite elements of the thin-walled domain. The sensitivity analysis lies in comparison of the element solutions corresponding to two values of the order p, namely current and potentially eliminating the locking. The local solutions are obtained from the element residual method. The elaborated algorithms are original, relatively simple, extremely reliable, and highly effective.

Download Full-text

3D Coupled Thermomechanical Finite Element Analysis of Ultrasonic Consolidation

Materials Science Forum ◽

10.4028/www.scientific.net/msf.539-543.2651 ◽

2007 ◽

Vol 539-543 ◽

pp. 2651-2656 ◽

Cited By ~ 5

Author(s):

C.J. Huang ◽

E. Ghassemieh

Keyword(s):

Finite Element Analysis ◽

Finite Element ◽

Friction Coefficient ◽

Stress Field ◽

Ultrasonic Wave ◽

Ultrasonic Vibration ◽

Softening Effect ◽

Element Analysis ◽

Consolidation Process ◽

Ultrasonic Consolidation

A 3-D coupled temperature-displacement finite element analysis is performed to study an ultrasonic consolidation process. Results show that ultrasonic wave is effective in causing deformation in aluminum foils. Ultrasonic vibration leads to an oscillating stress field. The oscillation of stress in substrate lags behind the ultrasonic vibration by about 0.1 cycle of ultrasonic wave. The upper foil, which is in contact with the substrate, has the most severe deformation. The substrate undergoes little deformation. Apparent material softening by ultrasonic wave, which is of great concern for decades, is successfully simulated. The higher the friction coefficient, the more obvious the apparent material softening effect.

Download Full-text