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Archives of Computational Methods in Engineering

, Volume 26, Issue 4, pp 1117–1151 | Cite as

An Overview of Mixed Finite Elements for the Analysis of Inelastic Bidimensional Structures

  • Nicola A. NodargiEmail author
Original Paper

Abstract

As inelastic structures are ubiquitous in many engineering fields, a central task in computational mechanics is to develop accurate, robust and efficient tools for their analysis. Motivated by the poor performances exhibited by standard displacement-based finite element formulations, attention is here focused on the use of mixed methods as approximation technique, within the small strain framework, for the mechanical problem of inelastic bidimensional structures. Despite a great flexibility characterizes mixed element formulations, several theoretical and numerical aspects have to be carefully taken into account in the design of a high-performance element. The present work aims at providing the basis for methodological analysis and comparison in such aspects, within the unified mathematical setting supplied by generalized standard material model and with special interest towards elastoplastic media. A critical review of the state-of-the-art computational methods is delivered in regard to variational formulations, selection of interpolation spaces, numerical solution strategies and numerical stability. Though those arguments are interrelated, a topic-oriented presentation is resorted to, for the very rich available literature to be properly examined. Finally, the performances of several significant mixed finite element formulations are investigated in numerical simulations.

Notes

Acknowledgements

The author expresses his sincere gratitude to Professor Paolo Bisegna for valuable comments and stimulating discussions on the present work.

Compliance with Ethical Standards

Conflict of interest

The author declares that he has no conflict of interest.

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Copyright information

© CIMNE, Barcelona, Spain 2018

Authors and Affiliations

  1. 1.Department of Civil Engineering and Computer ScienceUniversity of Rome Tor VergataRomeItaly

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