Hybrid equilibrium hexahedral elements and super-elements

Communications in Numerical Methods in Engineering

Volumn 24, Issue 2, 2008, Pages 157-165

  Almeida Pereira, Orlando J B ^a  

^a INSTITUTO SUPERIOR TÉCNICO   (Portugal)

Author keywords

Convergence; Equilibrium finite elements; Linear elasticity; Spurious kinematic modes

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; ELASTICITY; KINEMATICS;

EQUILIBRIUM FINITE ELEMENT; SPURIOUS KINEMATIC MODES; SUPER-ELEMENTS;

FINITE ELEMENT METHOD;

CONVERGENCE OF NUMERICAL METHODS; ELASTICITY; FINITE ELEMENT METHOD; KINEMATICS;

EID: 39549120899     PISSN: 10698299     EISSN: 10990887     Source Type: Journal    
DOI: 10.1002/cnm.967     Document Type: Article

References (17)

1. Fraeijs de Veubeke BM. Upper and lower bounds in matrix structural analysis. AGARDograf 1964; 72:165-201.
2. Almeida JPM, Pereira OJBA. Upper bounds of the error in local quantities using equilibrated and compatible finite element solutions for linear elastic problems. Computer Methods in Applied Mechanics and Engineering 2006; 195:279-296.
3. Ladevèze P, Leguillon D. Error estimate procedure in the finite element method and applications. SIAM Journal on Numerical Analysis 1983; 20(3):483-509.
4. Pereira OJBA. Utilização de Elementos Finitos de Equilibrio em Refinamento Adaptativo. Ph.D. Thesis, Technical University of Lisbon, 1996.
5. Pereira OJBA, Almeida JPM, Maunder EAW. Adaptive methods for hybrid equilibrium finite element models. Computer Methods in Applied Mechanics and Engineering 1999; 176:19-39.
6. Almeida JPM, Freitas JAT. An alternative approach to the formulation of hybrid equilibrium finite elements. Computers and Structures 1991; 40:1043-1047.
7. Almeida JPM, Pereira OJBA. A set of hybrid equilibrium finite element models for the analysis of three-dimensional solids. International Journal for Numerical Methods in Engineering 1996; 39:2789-2802.
8. Fraeijs de Veubeke BM. Diffusive equilibrium models. In B. M. Fraeijs de Veubeke Memorial Volume of Selected Papers, Geradin M (ed.). Sijthoff & Noordhoff: Alphen aan den Rijn, The Netherlands, 1980; 569-628.
9. Maunder EAW, Almeida JPM. Hybrid-equilibrium elements with control of spurious kinematic modes. Computer Assisted Mechanics and Engineering Sciences 1997; 4:587-605.
10. Kempeneers M, Debongnie JF, Beckers P. Pure equilibrium tetrahedral finite elements and global error estimation by dual analysis. Computer Methods in Applied Mechanics and Engineering 2005, submitted.
11. Pereira OJBA, Almeida JPM. Aplicação de Elementos Finitos de Equilíbrio à Estimação do Erro ent Malhas de Elementos Finitos Utilizadas na Análise de Barragens Abóbada. Revista Portuguesa de Engenharia de Estruturas 2004; 53:31-40.
12. Watwood VB, Hartz BJ. An equilibrium stress field model for finite element solutions of two dimensional elastoplastic problems. International Journal of Solids and Structures 1968; 4:857-873.
13. Ramsay ACA, Almeida JPM, Maunder EAW. Curious convergence with hypo-static hybrid equilibrium models. Communications in Numerical Methods in Engineering 1997; 13:541-552.
14. Sander G. Application of the dual analysis principle. In High Speed Computing of Elastic Structures, Fraeijs de Veubeke BM (ed.). University of Liège: 1971; 167-207.
15. Maunder EAW, Almeida JPM, Ramsay ACA. A general formulation of equilibrium macro-elements with control of spurious kinematic modes. International Journal for Numerical Methods in Engineering 1996; 39:3175-3194.
16. Pissanetzky S. Sparse Matrix Technology. Academic Press: London, 1984.
17. Richardson LF. The approximate arithmetical solution by finite differences of physical problems involving differential equations, with an application to the stresses in a masonry dam. Transactions of the Royal Society of London, Series A 1910; 210:307-357.