Some notes on the early history of hybrid stress finite element method

International Journal for Numerical Methods in Engineering

Volumn 47, Issue 1-3, 2000, Pages 419-425

  Pian, Theodore H H ^a  

^a Massachusetts Institute of Technology Cambridge   (United States)

Author keywords

Finite element methods; Hybrid elements; Variational principles

Indexed keywords

STRESS ANALYSIS; VARIATIONAL TECHNIQUES;

HELLINGER-REISSNER PRINCIPLE;

FINITE ELEMENT METHOD;

EID: 0041112054     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/(sici)1097-0207(20000110/30)47:1/3<419::aid-nme778>3.0.co;2-%23     Document Type: Article

References (10)

1. Pian THH. Derivation of element stiffness matrices by assumed stress distributions. AIAA Journal 1964; 2:1333-1336.
2. Pian THH. Finite element methods by variational principles with relaxed continuity requirement. In Variational Methods in Engineering, Brebbia CA, Tottenham H (eds). Southampton University Press: Southampton, 1973.
3. Washizu K. Variational Principles in Elasticity. Baifukan: Tokyo, 1972.
4. Fröier M, Nilsson L, Samuelsson A. The rectangular plane stress element by Turner, Pian and Wilson. International Journal for Numerical Methods in Engineering 1974; 8:433-437.
5. Turner MJ, Clough RJ, Martin HC, Topp LJ. Stiffness and deflection analysis of complex structures. Journal of Aerosol Science 1956; 23:805-823.
6. Wilson EL, Taylor RL, Doherty WP, Glaboussi J. Incompatible displacement models. In Numerical and Computer Methods in Structural Mechanics, Fenves SJ et al (eds). Academic Press: New York, 1973; 41-57.
7. Gallagher RH. Comments on Derivation of element stiffness matrices by assumed stress distributions. AIAA Journal 1965; 3:186-187.
8. Pian THH. On the equivalence of non-conforming element and hybrid stress element. Applied Mathematics and Mechanics 1982; 3:773-776.
9. Pian THH, Sumihara K. Rational approach for assumed stress finite elements. International Journal for Numerical Methods in Engineering 1984; 20:1685-1695.
10. B. Fraeijs de Veubeke. Displacement and Equilibrium models in finite element method. In Stress Analysis, Zienkiewicz OC, Holister GS (eds). Wiley: New York, 1964.