Three-dimensional hybrid-Trefftz stress elements

International Journal for Numerical Methods in Engineering

Volumn 47, Issue 5, 2000, Pages 927-950

  De Freitas, J A Teixeira ^a   Bussamra, F L S ^b  

^a INSTITUTO SUPERIOR TÉCNICO   (Portugal)

^b UNIVERSITY OF SÃO PAULO   (Brazil)

Author keywords

Hybrid trefftz elements; Three dimensional elasticity

Indexed keywords

HYBRID-TREFFTZ STRESS ELEMENTS;

APPROXIMATION THEORY; DIFFERENTIAL EQUATIONS; FINITE ELEMENT METHOD; MATHEMATICAL MODELS; POLYNOMIALS; STRESS ANALYSIS;

ELASTICITY;

EID: 0041116320     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0207(20000220)47:5<927::AID-NME805>3.0.CO;2-B     Document Type: Article

References (41)

1. Freitas JAT. Duality and symmetry in mixed integral methods of elastostatics. International Journal for Numerical Methods in Engineering 1989; 28:1161-1179.
2. Munro J, Smith DL. Linear programming duality in plastic analysis and synthesis. International Symposium on Computer Aided Structural Design, Coventry, 1972.
3. Pian THH, Tong P. Basis of finite element methods for solid continua. International Journal for Numerical Methods in Engineering 1969; 1:3-28.
4. Brezzi F, Fortin M. Mixed and Hybrid Finite Element Methods, Springer: New York, 1991.
5. Freitas JAT, Pereira EMBR. Application of the Mathieu series to the boundary integral method. Computers and Structures 1991; 40:1307-1314.
6. Freitas JAT, Ji ZY. Hybrid-Trefftz boundary integral formulation for the simulation of singular stress fields. International Journal for Numerical Methods in Engineering 1996; 39:281-308.
7. Freitas JAT. Hybrid-Trefftz displacement and stress elements for elastodynamic analysis in the frequency domain. Computer Assisted Mechanics and Engineering Sciences 1997; 4:345-368.
8. Freitas JAT, Wang ZM. Hybrid-Trefftz stress elements for elastoplasticity. International Journal for Numerical Methods in Engineering 1998; 43:655-683.
9. Jirousek J, Wróblewski A. T-elements: state of the art and future trends. Archive Computer Methods in Engineering 1996; 3:323-434.
10. Peters K, Stein E, Wagner W. A new boundary-type finite element for 2-D and 3-D elastic structures. International Journal for Numerical Methods in Engineering 1994; 37:1009-1025.
11. Freitas JAT. Formulation of elastostatic hybrid-Trefftz stress elements. Computer Methods in Applied Mechanics and Engineering 1997; 153:127-151.
12. Freitas JAT, Almeida JPM, Pereira EMBR. Alternative hybrid formulations for the finite element method. In FEM-Today And The Future, Robinson J (ed.). Robinson and Associates, 1993.
13. Freitas JAT, Almeida JPM, Pereira EMBR. Non-conventional formulations for the finite element method. International Journal for Structural Engineering and Mechanics 1996; 4:655-678.
14. Trefftz E, Ein Gegenstück zum Ritzchen Verfahren. Proceedings of the Second International Congress Applied Mechanics, Zurich, Robinson and Associates: Bridestowe, 1926.
15. 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.
16. De Veubeke F. Upper and lower bounds in matrix structural analysis. ACARDograf, 1964; 72:165-201.
17. Maunder EAW. A reappraisal of compound equilibrium finite elements. Proceedings of the 12th Canadian Congress Applied Mechanics, Carleton University Ottawa, 1989.
18. De Veubeke F, Zienkiewicz OC. Strain energy bounds in finite element analysis by slab analogy. Journal of Strain Analysis 1967; 2:265-271.
19. Robinson J. Basis for isoparametric stress elements. Computer Methods in Applied Mechanics and Engineering 1973; 2:43-63.
20. 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.
21. Papkovitch PF. Solution général des équations différentielles fundamentals d'élasticité, exprimée par trois functions harmoniques. Comptes Rendues Académie des Sciences Paris 1932; 195:513-515, 754-756.
22. Neuber H. Ein neuer ansatz zur lösung räumlicher probleme der elastizitä theorie. Zeitschrift fur Angewandte Mathematik und Mechanik 1934; 14:203-209.
23. Venkatesh DN, Shrinivasa U. Generation of an eight node brick element using Papkovitch-Neuber functions. Computers and Structures 1995; 54:1077-1084.
24. Freitas JAT, Cismasiu C, Wang ZM. Comparative analysis of hybrid-Trefftz stress and displacement elements. Archives of Computational Methods in Engineering 1999; 6:1-26.
25. Stroud AH. Approximate Calculation of Multiple Integrals. Prentice Hall: New York, 1971.
26. Dunavant DA. High degree efficient symmetrical Gaussian rules for the triangle. International Journal for Numerical Methods in Engineering 1985; 21:1129-1148.
27. Almeida JPM, Freitas JAT. On the parallel implementation of non-conventional finite element formulations. In Advanced Finite Element Solution Techniques, Papadrakakis M (ed.). CIMNE: Barcelona, 1995.
28. Cismasiu I, Almeida JPM, Castro LMSS, Harbis D. Parallel solution techniques for hybrid-mixed finite element models. In Innovative Computational Methods for Structural Mechanics, Papadrakakis M (ed.). Saxe-Coburg Publisher, Edinburgh, 1998.
29. Castro LMSS. Wavelets and walsh series for finite elements. Ph.D. Thesis, Technical University of Lisbon, 1996 (in Portuguese).
30. MacNeal RH, Harder RL. A proposed standard set of problems to test finite element accuracy. Finite Elements for Analysis and Design 1985; 1:3-20.
31. Taylor RL, Beresford PJ, Wilson EL. A non-conforming element for stress analysis. International Journal for Numerical Methods in Engineering 1976; 10:1211-1219.
32. Lu XY, Liu YW, Xu HR, Yao CX, Chen JT. Investigation and improvement of Wilson nonconforming element. Acta Mechanica Sinica 1989; 21:379-384.
33. Pian THH, Tong P. Relations between incompatible displacement model and hybrid stress model. International Journal for Numerical Methods in Engineering 1986; 22:173-181.
34. Sze KY, Ghali A. Hybrid hexahedral element for solids, plates, shells and beams by selective scaling. International Journal for Numerical Methods in Engineering 1993; 36:1519-1540.
35. Ausserer MF, Lee SW. An eighteen-node element for thin shell analysis. International Journal for Numerical Methods in Engineering 1988; 26:1345-1364.
36. Chen W, Cheung YK. Three-dimensional 8-node and 20-node refined hybrid isoparametric elements. International Journal for Numerical Methods in Engineering 1992; 35:1871-1889.
37. Venkatesh DN, Shrinivasa U. Hexahedral element using PN functions - application to beams. Computers and Structures 1996; 60(2):305-313.
38. Pereira EMBR, Freitas JAT. A mixed-hybrid finite element model based on orthogonal functions. International Journal for Numerical Methods in Engineering 1996; 39:1295-1312.
39. Pereira OJBA, Almeida JPM, Maunder EAW. Adaptive methods and related issues from the viewpoint of hybrid equilibrium finite element model. In Advances in Adaptive Computational Methods, Ladevèze P, Oden JT (eds). Elsevier: Amsterdam, 1998.
40. Pereira EMBR. Stress finite elements - application to structural analysis. Ph.D. Thesis, Technical University of Lisbon, 1996 (in Portuguese).
41. Piltner R. The application of a complex 3-dimensional elasticity solution representation for the analysis of a thick rectangular plate. Acta Mechanica 1988; 75:77-91.