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The C-complementarities in the finite element method (FEM) are five canonical principles, completeness, continuity, consistency, correctness and correspondence, that guide the finite element method. These canonical virtues cannot be achieved at the same time, these are complementarities. While the first four are prescriptive rules to ensure robust elements, the last is a descriptive rule defining exactly how the procedure works from an organising principle like the least action principle. In science, as well as in art (life), one finds that it is not possible to achieve all virtues at the same time. Confucius noticed that life is full of contradictions and conflicts and what is most important is to seek harmony and balance. It is the same with finite element computation.


References

  1. Prathap, G. and Mukherjee, S. (2004), Management-by-stress Model of Finite Element Computation, Research Report CM 0405, CSIR Centre for Mathematical Modelling and Computer Simulation, Bangalore, November 2004.[1]
  2. Vinayak, RU and Prathap, Gangan and Naganarayana, BP (1996), Beam elements based on a higher order theory-I: Formulation and analysis of performance, Computers & Structures, 58 (4). pp. 775-789. Full text
  3. Prathap, Gangan and Vinayak, RU and Naganarayana, BP (1996), Beam elements based on a higher order theory-II - Boundary layer sensitivity and stress oscillations, Computers & Structures, 58 (4). pp. 791-796. Full text
  4. Prathap, Gangan (1996), Barlow points and gauss points and the aliasing and best fit paradigms, Computers and Structures, 58 (2). pp. 321-325.
  5. Prathap, Gangan and Vinayak, RU (1996), Best-fit stress performance of a higher-order beam element, Communications in Numerical Methods in Engineering, 12 (4). pp. 229-234. ISSN 0748-8025
  6. Prathap, Gangan (1996), Barlow points and gauss points and the aliasing and best fit paradigms, Computers & structures, 58 (2). pp. 321-325.
  7. Murthy, MVV and Prathap, Gangan (1996), Shear force predictions from RBF corrected QUAD4 elements, Communications in Numerical Methods in Engineering, 12 (2). pp. 135-140. ISSN 1552-485X.
  8. Prathap, Gangan and Naganarayana, BP (1995), Consistent thermal stress evaluation in finite elements, Computers and Structures, 54 (3). pp. 415-426.
  9. G. Prathap, (1996), Finite Element Analysis and the Stress Correspondence Paradigm, Sadhana, 21,525-546.
  10. Prathap, G. (1993), The Finite Element Method in Structural Mechanics, Kluwer Academic Press, Dordrecht.
  11. Prathap, Gangan and Naganarayana, BP (1992), Stress oscillations and spurious load mechanisms in variationally inconsistent assumed strain formulations, International Journal for Numerical Methods in Engineering, 33 (10). pp. 2181-2197. ISSN 0029-5981.Full text
  12. Prathap, Gangan and Naganarayana, BP and Sudhakar, B (1991), Development of general purpose finite element package for structural analysis of Isotropic, Anisotropic and Layered Composite Structures: Progress Report. Technical Report. National Aeronautical Laboratory, Bangalore, India.
  13. Prathap, Gangan and Naganarayana, BP (1990), Consistency force resultant distributions in displacement elements with varying sectional properties, International Journal for Numerical Methods in Engineering, 29 (4). pp. 775-783.Full text
  14. Somashekar, BR and Prathap, Gangan and Ramesh Babu, C. (1987), A Field-consistent, four-noded, laminated anisotropic plate/ shell element, Computers & Structures, 25 (3). pp. 345-353. Full text
  15. Prathap, Gangan and Ramesh Babu, C (1987), Accurate force evaluation with a simple bi-linear, plate bending element, Computers and Structures, 25 (2). pp. 259-270. ISSN 0045-7949. Full text
  16. Rameshbabu, C and Subramanian, G and Prathap, Gangan (1987), Mechanics of field-consistency in finite element analysis - A penalty function approach, Computers and Structures, 25 (2). pp. 161-173. ISSN 0045-7949 Full text
  17. Prathap, Gangan and Ramesh Babu, C and Subramanian, G (1987), Stress oscillations in plane stress modelling of flexure - A field-consistency interpretation, International Journal for Numerical Methods in Engineering, 24 (4). pp. 711-724. ISSN 0029-5981
  18. Prathap, Gangan (1986), Field-consistency - Toward a science of constrained multi-strain-field finite element formulations, Sadhana - Academy Proceedings in Engineering Sciences, 9 (4). pp. 319-343. Full text
  19. Prathap, Gangan (1985), Simple plate/shell triangle, International Journal for Numerical Methods in Engineering, 21 (6). pp. 1149-1156. ISSN 0029-5981.
  20. Prathap, Gangan (1985), A Co continuous four-noded cylindrical shell element, Computers and Structures, 21 (5). pp. 995-999. ISSN 0045-7949
  21. Prathap, Gangan (1985), Additional stiffness parameter measure of error of the second kind in the finite element method, International Journal for Numerical Methods in Engineering, 21 (6). pp. 1001-1012.
  22. Prathap, Gangan (1985), Poor bending response of the four-node plane stress quadrilateral, International Journal for Numerical Methods in Engineering, 21 (5). pp. 825-835.
  23. Prathap, Gangan (1984), An optimally constrained 4 node quadrilateral thin plate bending element, Computers and Structures, 18 (5). pp. 789-794. ISSN 0045-7949
  24. Prathap, Gangan and Bhashyam, GR (1982), Reduced integration and the shear-flexible beam element. International Journal for Numerical Methods in Engineering, 18. pp. 195-210. ISSN 0029-5981.
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