VARIATIONAL FORMULATIONS OF NUMERICAL METHODS IN SOLID CONTINUA

For problems in solid continua both finite element and finite difference methods can be formulated by variational principles; namely, the potential energy and complementary energy principles and Reissner's principle. Example problems demonstrate that the equations resulting from both methods are reducible to systems of algebraic equations with only the values of the field variables at the described mesh points as the unknowns. For many problems the resulting equations by both methods are identical. The finite element method, thus, may be considered as a rational and systematic approach for setting up finite difference equations. Only the finite element method can be formulated by the modified variational principles which take into account the discontinuity of the field variables at the interelement boundary. There exist many finite element models from which a more efficient numerical scheme can be selected.

• Supplemental Notes:
  • Published in Proceedings of Symposium on Computer-Aided Engineering Solid Mechanics Division, Waterloo, Ontario, Canada, 11-13 May 1971, pp 421-448 1971. Reprint Study number 5, Computer-Aided Engineering
• Corporate Authors:

  Massachusetts Institute of Technology

  Department of Aeronautics and Astronautics
  77 Massachusetts Avenue
  Cambridge, MA  United States  02139
• Authors:
  • Pian, THH
• Publication Date: 1971

Media Info

• Pagination: 29 p.

Subject/Index Terms

• TRT Terms: Finite differences; Finite element method; Structural analysis
• Subject Areas: Marine Transportation; Materials;

Filing Info

• Accession Number: 00034881
• Record Type: Publication
• Source Agency: National Technical Information Service
• Report/Paper Numbers: AFOSR-TR-72-0958
• Contract Numbers: F44620-67-C-0019
• Files: TRIS
• Created Date: Oct 27 1973 12:00AM