Geometric Nonlinearity : Potential Energy , Complementary Energy , and the Gap Function

@inproceedings{Gao1989GeometricN,
  title={Geometric Nonlinearity : Potential Energy , Complementary Energy , and the Gap Function},
  author={Yang Gao and Gilbert Strang},
  year={1989}
}
Dual minimum principles for displacements and stresses are well established for linear variational problems and also for nonlinear (and monotone) constitutive laws. This paper studies the problem of geometric nonlinearity. By introducing a gap function, we recover complementary variational principles in the equilibrium problems of mathematical physics. When the gap function is nonnegative those become minimum principles. The theory is based on convex analysis, and the applications made here are… CONTINUE READING
Highly Influential
This paper has highly influenced 18 other papers. REVIEW HIGHLY INFLUENTIAL CITATIONS
49 Citations
8 References
Similar Papers

Citations

Publications citing this paper.
Showing 1-10 of 49 extracted citations

References

Publications referenced by this paper.
Showing 1-8 of 8 references

Dual extremum principles in finite deformation elastoplastic analysis

  • Yang Gao, Gilbert Strang
  • Acta Applicandae Mathematicae,
  • 1989
2 Excerpts

Variational principles in elasticity

  • E. Reissner
  • “Finite Element Handbook”, H. Kardestuncer, ed…
  • 1987
1 Excerpt

The complementary energy principle in finite elastostatics as a dual problem

  • J. J. Telega, W. R. Bielski
  • Lecture Notes in Engineering 19, pp. 62-81…
  • 1986

Inequality Problems in Mechanics and Applications

  • P. D. Panagiotopoulos
  • Birkhäuser, Basel
  • 1985
1 Excerpt

On the complementary energy principle in finite elasticity

  • J. J. Telega, W. R. Bielski
  • Intern. Conf. on Nonlinear Mechanics, Science…
  • 1985

Convex Analysis and Variational Problems

  • I. Ekeland, R. Temam
  • North-Holland, Amsterdam
  • 1976
2 Excerpts

A mathematical model for physical theories

  • E. Tonti
  • Fisica Matematica, Serie VIII, Vol. LII
  • 1972
1 Excerpt

Similar Papers

Loading similar papers…