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

  title={Geometric Nonlinearity : Potential Energy , Complementary Energy , and the Gap Function},
  author={Yang Gao and Gilbert Strang},
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
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