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Full text format delivery options are listed below| Title: Complementarity, polarity and triality in non-smooth, non-convex and non-conservative Hamilton systems |
| Author(s): David Yang Gao |
| Source: Philosophical Transactions: Mathematical, Physical & Engineering Sciences Volume: 359 Number: 1789 Page: 2347 -- 2367 |
| DOI: 10.1098/rsta.2001.0855 |
| Publisher: The Royal Society |
| Abstract: This paper presents a unified critical-point theory in non-smooth, non-convex and dissipative Hamilton systems. The canonical dual/polar transformation methods and the associated bi-duality and triality theories proposed recently in non-convex variational problems are generalized into fully nonlinear dissipative dynamical systems governed by non-smooth constitutive laws and boundary conditions. It is shown that, by this method, non-smooth and non-convex Hamilton systems can be reformulated into certain smooth dual, complementary and polar variational problems. Based on a newly proposed polar Hamiltonian, a nice bipolarity variational principle is established for three-dimensional non-smooth elastodynamical systems, and a potentially powerful complementary variational principle can be used for solving unilateral variational inequality problems governed by non-smooth boundary conditions. |
| Reference Links: 10 (View Links) |
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