Dual extremum principles in finite deformation elastoplastic analysis

Abstract

Dual extremum principles are established in this paper for the variational boundary-value problem of elasto-perfect pl/tsticity with large deformation. There exists a duality gap between the primal and dual variational problems. Our application to nonlinear limit analysis yields a pair of dual bounding theorems for the safety factor, when the gap has the right sign. It is proved that both the upper and lower bounds directly depend on the properties of the dual gap function.AMS subject classifications ~1980L 73Exx. 73Gxx.

Geometric nonlinearity: potential energy, complementary energy, and the gap function

“…(6) and (7) say that this difference is largest at the point on the curve-the point where e* = C(e). At that point the difference equals W*(e*), according to (6). Therefore, with the help of the figure, we obtain the fundamental property W*(e*) -max{ee* -W(e)}.…”

On the extreme variational principles for nonlinear elastic plates

“…These include the convexity of the total potential energy and the total complementary energy; the criteria for the existence and uniqueness of the variational solutions; and the saddle point condition for the generalized variational principles, etc. These properties are very important in both theoretical analysis and engineering applications.Recently, a systematic contribution has been given in [4,5] for nonlinear variational boundary value problems. By introducing a so-called dual gap function, a remarkable symmetry, which yields a series of important results in nonlinear mechanics [5][6][7], can be observed.…”

“…Recently, a systematic contribution has been given in [4,5] for nonlinear variational boundary value problems. By introducing a so-called dual gap function, a remarkable symmetry, which yields a series of important results in nonlinear mechanics [5][6][7], can be observed.…”

“…By introducing a so-called dual gap function, a remarkable symmetry, which yields a series of important results in nonlinear mechanics [5][6][7], can be observed. In this paper, we will present two dual-complementary extreme variational principles for Von Karman plates.…”

Dynamically loaded rigid-plastic analysis under large deformation

“…In the geometrical nonlinear structural analysis, this gap function also provides a global extremum creteria for the dualcomplementary variational problems (see [19,10]). In one-dimensional beam bending problem, the gap function will degeneralize to the following form (see .…”