Control variational method approach to bending and contact problems for Gao beam

Abstract

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Identification Problem for Nonlinear Gao Beam

“…then for any (E, ν) ∈ U ad there exists a unique solution w := w(E, ν) to the problem (12). This can be proven using the results established in [12]. Note that…”

“…as w solves (12). Since there exists a unique solution to this problem, the whole sequence {w n } tends weakly to w ∈ V.…”

“…Existence of a unique solution of the considered problem (4) has been studied in [12]. In particular it was shown that if (A1) f ∈ L 2 ((0, L)); (A2) E, I, α, µ are positive constants; (A3) P < P, where P = 1…”

“…where w(E, ν) solves the state problem (12) and J : V −→ R is a cost functional. (13) If (E * , ν * ) is a solution to (13) and w * := w(E * , ν * ) solves (P (E * , ν * )), then the pair ((E * , ν * ), w * ) is called an optimal pair of problem (13).…”

On SDP method for solving canonical dual problem in post buckling of large deformed elastic beam

“…In this case, Π EB (w) and Π(w) are strictly are strictly convex on U a , therefore, both the Euler-Bernoulli beam (5) and the nonlinear Gao beam (1) can have only one solution (see Lemma 2.1. and Theorem 2.1 in [27]). Dually, in the post-buckling state, i.e.…”