COMPOSITE PLATES IN POSTBUCKLING: DUAL EXTREMAL VARIATIONAL PRINCIPLES, ENERGY FEATURES, STABILITY, LAY-UP OPTIMALITY CONDITIONS VIA COMPLEMENTARY ENERGY APPROACH

In the present paper the composite plates in postbuckling are explored. The dual extremal variational principles are created. The principles generalize the stationary ones obtained earlier. The stability of the plate near the single-modal bifurcation point is proven. Some useful energy relations are established. It is also demonstrated that the total complementary energy may be considered as a measure of the compliance for the post-buckled composite plate. The latter measure leads to the same lay-up optimality conditions as obtained earlier via the maximization of the total potential energy. Basing on the complementary variational principle, a monotonic plate compliance minimization approach is proposed. The approach allows determining the stiffest lay-up.

Generalized Quasi-Variational Principles and Application in Nonlinear Non-Conservative Elasto-Dynamics

The generalized quasi-variational principles with two kinds of variables of time initial value problem were established in nonlinear non-conservative elasto-dynamics. Then, the analytic solution of time initial value problem of a typical non-conservative elasto-dynamics was studied by applying the obtained quasi-complementary variational principle.

Inequalities associated with the inversion of elastic stress-deformation relations and their implications

For an elastic solid the constitutive law can be written in terms of the deformation gradient α and its conjugate nominal stress s ≡ s(α), and also in terms of the right stretch u and its conjugate stress τ ≡ τ(u). It is shown that for isotropic elastic solids s(α) is invertible, in the local sense, for all u in the domain of u-space where τ(u) is locally invertible, with the exception of certain configurations which correspond to planes in τ-space.In the global sense a given s corresponds to four distinct τ's, and s is invertible to give four distinct α's when the corresponding τ's are uniquely invertible. That there are four branches of the inversion α(s) is of fundamental importance in that it clarifiesthe extent to which non-uniqueness of solution of boundary-value problems can be expected.The implications of these results in respect of the complementary variational principle are discussed, and the controversy surrounding the use of nominal stress in this principle resolved.Consequences of the required restrictions on τ(u) are examined and discussed in relation to inequalities which may be regarded as entailing physically reasonable response. It is intimated that τ(u) is invertible in the domain of elastic response.