A force method for elastic-plastic analysis of frames by quadratic optimization

An efficient mathematical programming method for the elastoplastic analysis of frames

“…The most natural formulation therefore appears to be within the framework of the force method of analysis, since equilibrium may be expressed accurately as a linear combination of the hyperstatic forces and the applied loading. On the contrary, if one uses the displacement method of analysis, a degree of approximation is needed (Pereira et al [17]). Nevertheless, the displacement method has been almost exclusively in use, because it is easier to automate.…”

Return-Mapping Algorithms for Associative Plasticity Using Conic Optimization

“…Therefore, in order to model constitutive laws based on nonlinear yield surfaces an approximation is required. Follow-ing this idea, Pereira et al [18] introduce a force method approach for the elastoplastic analysis for frames using QP.…”

“…In the SDP case, the conic constraint is given in terms of the positive semidefinite cone C P SD , which represents the space of all positive semidefinite matrices, i.e., C P SD = {X ∈ S n |X 0} , (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19) where S n represents the space of all n × n real symmetric matrices and denotes…”

“…The Drucker-Prager criterion is a generalization of the von Mises criterion in which a hydrostatic pressure sensitivity term is introduced. This sensitivity is enforced by adding a term in (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16), which is related to the first stress tensor invariant I 1 (X), i.e., 1 3 γI 1 (X) + J 2 (X) = κ DP , (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18) where γ and κ DP are material parameters, that can be obtained from experimental data, and I 1 (X) = tr(X) is related to the hydrostatic pressure m(X) as I 1 (X) = 3m(X). Clearly, for γ = 0, the von Mises criterion is retrieved.…”

“…. (4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20) Consider also the following vectorial notation for the stresses and engineering strains…”