Fiber‐based shakedown analysis of three‐dimensional frames under multiple load combinations: Mixed finite elements and incremental‐iterative solution

Abstract

SummaryThis work presents an efficient fiber analysis for evaluating the shakedown safety factor of three‐dimensional frames under multiple load combinations. Mixed finite elements are employed for an accurate discretization. A continuation method, similar to a standard elasto‐plastic analysis, is used at structural level. It evaluates a pseudo‐equilibrium path made of a sequence of safe states with a converging nondecreasing load factor. Each point of the path is obtained by finding kinematic variables corresponding to self‐equilibrated stresses satisfying Melan's condition for the current load factor to be safe. The stress admissible domain is defined at fiber level as a function of the load factor using the maximum and minimum effect due to all loads. An iterative state determination provides finite element stresses corresponding to assigned kinematic variables and load factor. The overall analysis differs from previous proposals for two novelty points. Firstly, a direct application of the Newton method can be employed, without any need for constrained optimization solvers. Moreover, dimension and complexity of the load domain do not affect the computational cost of the nonlinear analysis. Numerical tests show an accurate estimate of the safety factor using a small number of fibers and an efficient solution also for large buildings.

A mixed finite-element formulation for the elasto-plastic analysis of shell structures

“…Within this strategy, it is possible to efficiently extend the field of application of MISS-4 FE to elasto-plastic problems, obtaining good accuracy even at coarse meshes thanks to the equilibrated assumed stress fields. In is worth noting that the proposed decomposed formulation furnishes the same discrete equations as in other works [8,9,10]. Further details on the proposed approach can be found in [11].…”

A reduced order model for nonlinear time history seismic analyzes of elasto‐plastic 3D frame structures

“…For an anisotropic plastic behavior, as occurs for reinforced concrete buildings, two different plastic collapse mechanisms are evaluated for ± P. Each mechanism is obtained as the last displacement increment Δ𝐮 𝑐 corresponding to Δ𝜆 = 0 in the incremental-iterative solution of Equation ( 27) (see Magisano et al [32] and Magisano et al [37] ), that is, when plastic collapse occurs. Other solution strategies based on direct methods for limit analysis can be also adopted as in Skordeli et al, [42] Spiliopoulos and Dais, [43] Bleyer and De Buhan, [44] El Boustani et al [45] The plastic mode is normalized as…”

“…Three Gauss‐Lobatto points are adopted, corresponding to the ends of the element plus the mid‐span section. The section constitutive law $$\mathbf {t}(\mathbf {\rho })$$ is defined by integrating the bilinear elasto‐perfectly plastic normal stress‐strain law over the section by means of a fiber approach [ 37 ] with the usual assumption of section remaining plane. [ 38 ] An elastic behavior for the tangential stress is assumed up to failure.…”

“…[ 32 ] and Magisano et al. [ 37 ] ), that is, when plastic collapse occurs. Other solution strategies based on direct methods for limit analysis can be also adopted as in Skordeli et al., [ 42 ] Spiliopoulos and Dais, [ 43 ] Bleyer and De Buhan, [ 44 ] El Boustani et al.…”

Shakedown analysis of 3D frames under multiple load combinations using mixed fiber beam elements

“…The stress admissible domain is defined at fiber level as a function of the load factor using the maximum and minimum effect due to all loads [3]. An iterative state determination provides finite element stresses corresponding to assigned kinematic variables and load factor [3]. The overall analysis differs from previous proposals for two novelty points.…”