A high-performance element for the analysis of 2D elastoplastic continua

Finite Element formulation for nonlinear analysis of masonry walls

“…Following [14], we reformulate the elasto-plastic response of the assumed stress Finite Element by adopting a kinematic approach. Such approach defines a discrete number of possible mechanisms, corresponding to the plastic deformations that the Element exhibits.…”

Strength domains and return algorithm for the lumped plasticity equivalent frame model of masonry structures

“…1 and: E = Young's modulus; G = shear modulus; A = cross-sectional area (rectangular section: A = lt); After expressing the integral in Eq. (20) in terms of M 1 and M 2 , and these as functions of the shear V and the bending moment M 0 at the center of the element:…”

“…In this study, a variational return algorithm, based on the Haar-Kármán principle, is proposed, which overcomes the aforementioned problems and leads to optimality characteristics of the nonlinear solution [19][20][21]. The bending and shear behaviors are represented by a strength domain defined at the element level, which accounts for the two bending moments at the ends of the element and the axial force.…”

A unified mathematical programming formulation of strain driven and interior point algorithms for shakedown and limit analysis

“…Assuming elastic perfectly plastic material the stress σ will be plastically admissible if where the yield function f is a sum of the homogeneous convex function ϕ and of the yield stress σ y ∈ℝ. In an FEM context of analysis the previous condition could be expressed in a weighted sense on the element, as proposed for example in 34, or tested in a finite number of points. For the sake of simplicity, we assume control of plastic admissibility in the N σ stress nodes so that t will be plastically admissible if where, from now on, vector inequality will be considered in a componentwise fashion and with σ gy : = σ y [ x g ].…”