Elastoplastic and limit analysis of 3D steel assemblies using second-order cone programming and dual finite-elements

Abstract

We investigate the use of a second-order cone programming (SOCP) framework for computing complex 3D steel assemblies in the context of elastoplasticity and limit analysis. Displacement and stress-based variational formulations are considered and appropriate finite-element discretization strategies are chosen, yielding respectively an upper and lower bound estimate of the exact solution. An efficient interior-point algorithm is used to solve the associated optimization problems. The discrete solution convergence is estimated by comparing both static and kinematic solutions, offering a way to perform local mesh adaptation. The proposed framework is illustrated on the design of a moment-transmitting assembly, its performance is assessed by comparison with classical elastoplastic computations using Abaqus and, finally, T-stub resistance and failure mechanisms when assessing the strength of a column base plate are compared with the Eurocodes design rules.

Extending interior‐point methods to nonlinear second‐order cone programming: Application to finite‐strain elastoplasticity

“…Restricting the above minimization to radial evolutions (see [9]) ofĖ p (t) over the time interval, we obtain the following incremental minimization principle:…”

“…In the field of non-smooth mechanics, interior-point methods (IPM) have recently emerged as interesting alternative resolution strategies e.g. for problems involving contact [1][2][3][4][5][6], elastoplasticity [1,[7][8][9], limit analysis [10][11][12][13][14], granular materials [15,16] or even viscoplastic fluids [17,18]. They are indeed well suited to model optimization problems involving non-smooth constraints [19], in particular when they can be expressed using self-dual second-order Lorentz cone or positive semi-definite matrix cones, yielding, respectively, problems belonging to the class of Second-Order Cone Programming (SOCP) [20,21] or Semi-Definite Programming (SDP).…”

“…This usually induces the introduction of additional auxiliary variables, thereby increasing the problem size [17]. However, such reformulations may not always be needed in a custom dedicated interior point solver [9,18]. For instance, elastoplastic or viscoplastic problems contain a smooth term (related to the elastic or viscous part) and a non-smooth term (the plastic part).…”

“…The present work aims at exploring one step further in the direction of extending IPM to other mechanical problems by tackling the case of finite-strain plasticity. Building upon previous works on a custom IPM solver including smooth convex terms [9,18], we investigate the case of problems containing smooth but non-convex terms. Obviously, proofs of convergence of the IPM algorithm will necessarily be lost in the non-convex case.…”

Numerical upper bounds to the ultimate load bearing capacity of three‐dimensional reinforced concrete structures

“…where C is the material cohesion, which is related to its uniaxial compressive strength by the classical relationship: = 2 cos 1 − sin ≅ 3.46 (25) so that (24) can be rewritten as:…”