Shakedown of Composite Frames Taking into Account Plastic and Brittle Fracture of Elements

Abstract

In the paper the mathematical model of the optimization problem of limit and shakedown analysis for composite plane frames, containing elastic-plastic and brittle elements under low-cyclic loading, is proposed. It is assumed that the load varies randomly within the specified domain, and limited plastic redistribution of forces in such structures occurs. An example of the shakedown analyses of the composite frame is given.

Optimization of the Structures at Shakedown and Rosen’s Optimality Criterion

“…Although despite that the structures is at shakedown, there may appear such deformations and displacements, which can violate the exploitation conditions (serviceability limit state (SLS) requirements) [14,17,19,22,30]. Therefore in structural engineering it is important to know not only the true internal forces of the structure, which experienced plastic deformations, but did not reached the cyclic plastic collapse, but also the true deformations and displacements (the analysis problems of the structures) [1,2,4,7]. Many works on the theme of analysis and optimization of the structures deals with equations and dependencies for total (summarized) internal forces and displacements.…”

Shakedown Analysis of Composite Steel-Concrete Frame Systems with Plastic and Brittle Elements Under Seismic Action

“…The earthquake analysis of buildings and structures can be performed by finding solution of the optimization problem of shakedown analysis, which also takes into account the nonlinear properties of materials [4][5][6][7][8][9][10][11][12][13][14][15]. Such analysis has several advantages: -External actions are introduced as the set of the load cases, that's why we can solve the problem for all direction of seismic load and for every scheme of live load at once; -As part of the solution of the optimization problem we can take into account the elastic-plastic and brittle behavior of the elements [7,15,16]. This paper presents a mathematical model of the shakedown and limit analysis of the buildings with elastic-plastic and brittle elements.…”

Optimal Shakedown of the Thin-Wall Metal Structures Under Strength and Stiffness Constraints

“…Sensitivity analysis of the stability problems of thin-walled structures presented in [17] The right approach is possible either by laborious analyzing of load history in time without any warranty of accounting for the worst histories of independent load cases, or for the entire class of loading as provided in the theory of shakedown analysis (SDA) [1,5,6,8,9,12,[14][15][16]19,20,22,26,27,[29][30][31][32]. The example of such shakedown approach to the steel frames confined with 1st class cross-sections was published in a paper by Atkočiūnas & Venskus [10]; a shakedown limit analysis of the reinforced concrete frames has been done by Alawdin & Bulanov [2]; an updated mathematical model for optimal shakedown analysis of plane reinforced concrete frames according to Eurocodes has been introduced by Alawdin & Liepa [3]. The design of elastic-plastic metal frames is performed using the Eurocode 3 (EC3) [13] or other standards, but the algorithms for strength and stiffness evaluation of TWM structures elements are not fully described in these standards.…”