Biparametric shakedown design of steel frame structures

Abstract

The paper presents a mathematical model created for solving the biparametric optimization problem of minimal volume design steel frame structures at shakedown. The shakedown and stability (for a part of the truss) constraints-conditions as well as the structure's stiffness requirements (i.e. the restriction of displacements and deflections) are evaluated. Extreme energy principles of the deformable body mechanics, as well as shakedown and mathematical programming theories of elastic-plastic structures are used in the work for creating the structure's volume optimization problem. Discretization is based on equilibrium finite elements with interpolation functions of internal forces. The elements are designed using HE, IPE, RHS steel profile assortments and considering dispersion of geometrical characteristics of profile assortment sets by principle of design biparameters. Biparametric design of steel structures is realized by using the tool system JWM SAOSYS Toolbox v0.47 created by the authors in MATLAB environment. A new analysis module EPSOptim-SD is also presented. The possibilities of the system SAOSYS are demonstrated by a numerical example of industrial building frame design with standard strength, stability and stiffness constraints. The assumption of small displacements is adopted in optimization of nonlinear problems.