Optimisation des structures métalliques élastoplastiques sous conditions de rigidité et de plasticité données

The Discrete Model and the Analysis of a Spherical Shell by Finite Equilibrium Elements

“…It also confirms the statement about the higher accuracy of the equilibrium finite elements compared to the displacement elements [5]. Therefore, the created element can be effectively used in the elastic-plastic shell analysis and optimization [11][12][13] 1. The presented element dependencies allow the equations, describing nodal displacements of a discrete model, to be directly derived by using the stiffness matrix of the elements (similar to the method of the displacement elements).…”

Biparametric Shakedown Design of Steel Frame Structures

“…The structure is modeled by the equilibrium finite elements with interpolation functions of internal forces [27][28][29]. The finite elements of truss (LINK11) and frame (BEAM31) types are used for discretization [16,17]. Yield and stability (truss elements) conditions are controlled at the nodes of the elements.…”

“…principles of crosssection geometry, the elements are designed using HE, IPE, RHS steel profile assortments and considering dispersion of geometrical characteristics of profile assortment sets [15][16][17]. The project of minimal volume V of the structure should be sought, when the optimality criterion is secured and strength, stiffness and stability (truss part) requirements are evaluated.…”

“…However, this approach is very unaccurate especially in the case of discrete optimization problems [13], when the evaluation of dispersion of geometrical characteristics of profile assortment sets is still important [14]. A new principle of biparametric optimization for optimal shakedown design is investigated in this paper, where already two design parameters of separate element's cross-section are selected for optimization [15][16][17]. This treatment expands the applicability of optimization problem in optimal design of steel frame structures by performing the optimization of biparameters in admissible fields of geometrical characteristics of profile assortment sets, and allows us to estimate the dispersion adequately.…”

“…The biparametric optimization principle of the main (leading) design geometry Π 0 of cross-sections and the control-corrective (driven) geometry Π 1 is used to realize the design of elements [15,17]. Idealization of distribution (expressed by approxima-tion of mean curves) of geometrical characteristics of steel profiles determines the application of the objective function, which approximately expresses the volume of the structure [16,17]. Similarly, the approximate minimization function of volume is well suited for practical application of the structures' optimization principles.…”