Simon Šilih

The multilevel MINLP optimization approach to structural synthesis: the simultaneous topology, material, standard and rounded dimension optimization

The paper describes the simultaneous topology, material, standard and rounded dimension optimization of mechanical structures, performed by the Mixed-Integer Non-linear Programming (MINLP) approach. Beside the generation of an MINLP mechanical superstructure, the development of a general multilevel MINLP formulation for a mechanical superstructure is presented. The consideration of the discrete materials as well as standard and particularly rounded dimensions in structural synthesis significantly increases the combinatorics of the discrete optimization, which as a result may become too difficult to solve. A Linked Multilevel Hierarchical Strategy (LMHS) has been introduced for the solving of such large combinatorial problems. In order to decrease the effect of non-convexities, the Modified Outer-Approximation/Equality-Relaxation (OA/ER) algorithm has been applied. Four numerical examples of different complexities are presented to illustrate the proposed multilevel MINLP optimization approach: the optimization of two steel trusses, a composite I beam and a hydraulic steel roller gate Intake gate, erected in Aswan II, Egypt.

Optimization based comparison between composite I beams and composite trusses

Abstract The paper presents the economical comparison between composite welded I beams and composite trusses, designed from hollow sections. The comparison was made for simply supported beams for different spans and different loads. Composite I beams and composite trusses were designed in accordance with Eurocode 4 for the conditions of both ultimate and serviceability limit states. The aim of the comparison was to find out the spans and loads, at which each of the different structures shows its advantages. In order to carry out a precise comparison between the two different composite systems, we applied a structural optimization method rather than classical structural analysis. The optimization was performed by the nonlinear programming approach. The economic objective function of self-manufacturing costs was defined for the optimization. This way, the obtained design solutions of both systems were not only optimal, but the optimization also caused that the design, resistance, stress and deflection (in)equality constraints were activated at the border of the feasible space. Consequently, the conditions of both the ultimate and serviceability limit states were fully exploited and there was no reserve of resistance for each of the two different structures. At this point the comparison between results of composite I beams and composite trusses was performed. Some contour diagrams are also shown at the end of the paper, which should enable researchers and engineers to come to a decision about different composite structures in a faster and more efficient way.

Shape and discrete sizing optimization of timber trusses by considering of joint flexibility

The paper presents the shape and discrete sizing optimization of timber trusses with the consideration of joint flexibility. The optimization was performed by the Mixed-Integer Non-linear Programming (MINLP) approach. In the optimization model an economic objective function for minimizing the structures self-manufacturing costs was defined. The design conditions in accordance with Eurocode 5 were considered as optimization constraints. The internal forces and deflections were calculated by finite element analysis. The structural stiffness matrix was composed by considering fictiously decreased cross-sectional areas of all the flexibly connected elements. The cross-section dimensions and the number of fasteners were defined as discrete sizing variables, while the joint coordinates were considered as shape variables. The applicability of the proposed approach is demonstrated through some numerical examples, presented at the end of the paper.

A parametric numerical study on the horizontal load-bearing capacity of the FPB-sheated timber framed wall elements with openings

The paper presents a parametric numerical study on the horizontal load-bearing capacitiy of timber framed wall elements coated with single fibre plaster boards (FPB) that can be used in the construction of single- or multi-storey prefabricated buildings. The research deals with both the full elements (without any opening) and with elements containing an opening. The key behaviour indicators like the racking stiffness and strength were determined and presented as ratios dependent on the opening area. A comparative study has proved that none of the methods from the literature that were previously developed for different types of wall elements can be accurately applied to the FPB-sheated panels. It has also been shown that the methods currently available in the European design codes underestimate the capacity of wall elements with openings. Based on the results some diagrams are proposed that enable quick and efficient determination of the essential properties of wall elements with arbitrary areas of openings and may thus represent a useful tool for the structural design process.

3.5 – Topology, Shape and Standard Sizing Optimization of Trusses Using MINLP Optimization Approach

The paper presents the simultaneous topology, shape and discrete/standard sizing optimization of steel trusses using Mixed-Integer Non-linear Programming (MINLP) approach. The discrete/continuous non-convex and non-linear optimization problems are solved by the Modified OA/ER algorithm. Two types of objective functions are introduced for the optimization, namely a volume/mass objective function and an economic objective function. The design constraints are defined in accordance to Eurocode 3. A numerical example is presented at the end of the paper in order to show the suitability of the proposed approach and to emphasize the importance of selecting a proper objective function.