Structural Topology Optimization with Stress Constraint Considering Loading Uncertainties

Abstract

This paper deals with the consideration of loading uncertainties in topology optimization via a fundamental optimization problem setting. Variability of loading in engineering design is realized e.g. in the action of various load combinations. In this study this phenomenon is modelled by the application of two mutually excluding (i.e. alternating) Optimization has since gained widespread application because efficiency and economical design are essential requirements in modern engineering. Continuous advance can be observed in several areas and applications in the industry not only in terms of practical design but also of fundamental research. The determination of the optimal structural topology is a branch of fundamental research, where the optimal topology is constructed in a design space based on given boundary conditions, serving as a decision support for actual design.The topology design historically started with the problem class of layout optimization of trusses and the works were called 'minimum volume design of frames' where the term 'frame' was historically used for what we now call a truss. The first important achievement in truss optimization was made by Maxwell [2], which deserves presentation here not only due to its significance but also because it is still unknown to many in the field. He considered the problem of attracting and repulsive forces between points set in the plane and proved a theorem regarding the equilibrium of the force system: 'In any system of points in equilibrium in a plane under the action of repulsions and attractions, the sum of the products of each attraction multiplied by the distance of the points between which it acts, is equal to the sum of the products of the repulsions multiplied each by the distance of the points between which it acts.' This statement can be formulated as t T t L t − c T c L c = 0 where T and L denote the force and the distance between two points, respectively, and indices t and c refer to tension (attraction) and compression (repulsion), respectively. For the derivation of this statement the principle of virtual work was applied with a uniform virtual deformation field.The far-reaching consequences of this theorem were not missed by Maxwell as he added therein: 'The importance of

Topology Optimisation in Structural Steel Design for Additive Manufacturing

“…The last, and possibly most severe, set of problems is related to the current methods for TO under multiple alternating loads. Notwithstanding some recent advances, current methods still face the inconvenience of non-unique solutions [459] and local extrema, as well as the difficult to account for loads with very different scales of intensity [458].…”

“…Works on dealing with alternating loads can be found early in the TO literature, including the 1970s Prager work [467], but hardly can be considered solutions for the complexity of the currently analysed problem. Recent works with alternating loads include Alkalla et al's Revolutionary Superposition Layout (RSL) method [468], as well as Lógó and Pintér contributions, [459,467]. Furthermore, Tsavdaridis et al managed to use a method to examine and overly stress paths and compose comprehensive layouts, optimized for several sets of loads [341], [469].…”

Robust Topology Optimization of Continuum Structures under the Hybrid Uncertainties: A Comparative Study

“…The majority of the most studies for structural TO are based on the deterministic assumption [1]. However, in real applications, uncertainty is inevitably observed due to insufficient knowledge, production error, changeable environment, and so on [2,3]. In this regard, the deterministic assumption may result in a topologically sensitive and vulnerable design, whose performance is often subject to variations when considering various uncertain factors.…”

Discrete Optimum Design of Planar Steel Curved Roof and Pitched Roof Portal Frames Using Metaheuristic Algorithms

“…Structural optimization, such as topology optimization [3][4][5], is one of the most studied research topics in engineering [6], and it has been attracted many research items. Since there is a limited number of existing resources in engineering design, designers attempt to find a solution fulfilling all requirements and have the lowest possible cost.…”