By Benoit Descamps
The writer of this publication offers a common, powerful, and easy-to-use procedure which can deal with many layout parameters efficiently.
Following an advent, bankruptcy 1 provides the overall recommendations of truss format optimization, ranging from topology optimization the place structural part sizes and process connectivity are concurrently optimized. to completely become aware of the possibility of truss format optimization for the layout of light-weight constructions, the respect of geometrical variables is then introduced.
Chapter 2 addresses truss geometry and topology optimization by way of combining mathematical programming and structural mechanics: the structural homes of the optimum answer are used for devising the unconventional formula. to prevent singularities coming up in optimum configurations, this method disaggregates the equilibrium equations and completely integrates their uncomplicated components in the optimization formula. The ensuing device accommodates elastic and plastic layout, tension and displacement constraints, in addition to self-weight and a number of loading. The inherent slenderness of light-weight buildings calls for the research of balance issues.
As a treatment, bankruptcy three proposes a conceptually basic yet effective solution to comprise neighborhood and nodal balance constraints within the formula. a number of numerical examples illustrate the impression of balance concerns at the optimum design.
Finally, the research on life like layout difficulties in bankruptcy four confirms the sensible applicability of the proposed process. it's proven how we will be able to generate a variety of optimum designs by way of various layout settings.
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Extra info for Computational Design of Lightweight Structures: Form Finding and Optimization
Alternatively, Pedersen [PED 69] investigated an approach where the static determinacy of the optimal solution is used. The same author proposed a sequential linear programming method for dealing with multiple loading [PED 72] and three-dimensional (3D) structures [PED 73]. Similarly, other optimization algorithms were speciﬁcally developed for the case of truss sizing and geometry optimization [SVA 81, ZHA 98] (see also [ROZ 95]). When cross-sectional areas are allowed to vanish, the problem is referred to as geometry and topology optimization.
Nb . 27] Introducing these variable changes in the minimum volume problem results in the linear programming formulation: Nb min t+ ∈RNb ,t− ∈RNb e=1 Nb subject to: e=1 le + t + t− e σ e − t+ e − te γ e = f , − t+ e ≥ 0, te ≥ 0, ∀e = 1, . . , Nb . 28c] − The problem structure implies that either t+ e or te will be non-zero at the optimum. The use of the speciﬁc linear programming algorithm will efﬁciently ﬁnd the global optimum for a very large design space [SOK 11]. Truss Layout Optimization 15 Using this formulation, much effort is currently devoted to developing adding member procedures for high-density ground structures [GIL 03, SOK 11, SOK 13].
Nb . 43c] Nevertheless, Stolpe and Svanberg [STO 01] proved that the trajectory of the -relaxation method may be non-smooth and even discontinuous. Even worse, its application to moderate-size structures introduces additional local optima [STO 03]. 5. Local buckling singularity The consideration of local buckling constraints exhibits similar issues with stress constraints. The problem was ﬁrst identiﬁed by Guo et al. [GUO 01]. 5(a)). 3 for 26 Computational Design of Lightweight Structures more details).
Computational Design of Lightweight Structures: Form Finding and Optimization by Benoit Descamps