By Benoit Descamps
The writer of this e-book provides a normal, strong, and easy-to-use process which may deal with many layout parameters efficiently.
Following an creation, bankruptcy 1 offers the final options of truss format optimization, ranging from topology optimization the place structural part sizes and approach connectivity are concurrently optimized. to totally notice the potential for truss structure optimization for the layout of light-weight constructions, the honour of geometrical variables is then introduced.
Chapter 2 addresses truss geometry and topology optimization via combining mathematical programming and structural mechanics: the structural houses of the optimum answer are used for devising the unconventional formula. to prevent singularities coming up in optimum configurations, this strategy disaggregates the equilibrium equations and completely integrates their simple 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 examine of balance issues.
As a treatment, bankruptcy three proposes a conceptually uncomplicated yet effective option to comprise neighborhood and nodal balance constraints within the formula. numerous numerical examples illustrate the effect 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 approach. it really is proven how we will generate more than a few optimum designs via various layout settings.
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Extra info for Computational Design of Lightweight Structures: Form Finding and Optimization
Example text
Nb . g. linear or quadratic programming). 34] is called simultaneous analysis and design in the literature [ARO 05]. In those formulations, both design and state variables are treated as optimization variables and the equilibrium equations set as equality constraints, which are solved by general-purpose nonlinear programming algorithms. Because we will follow the lines of this approach in our method, more details are given in Chapter 2. 11]. 2). The intent of positive lower bounds a − ∈ R+ on cross-sectional areas is to ensure that the stiffness matrix remains non-singular.
All the above-mentioned methods contribute to the field of geometry and topology. However, they suffer from either a lack of rigor in covering numerical singularities, they fail at 36 Computational Design of Lightweight Structures properly converging to local optima or they are meant to be applied on specific design problems of moderate size. In this chapter, a general approach for lightweight structures, able to handle various structural, geometrical and technological constraints, is proposed. Ideally, the method could also tackle very large problems with limited computational effort.
G. [MAK 10a]), the minimum volume problem with self-weight and multiple loading is generally not equivalent to compliance optimization [MEL 12]. Furthermore, the compatibility condition is required to obtain the actual stress field. To ensure meaningful solutions, limiting stresses in tension + − σ e,k ∈ R+ and compression σ e,k ∈ R+ are imposed for all structural loading cases and truss members. Moreover, nodal displacements can be restricted by different extrema denoted − + as ui,k ∈ R+ and ui,k ∈ R+ .