By Grégoire Allaire, François Jouve (auth.), Martin Philip Bendsøe, Niels Olhoff, Ole Sigmund (eds.)
ISBN-10: 1402047290
ISBN-13: 9781402047299
ISBN-10: 1402047525
ISBN-13: 9781402047527
This booklet includes the refereed and edited types of papers offered on the IUTAM Symposium on Topological layout Optimization of buildings, - chines and fabrics: prestige and views, held at Rungstedgaard, close to Copenhagen, Denmark, October 26–29, 2005. The symposium was once attended via seventy four scientists from 19 nations, and the programme used to be in depth and - cluded additionally evenings for shows and discussions. it's now greater than 15 years in the past that the so-called homogenization procedure used to be proposed as a foundation for computational potential to optimize the topology and form of continuum buildings. From at first being able in most cases of treating minimal compliance layout we now see the elemental fabric distribution concept of the technique utilized to quite a lot of structural and mechanical pr- lems in addition to to difficulties that couple structural reaction to different actual responses. additionally, the strategy has supplied perception for micro-mechanical st- ies, that means that the strategy has given suggestions to the realm which supplied impetus to the ?eld of topological layout optimization in its construction. eventually, topological layout is now an essential component of such a lot FEM software program structures and it has turn into a typical commercial instrument in a few ?elds. The IUTAM Symposium supplied a discussion board for the trade of rules for - ture advancements within the quarter of topological layout optimization. This enc- handed the applying to ?uid-solid interplay difficulties, acoustics difficulties, and to difficulties in biomechanics, in addition to to different multiphysics problems.
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Extra resources for IUTAM Symposium on Topological Design Optimization of Structures, Machines and Materials: Status and Perspectives
Example text
The costly grid discretization in the classical level set method is thus avoided. Therefore, we may call the method presented here parametric shape and topology optimization. A standard search method is to use the parameter sensitivity to define a search direction and a move step, such as the steepest descent method in mathematical programming. More elaborate techniques such as the method of moving asymptote (MMA) are also feasible. 6. NUMERICAL EXAMPLES OF A MICHELL TYPE STRUCTURE In this section, numerical examples in two dimensions are presented to illustrate the present RBF-level set method for structural topology optimization.
Radial basis functions are used to define a general implicit representation with weight coefficients as parameters. This enables level set algorithms to avoid a costly discrete computational scheme and use a mathem- Parametric Shape and Topology Optimization with Radial Basis Functions (a) Initial shape Figure 4. (a) Initial shape Figure 5. 21 (b) Initial level set function The initial design and level set function. (b) Initial level set function The final design and level set function. atically more convenient parameter search technique instead.
The symbol L represents the fluidstructural coupling matrix and the symbols K and M denote the N-dimensional structural stiffness and mass matrices, where N is the number of DOFs. The expression K − ωp2 M in (1) represents the dynamic stiffness matrix which we may denote by KD . The matrices G, H and Cα can be generated by the discretized Helmholtz integral and calculation of the spatial angle along the structural surface [14]. We consider a bi-material design problem where NE is the total number of finite elements and the symbol ρe denotes the volumetric density of the stiffer material in element e and plays the role of the design variable in the problem [9].
IUTAM Symposium on Topological Design Optimization of Structures, Machines and Materials: Status and Perspectives by Grégoire Allaire, François Jouve (auth.), Martin Philip Bendsøe, Niels Olhoff, Ole Sigmund (eds.)
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