349 research outputs found
SIMP-ALL: a generalized SIMP method based on the topological derivative concept
Topology optimization has emerged in the last years as a promising research fieldwith a wide range of applications. One of the most successful approaches, theSIMP method, is based on regularizing the problem and proposing a penaliza-tion interpolation function. In this work, we propose an alternative interpolationfunction, the SIMP-ALL method that is based on the topological derivative con-cept. First, we show the strong relation in plane linear elasticity between theHashin-Shtrikman (H-S) bounds and the topological derivative, providing anew interpretation of the last one. Then, we show that the SIMP-ALL interpo-lation remains always in between the H-S bounds regardless the materials tobe interpolated. This result allows us to interpret intermediate values as realmicrostructures. Finally, we verify numerically this result and we show the con-venience of the proposed SIMP-ALL interpolation for obtaining auto-penalizedoptimal design in a wider range of cases. A MATLAB code of the SIMP-ALLinterpolation function is also provide
Point configurations that are asymmetric yet balanced
A configuration of particles confined to a sphere is balanced if it is in
equilibrium under all force laws (that act between pairs of points with
strength given by a fixed function of distance). It is straightforward to show
that every sufficiently symmetrical configuration is balanced, but the converse
is far from obvious. In 1957 Leech completely classified the balanced
configurations in R^3, and his classification is equivalent to the converse for
R^3. In this paper we disprove the converse in high dimensions. We construct
several counterexamples, including one with trivial symmetry group.Comment: 10 page
Optimal Homogenization of Perfusion Flows in Microfluidic Bio-Reactors: A Numerical Study
In recent years, the interest in small-scale bio-reactors has increased dramatically. To ensure homogeneous conditions within the complete area of perfused microfluidic bio-reactors, we develop a general design of a continually feed bio-reactor with uniform perfusion flow. This is achieved by introducing a specific type of perfusion inlet to the reaction area. The geometry of these inlets are found using the methods of topology optimization and shape optimization. The results are compared with two different analytic models, from which a general parametric description of the design is obtained and tested numerically. Such a parametric description will generally be beneficial for the design of a broad range of microfluidic bioreactors used for, e.g., cell culturing and analysis and in feeding bio-arrays
Shape and topology optimization in Stokes flow with a phase field approach
In this paper we introduce a new formulation for shape optimization problems in fluids in a diffuse interface setting that can in particular handle topological changes. By adding the Ginzburg{Landau energy as a regularization to the objective functional and relaxing the non-permeability outside the fluid region by introducing a porous medium approach we hence obtain a phase field problem where the existence of a minimizer can be guaranteed. This problem is additionally related to a sharp interface problem, where the permeability of the non-fluid region is zero. In both the sharp and the diffuse interface setting we can derive necessary optimality conditions using only the natural regularity of the minimizers. We also pass to the limit in the first order
conditions
Fail-safe optimization of viscous dampers for seismic retrofitting
This paper presents a new optimization approach for designing minimum-cost
fail-safe distributions of fluid viscous dampers for seismic retrofitting.
Failure is modeled as either complete damage of the dampers or partial
degradation of the dampers' properties. In general, this leads to optimization
problems with large number of constraints. Thus, the use of a working-set
optimization algorithm is proposed. The main idea is to solve a sequence of
relaxed optimization sub-problems with a small sub-set of all constraints. The
algorithm terminates once a solution of a sub-problem is found that satisfies
all the constraints of the problem. The retrofitting cost is minimized with
constraints on the inter-story drifts at the peripheries of frame structures.
The structures considered are subjected to a realistic ensemble of ground
motions, and their response is evaluated with time-history analyses. The
transient optimization problem is efficiently solved with a gradient-based
sequential linear programming algorithm. The gradients of the response
functions are calculated with a consistent adjoint sensitivity analysis
procedure. Promising results attained for 3-D irregular frames are presented
and discussed. The numerical results highlight the fact that the optimized
layout and size of the dampers can change significantly even for moderate
levels of damage
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