2,526 research outputs found
On the Virtual Element Method for Topology Optimization on polygonal meshes: a numerical study
It is well known that the solution of topology optimization problems may be
affected both by the geometric properties of the computational mesh, which can
steer the minimization process towards local (and non-physical) minima, and by
the accuracy of the method employed to discretize the underlying differential
problem, which may not be able to correctly capture the physics of the problem.
In light of the above remarks, in this paper we consider polygonal meshes and
employ the virtual element method (VEM) to solve two classes of paradigmatic
topology optimization problems, one governed by nearly-incompressible and
compressible linear elasticity and the other by Stokes equations. Several
numerical results show the virtues of our polygonal VEM based approach with
respect to more standard methods
Constraint interface preconditioning for topology optimization problems
The discretization of constrained nonlinear optimization problems arising in
the field of topology optimization yields algebraic systems which are
challenging to solve in practice, due to pathological ill-conditioning, strong
nonlinearity and size. In this work we propose a methodology which brings
together existing fast algorithms, namely, interior-point for the optimization
problem and a novel substructuring domain decomposition method for the ensuing
large-scale linear systems. The main contribution is the choice of interface
preconditioner which allows for the acceleration of the domain decomposition
method, leading to performance independent of problem size.Comment: To be published in SIAM J. Sci. Com
A variational growth approach to topology optimization
In this contribution we present an overview of our work on a novel approach to topology optimization based on growth processes [1, 2, 3]. A compliance parameter to describe the spatial distribution of mass is introduced. It serves as an internal variable for which an associated evolution equation is derived using Hamilton’s principle. The well-known problem of checkerboarding is faced with energy regularization techniques. Numerical examples are given for demonstration purposes
Topology optimization of multiple anisotropic materials, with application to self-assembling diblock copolymers
We propose a solution strategy for a multimaterial minimum compliance
topology optimization problem, which consists in finding the optimal allocation
of a finite number of candidate (possibly anisotropic) materials inside a
reference domain, with the aim of maximizing the stiffness of the body. As a
relevant and novel application we consider the optimization of self-assembled
structures obtained by means of diblock copolymers. Such polymers are a class
of self-assembling materials which spontaneously synthesize periodic
microstructures at the nanoscale, whose anisotropic features can be exploited
to build structures with optimal elastic response, resembling biological
tissues exhibiting microstructures, such as bones and wood. For this purpose we
present a new generalization of the classical Optimality Criteria algorithm to
encompass a wider class of problems, where multiple candidate materials are
considered, the orientation of the anisotropic materials is optimized, and the
elastic properties of the materials are assumed to depend on a scalar
parameter, which is optimized simultaneously to the material allocation and
orientation. Well-posedness of the optimization problem and well-definition of
the presented algorithm are narrowly treated and proved. The capabilities of
the proposed method are assessed through several numerical tests
Designing Volumetric Truss Structures
We present the first algorithm for designing volumetric Michell Trusses. Our
method uses a parametrization approach to generate trusses made of structural
elements aligned with the primary direction of an object's stress field. Such
trusses exhibit high strength-to-weight ratios. We demonstrate the structural
robustness of our designs via a posteriori physical simulation. We believe our
algorithm serves as an important complement to existing structural optimization
tools and as a novel standalone design tool itself
Revisiting topology optimization with buckling constraints
We review some features of topology optimization with a lower bound on the
critical load factor, as computed by linearized buckling analysis. The change
of the optimized design, the competition between stiffness and stability
requirements and the activation of several buckling modes, depending on the
value of such lower bound, are studied. We also discuss some specific issues
which are of particular interest for this problem, as the use of non-conforming
finite elements for the analysis, the use of inconsistent sensitivities in the
optimization and the replacement of the single eigenvalue constraints with an
aggregated measure. We discuss the influence of these practices on the
optimization result, giving some recommendations.Comment: 15 pages, 12 figures, 2 table
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