21 research outputs found
Modular-topology optimization of structures and mechanisms with free material design and clustering
Topology optimization of modular structures and mechanisms enables balancing
the performance of automatically-generated individualized designs, as required
by Industry 4.0, with enhanced sustainability by means of component reuse. For
optimal modular design, two key questions must be answered: (i) what should the
topology of individual modules be like and (ii) how should modules be arranged
at the product scale? We address these challenges by proposing a bi-level
sequential strategy that combines free material design, clustering techniques,
and topology optimization. First, using free material optimization enhanced
with post-processing for checkerboard suppression, we determine the
distribution of elasticity tensors at the product scale. To extract the
sought-after modular arrangement, we partition the obtained elasticity tensors
with a novel deterministic clustering algorithm and interpret its outputs
within Wang tiling formalism. Finally, we design interiors of individual
modules by solving a single-scale topology optimization problem with the design
space reduced by modular mapping, conveniently starting from an initial guess
provided by free material optimization. We illustrate these developments with
three benchmarks first, covering compliance minimization of modular structures,
and, for the first time, the design of non-periodic compliant modular
mechanisms. Furthermore, we design a set of modules reusable in an inverter and
in gripper mechanisms, which ultimately pave the way towards the rational
design of modular architectured (meta)materials.Comment: 30 page
SYNTHESIZED ENRICHMENT FUNCTIONS FOR EXTENDED FINITE ELEMENT ANALYSES WITH FULLY RESOLVED MICROSTRUCTURE
Inspired by the first order numerical homogenization, we present a method for extracting continuous fluctuation fields from the Wang tile based compression of a material microstructure. The fluctuation fields are then used as enrichment basis in Extended Finite Element Method (XFEM) to reduce number of unknowns in problems with fully resolved microstructural geometry synthesized by means of the tiling concept. In addition, the XFEM basis functions are taken as reduced modes of a detailed discretization in order to circumvent the need for non-standard numerical quadratures. The methodology is illustrated with a scalar steady-state problem
Microstructure reconstruction via artificial neural networks: a combination of causal and non-causal approach
We investigate the applicability of artificial neural networks (ANNs) in reconstructing a sample image of a sponge-like microstructure. We propose to reconstruct the image by predicting the phase of the current pixel based on its causal neighbourhood, and subsequently, use a non-causal ANN model to smooth out the reconstructed image as a form of post-processing. We also consider the impacts of different configurations of the ANN model (e.g., the number of densely connected layers, the number of neurons in each layer, the size of both the causal and non-causal neighbourhood) on the models’ predictive abilities quantified by the discrepancy between the spatial statistics of the reference and the reconstructed sample
Reduced integration schemes in micromorphic computational homogenization of elastomeric mechanical metamaterials
AbstractExotic behaviour of mechanical metamaterials often relies on an internal transformation of the underlying microstructure triggered by its local instabilities, rearrangements, and rotations. Depending on the presence and magnitude of such a transformation, effective properties of a metamaterial may change significantly. To capture this phenomenon accurately and efficiently, homogenization schemes are required that reflect microstructural as well as macro-structural instabilities, large deformations, and non-local effects. To this end, a micromorphic computational homogenization scheme has recently been developed, which employs the particular microstructural transformation as a non-local mechanism, magnitude of which is governed by an additional coupled partial differential equation. Upon discretizing the resulting problem it turns out that the macroscopic stiffness matrix requires integration of macro-element basis functions as well as their derivatives, thus calling for higher-order integration rules. Because evaluation of a constitutive law in multiscale schemes involves an expensive solution of a non-linear boundary value problem, computational efficiency of the micromorphic scheme can be improved by reducing the number of integration points. Therefore, the goal of this paper is to investigate reduced-order schemes in computational homogenization, with emphasis on the stability of the resulting elements. In particular, arguments for lowering the order of integration from expensive mass-matrix to a cheaper stiffness-matrix equivalent are outlined first. An efficient one-point integration quadrilateral element is then introduced and a proper hourglass stabilization is discussed. Performance of the resulting set of elements is finally tested on a benchmark bending example, showing that we achieve accuracy comparable to the full quadrature rules, whereas computational cost decreases proportionally to the reduction in the number of quadrature points used
Comparison of FETI-based domain decomposition methods for topology optimization problems
We critically assess the performance of several variants of dual and dual-primal domain decomposition strategies in problems with fixed subdomain partitioning and high heterogeneity in stiffness coefficients typically arising in topology optimization of modular structures. Our study considers Total FETI and FETI Dual-Primal methods along with three enhancements: k-scaling, full orthogonalization of the search directions, and considering multiple search-direction at once, which gives us twelve variants in total. We test these variants both on academic examples and snapshots of topology optimization iterations. Based on the results, we conclude that (i) the original methods exhibit very slow convergence in the presence of severe heterogeneity in stiffness coefficients, which makes them practically useless, (ii) the full orthogonalization enhancement helps only for mild heterogeneity, and (iii) the only robust method is FETI Dual-Primal with multiple search direction and k-scaling
Reduced integration schemes in micromorphic computational homogenization of elastomeric mechanical metamaterials
Exotic behaviour of mechanical metamaterials often relies on an internal
transformation of the underlying microstructure triggered by its local
instabilities, rearrangements, and rotations. Depending on the presence and
magnitude of such a transformation, effective properties of a metamaterial may
change significantly. To capture this phenomenon accurately and efficiently,
homogenization schemes are required that reflect microstructural as well as
macro-structural instabilities, large deformations, and non-local effects. To
this end, a micromorphic computational homogenization scheme has recently been
developed, which employs the particular microstructural transformation as a
non-local mechanism, magnitude of which is governed by an additional coupled
partial differential equation. Upon discretizing the resulting problem it turns
out that the macroscopic stiffness matrix requires integration of macro-element
basis functions as well as their derivatives, thus calling for a higher-order
integration rules. Because evaluation of constitutive law in multiscale schemes
involves an expensive solution of a non-linear boundary value problem,
computational efficiency can be improved by reducing the number of integration
points. Therefore, the goal of this paper is to investigate reduced-order
schemes in computational homogenization, with emphasis on the stability of the
resulting elements. In particular, arguments for lowering the order of
integration from the expensive mass-matrix to a cheaper stiffness-matrix
equivalent are first outlined. An efficient one-point integration quadrilateral
element is then introduced and proper hourglass stabilization discussed.
Performance of the resulting set of elements is finally tested on a benchmark
bending example, showing that we achieve accuracy comparable to the full
quadrature rules.Comment: 21 pages, 8 figures, 3 tables, abstract shortened to fulfill 1920
character limit, small changes after revie