Papers by Mazdak Tootkaboni
Structural and Multidisciplinary Optimization, 2020
A computational strategy is proposed to circumvent some of the major issues that arise in the cla... more A computational strategy is proposed to circumvent some of the major issues that arise in the classical threshold-based approach to discrete topology optimization. These include the lack of an integrated element removal strategy to prevent the emergence of hair-like elements, the inability to effectively enforce a minimum member size of arbitrary magnitude, and high sensitivity of the final solution to the choice of ground structure. The proposed strategy draws upon the ideas used to arrive at mesh-independent solutions in continuum topology optimization and enables efficient imposition of a minimum size constraint onto the set of non vanishing elements. This is achieved via augmenting the design variables by a set of auxiliary variables, called existence variables, that not only prove very effective in addressing the aforementioned issues but also bring in a set of added benefits such as better convergence and complexity control. 2D and 3D examples from trusslike structures are presented to demonstrate the superiority of the proposed approach over the classical approach to discrete topology optimization.
Additive Manufacturing, 2018
Hollow microlattices constitute a model topology for architected materials, as they combine excel... more Hollow microlattices constitute a model topology for architected materials, as they combine excellent specific stiffness and strength with relative ease of manufacturing. The most scalable manufacturing technique to date encompasses fabrication of a sacrificial polymeric template by the Self Propagating Photopolymer Waveguide (SPPW) process, followed by thin film coating and removal of the substrate. Accurate modeling of mechanical properties (e.g., stiffness, strength) of hollow microlattices is challenging, primarily due to the complex stress state around the hollow nodes and the existence of manufacturing-induced geometric imperfections (e.g. cracks, non-circularity, etc.). In this work, we use a variety of measuring techniques (SEM imaging, CT scanning, etc.) to characterize the geometric imperfections in a nickel-based ultralight hollow microlattice and investigate their effect on the compressive strength of the lattice. At the strut level, where a more quantitative description of geometric defects is available, the gathered data is used to build a stochastic field model of geometric imperfections using Proper Orthogonal Decomposition. Using Monte Carlo simulations, the critical buckling loads of a large set of imperfect bars created using the stochastic model are then extracted by Finite Elements Analysis. The statistics of the buckling strength in artificially generated bars is then used to explain the scatter in the strength of CT-derived bars and its correlation with the lattice strength measured experimentally. Although the quantitative results are specific to microlattices fabricated by SPPW templating, the methodology presented herein is equally applicable to architected materials produced by other manufacturing processes.
International Journal of Solids and Structures, 2015
This paper investigates the optimal architecture of planar micro lattice materials for minimum we... more This paper investigates the optimal architecture of planar micro lattice materials for minimum weight under simultaneous axial and shear stiffness constraints. A well-established structural topology optimization approach is used, where the unit cell is composed of a network of beam elements (Timoshenko beams are used instead of truss elements to allow modeling of bending-dominated architectures); starting from a dense unit cell initial mesh, the algorithm progressively eliminates inefficient elements and resizes the essential load-bearing elements, finally converging to an optimal unit cell architecture. This architecture is repeated in both directions to generate the infinite lattice. Hollow circular cross-sections are assumed for all elements, although the shape of the cross-section has minimal effect on most optimal topologies under the linear elasticity assumption made throughout this work. As optimal designs identified by structural topology optimization algorithms are strongly dependent on initial conditions, a careful analysis of the effect of mesh connectivity, unit cell aspect ratio and mesh density is conducted. This study identifies hierarchical lattices that are significantly more efficient than any isotropic lattice (including the widely studied triangular, hexagonal and Kagomé lattices) for a wide range of axial and shear stiffness combinations. As isotropy is not always a design requirement (particularly in the context of sandwich core design, where shear stiffness is generally more important than compressive stiffness), these optimal architectures can outperform any established topology. Extension to 3D lattices is straightforward.
Computers & Structures, 2011
Topology optimization often leads to structures consisting of slender elements which are particul... more Topology optimization often leads to structures consisting of slender elements which are particularly sensitive to geometric imperfections. Such imperfections might affect the structural stability and induce large displacement effects in these slender structures. This paper therefore presents a robust approach to topology optimization which accounts for geometric imperfections and their potentially detrimental influence on the structural stability. Geometric nonlinear effects are incorporated in the optimization by means of a Total Lagrangian finite element formulation in the minimization of endcompliance. Geometric imperfections are modeled as a vector-valued random field in the design domain. The resulting uncertain performance of the design is taken into account by minimizing a weighted sum of the mean and standard deviation of the compliance in the robust optimization problem. These stochastic moments are typically estimated by means of sampling methods such as Monte Carlo simulation. However, these methods require multiple independent nonlinear finite element analyses in each design iteration of the optimization algorithm. An efficient solution algorithm which uses adjoint differentiation in a second-order perturbation method is therefore developed to estimate the stochastic moments during the optimization. Two applications with structures that exhibit different types of structural instabilities are examined. In both cases, it is demonstrated by means of an extensive
Computer Methods in Applied Mechanics and Engineering, 2018
We present a conceptual framework and the computational tools to study the value of the material ... more We present a conceptual framework and the computational tools to study the value of the material responses in designing material characterization tests to identify the material model under uncertainty. A computational framework is first developed to estimate the information gained by observing a material response as a measure of the value of the experiment. The proposed framework is then extended to estimate the mutual information between the material response space and the material model space as a basis for ranking the available material response candidates as they relate to reducing the uncertainty of the inferred model. We then define a design problem where a tunable parameter, referred to as the design parameter, is identified so as to render two different material responses to be of the same value from an information content point of view. We finally study the value of the material responses, obtained in a spherical indentation test, i.e. reaction force-indenter displacement, maximum indentation load and the residual imprint, where it is shown that the proposed framework offers a computationally affordable and uncertainty-aware platform to design material characterization tests.
Computer Methods in Applied Mechanics and Engineering, 2017
Highlights • Topology optimization of multiphase architected materials for energy dissipation. • ... more Highlights • Topology optimization of multiphase architected materials for energy dissipation. • Novel strategies for the interpolation of material properties in topology optimization. • Efficient tools for estimating damping capacity and stiffness of multiphase materials. • Multiphase cellular materials topologies for single and multiple target frequencies. • Superior hybrid cellular topologies with high stiffness and damping and low density.
Topology optimization of a continuum structure with volume constraint(s) on its subdomain(s) is i... more Topology optimization of a continuum structure with volume constraint(s) on its subdomain(s) is investigated by a heuristic approach simulating the bone remodelling process. The essentials of the present approach are summarized as follows. Firstly, the structure is regarded as a piece of bone and the topology optimization process is equivalent to the bone remodelling process. Secondly, according to the dead zone in bone remodelling theory, global and local floating intervals of reference strain energy density (SED) are proposed and the update of the design variable of a material point is determined by the comparison between the local SED and the current interval of reference SED. Thirdly, to satisfy the global constraints in an optimization problem, the global reference interval changes in simulation. Finally, to satisfy the local volume constraints of subdomains in structure, the same amount of local reference intervals changes in simulation. Numerical example is employed to demonstrate the effects of the local volume constraint(s) on the optimal topologies of structures.
Uploads
Papers by Mazdak Tootkaboni