Convex topology optimization for hyperelastic trusses based on the ground-structure approach

Ramos, Adeildo S.; Paulino, Gláucio H.

doi:10.1007/s00158-014-1147-2

Cited by 34 publications

(12 citation statements)

References 23 publications

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“…This is the plastic layout optimization version of the ground structure method (Gilbert and Tyas 2003;Achtziger 2007;Sokół 2011;Zegard and Paulino 2014a;Zegard 2014), and is the method of choice in the present work. However, it should be noted that the manufacturing approach proposed here is also applicable to the elastic layout optimization version of the method (Christensen and Klarbring 2009;Ramos and Paulino 2014). This brief overview of the method is presented for the purpose of completeness.…”

Section: Overview Of the Ground Structure Methodsmentioning

confidence: 99%

Bridging topology optimization and additive manufacturing

Zegard

Paulino

2015

Struct Multidisc Optim

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Topology optimization is a technique that allows for increasingly efficient designs with minimal a priori decisions. Because of the complexity and intricacy of the solutions obtained, topology optimization was often constrained to research and theoretical studies. Additive manufacturing, a rapidly evolving field, fills the gap between topology optimization and application. Additive manufacturing has minimal limitations on the shape and complexity of the design, and is currently evolving towards new materials, higher precision and larger build sizes. Two topology optimization methods are addressed: the ground structure method and density-based topology optimization. The results obtained from these topology optimization methods require some degree of post-processing before they can be manufactured. A simple procedure is described by which output suitable for additive manufacturing can be generated. In this process, some inherent issues of the optimization technique may be magnified resulting in an unfeasible or bad product. In addition, this work aims to address some of these issues and propose methodologies by which they may be alleviated. The proposed framework has applications in a number Electronic supplementary material The online version of this article (of fields, with specific examples given from the fields of health, architecture and engineering. In addition, the generated output allows for simple communication, editing, and combination of the results into more complex designs. For the specific case of three-dimensional density-based topology optimization, a tool suitable for result inspection and generation of additive manufacturing output is also provided.

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Section: Overview Of the Ground Structure Methodsmentioning

confidence: 99%

Bridging topology optimization and additive manufacturing

Zegard

Paulino

2015

Struct Multidisc Optim

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393

196

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“…Taking the special case with N = 2, we determine all of the material constants by providing α 1 , α 2 and the initial tangent modulus C 0 . An advantage of the Ogden model is that it can represent a range of hyperelastic behaviour by fine-tuning a few parameters [40,45]. For example, there are three Ogden material models shown in figure 5.…”

Section: (E) Constitutive Relationships For Barsmentioning

confidence: 99%

Nonlinear mechanics of non-rigid origami: an efficient computational approach

2017

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Origami-inspired designs possess attractive applications to science and engineering (e.g. deployable, self-assembling, adaptable systems). The special geometric arrangement of panels and creases gives rise to unique mechanical properties of origami, such as reconfigurability, making origami designs well suited for tunable structures. Although often being ignored, origami structures exhibit additional soft modes beyond rigid folding due to the flexibility of thin sheets that further influence their behaviour. Actual behaviour of origami structures usually involves significant geometric nonlinearity, which amplifies the influence of additional soft modes. To investigate the nonlinear mechanics of origami structures with deformable panels, we present a structural engineering approach for simulating the nonlinear response of non-rigid origami structures. In this paper, we propose a fully nonlinear, displacement-based implicit formulation for performing static/quasi-static analyses of non-rigid origami structures based on 'bar-and-hinge' models. The formulation itself leads to an efficient and robust numerical implementation. Agreement between real models and numerical simulations demonstrates the ability of the proposed approach to capture key features of origami behaviour.

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“…The strain energy density function for the bilinear model is defined as

Ψ_{B i} false(normalλ false) = ({, \begin{matrix} array \\ array \frac{1}{2} E_{t} {(λ - 1)}^{2}, & array if λ > 1, \\ array \frac{1}{2} E_{c} {(λ - 1)}^{2}, & array otherwise, \end{matrix})

where E t and E c are Young's moduli for tension and compression, respectively. For more details of these material models, readers are referred to the studies of Ramos et al and Zhang et al…”

Section: Multimaterials Topology Optimizationmentioning

confidence: 99%

“…For the constitutive models of the numerical example, we employ a linear model, a bilinear model, and a (hyperelastic) Ogden‐based model, which allows a varied control of constitutive relationships and has the capability to reproduce a variety of hyperelastic models. For details of the constitutive models and strain energy density functions that form the basis of the structural analysis, readers are referred to the studies of Ramos Jr and Paulino and Zhang et al…”

Section: Examplesmentioning

confidence: 99%

Multimaterial topology optimization with multiple volume constraints: Combining the ZPR update with a ground‐structure algorithm to select a single material per overlapping set

Zhang

Paulino

Ramos

2018

Numerical Meth Engineering

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Multimaterial topology optimization often leads to members containing composite materials. However, in some instances, designers might be interested in using only one material for each member. Therefore, we propose an algorithm that selects a single preferred material from multiple materials per overlapping set. We develop the algorithm, based on the evaluation of both the strain energy and the cross-sectional area of each member, to control the material profile (ie, the number of materials) in each subdomain of the final design. This algorithm actively and iteratively selects materials to ensure that a single material is used for each member. In this work, we adopt a multimaterial formulation that handles an arbitrary number of volume constraints and candidate materials. To efficiently handle such volume constraints, we employ the ZPR (Zhang-Paulino-Ramos) design variable update scheme for multimaterial optimization, which is based upon the separability of the dual objective function of the convex subproblem with respect to Lagrange multipliers. We provide an alternative derivation of this update scheme based on the Karush-Kuhn-Tucker conditions. Through numerical examples, we demonstrate that the proposed material selection algorithm, which can be readily implemented in multimaterial optimization, along with the ZPR update scheme, is robust and effective for selecting a single preferred material among multiple materials. KEYWORDSground structure method, material nonlinearity, material selection algorithm, multimaterial topology optimization, multiple volume constraints, ZPR update algorithm

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Convex topology optimization for hyperelastic trusses based on the ground-structure approach

Cited by 34 publications

References 23 publications

Bridging topology optimization and additive manufacturing

Bridging topology optimization and additive manufacturing

Nonlinear mechanics of non-rigid origami: an efficient computational approach

Multimaterial topology optimization with multiple volume constraints: Combining the ZPR update with a ground‐structure algorithm to select a single material per overlapping set

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