Bridging art and engineering using Escher-based virtual elements

Paulino, Gláucio H.; Gain, Arun L.

doi:10.1007/s00158-014-1179-7

Cited by 44 publications

(41 citation statements)

References 42 publications

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“…In the framework of Structural Mechanics, after the initial papers [26,30,15,43], many applications and developments were pursued by the community. Among the many publications, we here refer to a long but non exhaustive list [20,29,33,6,5,21,3,42,44,4,8,7,16,41,34,27,22]. Finally, it must be noted that other polytopal methods exist in the Structural Mechanics literature; we here limit ourselves in citing [39,18,23,28] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Curvilinear Virtual Elements for 2D solid mechanics applications

Artioli

Veiga

Dassi

2020

Computer Methods in Applied Mechanics and Engineering

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In the present work we generalize the curvilinear Virtual Element technology, introduced for a simple linear scalar problem in a previous work, to generic 2D solid mechanic problems in small deformations. Such generalization also includes the development of a novel Virtual Element space for displacements that contains rigid body motions. Our approach can accept a generic black-box (elastic or inelastic) constitutive algorithm and, in addition, can make use of curved edges thus leading to an exact approximation of the geometry. Rigorous theoretical interpolation properties for the new space on curvilinear elements are derived. We undergo an extensive numerical test campaign, both on elastic and inelastic problems, to assess the behavior of the scheme. The results are very promising and underline the advantages of the curved VEM approach over the standard one in the presence of curved geometries. * artioli@ing.uniroma2.it †

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Section: Introductionmentioning

confidence: 99%

Curvilinear Virtual Elements for 2D solid mechanics applications

Artioli

Veiga

Dassi

2020

Computer Methods in Applied Mechanics and Engineering

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“…Indeed, polytopal meshes can be very useful for a wide range of reasons including meshing of the domain, automatic use of hanging nodes, moving meshes and adaptivity. VEM has been applied successfully in a large range of problems; see for instance [1,3,6,7,8,10,12,13,16,18,29,31,32,33].…”

Section: Introductionmentioning

confidence: 99%

A posteriori error estimates for a Virtual Element Method for the Steklov eigenvalue problem

Mora

Rivera

Rodrı́guez

2017

Computers & Mathematics with Applications

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“…Different manufacturing constraints for topology optimization have been investigated [Sigmund 2009], however, there exists little work regarding aesthetics. Paulino et. al.…”

Section: Related Workmentioning

confidence: 99%

Structure and appearance optimization for controllable shape design

et al. 2015

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Figure 1: Our technique automatically generates rigid shapes answering a specific loading scenario and resembling an input exemplar pattern, while using a user-specified quantity of material. Top left: Loading scenario; in this case the synthesized shape is anchored to the ground by its bottom left/right corners, while supporting a road through four attachments. Each attachment contains an empty region (white) surrounded by a solid boundary (blue), serving as a socket to plug in the road plank. Bottom left: Two exemplars defining the desired appearance. Second column: Two synthesized bridges answering the loading scenario but each using a different exemplar. Photograph: Fabricated objects using the synthesized shapes.

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Bridging art and engineering using Escher-based virtual elements

Cited by 44 publications

References 42 publications

Curvilinear Virtual Elements for 2D solid mechanics applications

Curvilinear Virtual Elements for 2D solid mechanics applications

A posteriori error estimates for a Virtual Element Method for the Steklov eigenvalue problem

Structure and appearance optimization for controllable shape design

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