Show simple item record

dc.contributor.authorGuest, Simon
dc.contributor.authorFowler, PW
dc.contributor.authorSchulze, B
dc.date.accessioned2018-10-10T17:30:25Z
dc.date.available2018-10-10T17:30:25Z
dc.date.issued2018-10-01
dc.identifier.issn0020-7683
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/283570
dc.description.abstractBlock-and-hole polyhedra can be derived from a bar-joint triangulation of a polyhedron by a stepwise construction: select a set of non-overlapping disks defined by edge-cycles of the triangulation of length at least 4; then modify the interior of each disk by an addition or deletion operation on vertices and edges so that it becomes either a rigid block or a hole. The construction has a body-hinge analogue. Models of many classical objects such as the Sarrus linkage can be modelled by block-and-hole polyhedra. Symmetry extensions of counting rules for mobility (the balance of mechanisms and states of self-stress) are obtained for the bar-joint and body-hinge models. The extended rules detect mechanisms in many cases where pure counting would predict an isostatic framework. Relations between structures where blocks and holes are swapped have a simple form. Examples illustrate the finer classification of isostatic and near-isostatic block-and-hole polyhedra achievable by using symmetry. The present approach also explains a puzzle in standard models of mobility. In the bar-joint model, a fully triangulated polyhedron is isostatic, but in a body-hinge version it is heavily overconstrained. When the bodies are panels with hinge lines intersecting at vertices, the overconstraints can be explained in local mechanical terms, with a direct symmetry description. A generalisation of the symmetry formula explains the extra states of self-stress in panel-hinge models of block-and-hole polyhedra.
dc.publisherElsevier BV
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.titleMobility of symmetric block-and-hole polyhedra
dc.typeArticle
prism.endingPage51
prism.publicationDate2018
prism.publicationNameInternational Journal of Solids and Structures
prism.startingPage40
prism.volume150
dc.identifier.doi10.17863/CAM.30932
dcterms.dateAccepted2018-05-31
rioxxterms.versionofrecord10.1016/j.ijsolstr.2018.05.029
rioxxterms.licenseref.urihttp://www.rioxx.net/licenses/all-rights-reserved
rioxxterms.licenseref.startdate2018-10-01
dc.contributor.orcidGuest, Simon [0000-0002-0152-6579]
dc.contributor.orcidSchulze, B [0000-0002-6272-4296]
dc.identifier.eissn1879-2146
rioxxterms.typeJournal Article/Review


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record

Attribution 4.0 International
Except where otherwise noted, this item's licence is described as Attribution 4.0 International