Phi-Functions for 2D Objects Formed by Line Segments and Circular Arcs

Chernov, N.; Stoyan, Yu. G.; Romanova, Tatiana; Pankratov, Alexander

doi:10.1155/2012/346358

Cited by 37 publications

(32 citation statements)

References 14 publications

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“…For the prescribed models, most are commonly used to analyze simplified polygons fixed in a specific orientation denoted as phi-objects [74]. Similar phi-object models are presented in [75,76]. In FFF printing processes, the operator commonly selects the build orientation based on metrics related to print quality, dimensional stability and mechanical properties.…”

Section: Areas Of Improvement and Comparison To Other Technologiesmentioning

confidence: 99%

Open Source Multi-Head 3D Printer for Polymer-Metal Composite Component Manufacturing

Laureto

Pearce

2017

Technologies

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Abstract:As low-cost desktop 3D printing is now dominated by free and open source self-replicating rapid prototype (RepRap) derivatives, there is an intense interest in extending the scope of potential applications to manufacturing. This study describes a manufacturing technology that enables a constrained set of polymer-metal composite components. This paper provides (1) free and open source hardware and (2) software for printing systems that achieves metal wire embedment into a polymer matrix 3D-printed part via a novel weaving and wrapping method using (3) OpenSCAD and parametric coding for customized g-code commands. Composite parts are evaluated from the technical viability of manufacturing and quality. The results show that utilizing a multi-polymer head system for multi-component manufacturing reduces manufacturing time and reduces the embodied energy of manufacturing. Finally, it is concluded that an open source software and hardware tool chain can provide low-cost industrial manufacturing of complex metal-polymer composite-based products.

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Section: Areas Of Improvement and Comparison To Other Technologiesmentioning

confidence: 99%

Open Source Multi-Head 3D Printer for Polymer-Metal Composite Component Manufacturing

Laureto

Pearce

2017

Technologies

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“…In order to model an arbitrary object, the object needs to be decomposed into basic and primitive objects. Chernov et al (2012) provides a decomposition algorithm for this purpose. They define four types of basic objects.…”

Section: Phi-objects For Modelling Forbidden Regionsmentioning

confidence: 99%

“…These are (i) a convex polygon ( Figure 5(a)), formed by an intersection of three or more half-planes, (ii) a circular segment (Figure 5(b)), as an intersection of a circle and a half-plane, (iii) a hat ( Figure 5(c)), formed by an intersection of a complement of a circle and two half-planes that corresponding boundaries are tangent to the circle and (iv) a horn ( Figure 5(d)), an intersection of a circle, a complement of a circle and a half-plane. Chernov et al (2012) showed that any arbitrarily shaped composed object bounded by circular arcs and line segments can automatically be decomposed into a set of defined basic objects by the given algorithm.…”

Section: Phi-objects For Modelling Forbidden Regionsmentioning

confidence: 99%

A modelling framework for solving restricted planar location problems using phi-objects

Oğuz

Bektaş

Bennell

et al. 2016

Journal of the Operational Research Society

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This paper presents a general modelling framework for restricted facility location problems with arbitrarily shaped forbidden regions or barriers, where regions are modelled using phi-objects. Phi-objects are an efficient tool in mathematical modelling of 2D and 3D geometric optimization problems, and are widely used in cutting and packing problems and covering problems. The paper shows that the proposed modelling framework can be applied to both median and centre facility location problems, either with barriers or forbidden regions. The resulting models are either mixed-integer linear or non-linear programming formulations, depending on the shape of the restricted region and the considered distance measure. Using the new framework, all instances from the existing literature for this class of problems are solved to optimality. The paper also introduces and optimally solves a realistic multifacility problem instance derived from an archipelago vulnerable to earthquakes. This problem instance is significantly more complex than any other instance described in the literature.

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“…A tutorial covering the core geometric methodologies currently applied by researchers in cutting and packing of irregular shapes is presented by [4]. Tools of mathematical modeling of arbitrary object packing problems are given by [6,10,11]. Complexity investigations for cutting and packing problems can be found in [7,9,12,20] .…”

Section: Related Workmentioning

confidence: 99%

“…The objectives we consider here are linear { 2 3 4 6 , , , F F F F } or quadratic { 1 5 , F F }. The phi-functions in (5) are composed of min -and max -combinations of linear and\or non-linear functions including sin -and cos -terms [11]. System 0 λ ≥ , involves linear and\or non-linear functions including sin -and cos -terms.…”

Section: Mathematical Modelmentioning

confidence: 99%

Optimal clustering of a pair of irregular objects

Bennell¹,

Scheithauer

Stoyan

et al. 2014

J Glob Optim

Self Cite

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Abstract.Cutting and packing problems arise in many fields of applications and theory. When dealing with irregular objects, an important subproblem is the identification of the optimal clustering of two objects. Within this paper we consider a container (rectangle, circle, convex polygon) of variable sizes and two irregular objects bounded by circular arcs and/or line segments, that can be continuously translated and rotated. In addition minimal allowable distances between objects and between each object and the frontier of a container, may be imposed. The objects should be arranged within a container such that a given objective will reach its minimal value. We consider a polynomial function as the objective, which depends on the variable parameters associated with the objects and the container. The paper presents a universal mathematical model and a solution strategy which are based on the concept of phi-functions and provide new benchmark instances of finding the containing region that has either minimal area, perimeter or homothetic coefficient of a given container, as well as finding the convex polygonal hull (or its approximation) of a pair of objects.

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Phi-Functions for 2D Objects Formed by Line Segments and Circular Arcs

Cited by 37 publications

References 14 publications

Open Source Multi-Head 3D Printer for Polymer-Metal Composite Component Manufacturing

Open Source Multi-Head 3D Printer for Polymer-Metal Composite Component Manufacturing

A modelling framework for solving restricted planar location problems using phi-objects

Optimal clustering of a pair of irregular objects

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