Algorithm and Software for Integration over a Convex Polyhedron

2006 ◽  
pp. 273-283 ◽  
Author(s):  
Mark Korenblit ◽  
Efraim Shmerling
Keyword(s):  
Convex Polyhedron

scholarly journals Data-based polyhedron model for optimization of engineering structures involving uncertainties

2021 ◽  
Vol 2 ◽  
Author(s):  
Zhiping Qiu ◽  
Han Wu ◽  
Isaac Elishakoff ◽  
Dongliang Liu
Keyword(s):  
Linear Programming ◽  
Convex Polyhedron ◽  
Linear Optimization ◽  
Optimal Solution ◽  
Composite Plates ◽  
Convex Polyhedra ◽  
Chebyshev Inequality ◽  
Engineering Structures ◽  
Load Bearing ◽  
Polyhedron Model

Abstract This paper studies the data-based polyhedron model and its application in uncertain linear optimization of engineering structures, especially in the absence of information either on probabilistic properties or about membership functions in the fussy sets-based approach, in which situation it is more appropriate to quantify the uncertainties by convex polyhedra. Firstly, we introduce the uncertainty quantification method of the convex polyhedron approach and the model modification method by Chebyshev inequality. Secondly, the characteristics of the optimal solution of convex polyhedron linear programming are investigated. Then the vertex solution of convex polyhedron linear programming is presented and proven. Next, the application of convex polyhedron linear programming in the static load-bearing capacity problem is introduced. Finally, the effectiveness of the vertex solution is verified by an example of the plane truss bearing problem, and the efficiency is verified by a load-bearing problem of stiffened composite plates.

On antipodes on a convex polyhedron

2005 ◽  
Vol 5 (4) ◽  
Author(s):  
Joël Rouyer
Keyword(s):  
Convex Polyhedron

scholarly journals Convex Polyhedron Method to Stability of Continuous Systems with Two Additive Time-Varying Delay Components

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Tiejun Li ◽  
Junkang Tian
Keyword(s):  
Stability Criterion ◽  
Convex Polyhedron ◽  
Linear Matrix ◽  
Continuous Systems ◽  
Time Varying ◽  
Time Varying Delay ◽  
Polyhedron Method ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Varying Delay

This paper is concerned with delay-dependent stability for continuous systems with two additive time-varying delay components. By constructing a new class of Lyapunov functional and using a new convex polyhedron method, a new delay-dependent stability criterion is derived in terms of linear matrix inequalities. The obtained stability criterion is less conservative than some existing ones. Finally, numerical examples are given to illustrate the effectiveness of the proposed method.

scholarly journals A fast algorithm for line clipping by convex polyhedron in E3

1997 ◽  
Vol 21 (2) ◽  
pp. 209-214 ◽  
Author(s):  
Václav Skala
Keyword(s):  
Fast Algorithm ◽  
Convex Polyhedron ◽  
Line Clipping

scholarly journals Can a convex polyhedron have a developable face-cycle?

2000 ◽  
Vol 235 (2) ◽  
pp. 267-270 ◽  
Author(s):  
Hiroshi Maehara
Keyword(s):  
Convex Polyhedron

scholarly journals Computing a flattest, undercut-free parting line for a convex polyhedron, with application to mold design

1999 ◽  
Vol 13 (4) ◽  
pp. 229-252 ◽  
Author(s):  
Jayanth Majhi ◽  
Prosenjit Gupta ◽  
Ravi Janardan
Keyword(s):  
Convex Polyhedron ◽  
Mold Design

scholarly journals The volume of a compact hyperbolic antiprism

2018 ◽  
Vol 27 (13) ◽  
pp. 1842010
Author(s):  
Nikolay Abrosimov ◽  
Bao Vuong
Keyword(s):  
Symmetry Group ◽  
Hyperbolic Space ◽  
Convex Polyhedron ◽  
Rotational Symmetry ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Dihedral Angles ◽  
Integral Formulas ◽  
Necessary And Sufficient

We consider a compact hyperbolic antiprism. It is a convex polyhedron with [Formula: see text] vertices in the hyperbolic space [Formula: see text]. This polyhedron has a symmetry group [Formula: see text] generated by a mirror-rotational symmetry of order [Formula: see text], i.e. rotation to the angle [Formula: see text] followed by a reflection. We establish necessary and sufficient conditions for the existence of such polyhedra in [Formula: see text]. Then we find relations between their dihedral angles and edge lengths in the form of a cosine rule. Finally, we obtain exact integral formulas expressing the volume of a hyperbolic antiprism in terms of the edge lengths.

scholarly journals Bracing Zonohedra With Special Faces

2015 ◽  
Vol 3 (1-2) ◽  
pp. 88-95 ◽  
Author(s):  
Gyula Nagy
Keyword(s):  
Convex Polyhedron ◽  
Three Dimensional ◽  
Equivalence Classes ◽  
Frame Structure ◽  
Sufficient Condition ◽  
Preliminary Design ◽  
Necessary And Sufficient Condition ◽  
Special Assumption ◽  
Centrally Symmetric ◽  
Necessary And Sufficient

Abstract The analysis of simpler preliminary design gives useful input for more complicated three-dimensional building frame structure. A zonohedron, as a preliminary structure of design, is a convex polyhedron for which each face possesses central symmetry. We considered zonohedron as a special framework with the special assumption that the polygonal faces can be deformed in such a way that faces remain planar and centrally symmetric, moreover the length of all edges remains unchanged. Introducing some diagonal braces we got a new mechanism. This paper deals with the flexibility of this kind of mechanisms, and investigates the rigidity of the braced framework. The flexibility of the framework can be characterized by some vectors, which represent equivalence classes of the edges. A necessary and sufficient condition for the rigidity of the braced rhombic face zonohedra is posed. A real mechanical construction, based on two simple elements, provides a CAD prototype of these new mechanisms.

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