Algebraic graph statics
نویسندگان
چکیده
This paper presents a general, non-procedural, algebraic approach to graphical analysis of structures. Using graph theoretical properties of reciprocal graphs, the geometrical relation between the form and force diagrams used in graphic statics is written algebraically. These formulations have been found to be equivalent to the equilibrium equations used in matrix analysis of planar, self-stressed structural systems. The significance and uses of this general approach are demonstrated through several examples and it is shown that it provides a robust back-end for a real-time, interactive and flexible computational implementation of traditional graphic statics. © 2014 Elsevier Ltd. All rights reserved.
منابع مشابه
The Banach Type Contraction for Mappings on Algebraic Cone Metric Spaces Associated with An Algebraic Distance and Endowed with a Graph
In this work, we define the notion of an algebraic distance in algebraic cone metric spaces defined by Niknam et al. [A. Niknam, S. Shamsi Gamchi and M. Janfada, Some results on TVS-cone normed spaces and algebraic cone metric spaces, Iranian J. Math. Sci. Infor. 9 (1) (2014), 71--80] and introduce some its elementary properties. Then we prove the existence and uniqueness of fixed point for a B...
متن کاملChebyshev's Algebraic Inequality and comparative statics under uncertainty
We apply a non-monotonic version of Chebyshev's Algebraic Inequality in problems of comparative statics under uncertainty. © 2006 Elsevier B.V. All rights reserved.
متن کاملThe traffic statics problem in a road network
In this study we define and solve the traffic statics problem in an open diverge-merge network based on a multi-commodity kinematic wave model, whose entropy conditions are given by invariant flux functions derived from macroscopic merging and diverging rules. In this problem, we are interested in finding stationary states on all links when origin demands, destination supplies, and route choice...
متن کاملTHE (△,□)-EDGE GRAPH G△,□ OF A GRAPH G
To a simple graph $G=(V,E)$, we correspond a simple graph $G_{triangle,square}$ whose vertex set is ${{x,y}: x,yin V}$ and two vertices ${x,y},{z,w}in G_{triangle,square}$ are adjacent if and only if ${x,z},{x,w},{y,z},{y,w}in Vcup E$. The graph $G_{triangle,square}$ is called the $(triangle,square)$-edge graph of the graph $G$. In this paper, our ultimate goal is to provide a link between the ...
متن کاملA Kind of Non-commuting Graph of Finite Groups
Let g be a fixed element of a finite group G. We introduce the g-noncommuting graph of G whose vertex set is whole elements of the group G and two vertices x,y are adjacent whenever [x,y] g and [y,x] g. We denote this graph by . In this paper, we present some graph theoretical properties of g-noncommuting graph. Specially, we investigate about its planarity and regularity, its clique number a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Computer-Aided Design
دوره 53 شماره
صفحات -
تاریخ انتشار 2014