Nonlinear Spatial Equilibria and Stability of Cables Under Uni-axial Torque and Thrust

1994 ◽  
Vol 61 (4) ◽  
pp. 879-886 ◽  
Author(s):  
C.-L. Lu ◽  
N. C. Perkins
Keyword(s):  
Closed Form ◽  
Elliptic Integral ◽  
Broad Class ◽  
Local Equilibrium ◽  
Three Dimensional ◽  
Equilibrium States ◽  
Form Complex ◽  
Closed Form Solutions ◽  
The Stability ◽  
Low Tension

Low tension cables subject to torque may form complex three-dimensional (spatial) equilibria. The resulting nonlinear static deformations, which are dominated by cable flexure and torsion, may produce interior loops or kinks that can seriously degrade the performance of the cable. Using Kirchhoffrod assumptions, a theoretical model governing cable flexure and torsion is derived herein and used to analyze (1) globally large equilibrium states, and (2) local equilibrium stability. For the broad class of problems described by pure boundary loading, the equilibrium boundary value problem is integrable and admits closed-form elliptic integral solutions. Attention is focused on the example problem of a cable subject to uni-axial torque and thrust. Closed-form solutions are presented for the complex three-dimensional equilibrium states which, heretofore, were analyzed using purely numerical methods. Moreover, the stability of these equilibrium states is assessed and new and important stability conclusions are drawn.

Solutions to the Vector Tetrahedron Equation

1965 ◽  
Vol 87 (2) ◽  
pp. 228-234 ◽  
Author(s):  
Milton A. Chace
Keyword(s):  
Closed Form ◽  
Digital Computer ◽  
Three Dimensional ◽  
Dimensional Vector ◽  
Spherical Coordinates ◽  
Tetrahedron Equation ◽  
Position Determination ◽  
Closed Form Solutions

A set of nine closed-form solutions are presented to the single, three-dimensional vector tetrahedron equation, sum of vectors equals zero. The set represents all possible combinations of unknown spherical coordinates among the vectors, assuming the coordinates are functionally independent. Optimum use is made of symmetry. The solutions are interpretable and can be evaluated reliably by digital computer in milliseconds. They have been successfully applied to position determination of many three-dimensional mechanisms.

scholarly journals Reconstruction of three-dimensional maps based on closed-form solutions of the variational problem of multisensor data registration

2019 ◽  
Vol 484 (6) ◽  
pp. 672-677
Author(s):  
A. V. Vokhmintcev ◽  
A. V. Melnikov ◽  
K. V. Mironov ◽  
V. V. Burlutskiy
Keyword(s):  
Closed Form ◽  
Large Scale ◽  
Three Dimensional ◽  
Dynamic Environment ◽  
Closed Form Solution ◽  
Point Clouds ◽  
Accurate Method ◽  
Form Solution ◽  
Closed Form Solutions ◽  
Reconstruction Methods

A closed-form solution is proposed for the problem of minimizing a functional consisting of two terms measuring mean-square distances for visually associated characteristic points on an image and meansquare distances for point clouds in terms of a point-to-plane metric. An accurate method for reconstructing three-dimensional dynamic environment is presented, and the properties of closed-form solutions are described. The proposed approach improves the accuracy and convergence of reconstruction methods for complex and large-scale scenes.

Kinematics of a Novel Single-Loop Under-Actuated Wrist

2012 ◽  
Author(s):  
Raffaele Di Gregorio
Keyword(s):  
Path Planning ◽  
Closed Form ◽  
Nonholonomic Constraint ◽  
Three Dimensional ◽  
Single Loop ◽  
Closed Form Solutions ◽  
Position Analysis ◽  
Tracking Tasks ◽  
Planning Algorithm ◽  
Path Planning Algorithm

A novel type of parallel wrist (PW) is proposed which, differently from previously presented PWs, features a single-loop architecture and only one nonholonomic constraint. Due to the presence of a nonholonomic constraint, the proposed PW type is under-actuated, that is, it is able to control the platform orientation in a three-dimensional workspace by employing only two actuated pairs, one prismatic (P) and the other revolute (R); and it cannot perform tracking tasks. Position analysis and path planning of this novel PW are studied. In particular, all the relevant position analysis problems are solved in closed form, and, based on these closed-form solutions, a path-planning algorithm is built.

On the Efficiency of Analyzing 3D Anisotropic, Transversely Isotropic, and Isotropic Bodies in BEM

2010 ◽  
Vol 26 (4) ◽  
pp. 483-491
Author(s):  
Y. C. Shiah ◽  
W. X. Sun
Keyword(s):  
Closed Form ◽  
Computational Efficiency ◽  
Transverse Isotropy ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Fundamental Solutions ◽  
Engineering Practice ◽  
Closed Form Solutions ◽  
Anisotropic Bodies ◽  
Isotropic Bodies

ABSTRACTDue to a lack of closed-form solutions for three dimensional anisotropic bodies, the computational burden of evaluating the fundamental solutions in the boundary element method (BEM) has been a research focus over the years. In engineering practice, transversely isotropic material has gained popularity in the use of composites. As a degenerate case of the generally anisotropic material, transverse isotropy still needs to be treated separately to ease the computations. This paper aims to investigate the computational efficiency of the BEM implementations for 3D anisotropic, transversely isotropic, and isotropic bodies. For evaluating the fundamental solutions of 3D anisotropy, the explicit formulations reported in [1,2] are implemented. For treating transversely isotropic materials, numerous closed form solutions have been reported in the literature. For the present study, the formulations presented by Pan and Chou [3] are particularly employed. At the end, a numerical example is presented to compare the computational efficiency of the three cases and to demonstrate how the CPU time varies with the number of meshes.

Some Fundamental Thermoelastic Problems in Orthotropic Slabs

1966 ◽  
Vol 33 (1) ◽  
pp. 45-51 ◽  
Author(s):  
B. R. Baker
Keyword(s):  
Steady State ◽  
Temperature Distribution ◽  
Closed Form ◽  
Fourier Transforms ◽  
Broad Class ◽  
Complex Stress ◽  
Closed Form Solutions ◽  
Definite Form ◽  
Stress Components ◽  
Thermoelastic Problems

Steady-state problems of stresses in orthotropic slabs subjected to forces and temperature distribution on the faces are solved by means of Fourier transforms. The usual direct applications in the literature are shown for simple examples to lead to divergent integrals but, by introduction of generalized transforms, a very broad class of problems can be handled. As a part of these considerations, a more definite form of Saint-Venant’s principle is obtained. For a certain class of material constants, it is possible to obtain closed-form solutions for stresses when concentrated loads or temperature sources are applied to the faces of the slab. Results are presented for several examples in the form of complex stress potentials and graphs of the corresponding stress components.

Optical solitons and closed form solutions to the (3+1)-dimensional resonant Schrödinger dynamical wave equation

2020 ◽  
Vol 34 (30) ◽  
pp. 2050291 ◽  
Author(s):  
Usman Younas ◽  
Aly R. Seadawy ◽  
M. Younis ◽  
S. T. R. Rizvi
Keyword(s):  
Closed Form ◽  
Gordon Equation ◽  
Velocity Dispersion ◽  
Group Velocity Dispersion ◽  
Three Dimensional ◽  
Soliton Solutions ◽  
Closed Form Solutions ◽  
Contour Plots ◽  
Complex Phenomena ◽  
Selection Of

This paper investigates the new solitons and closed form solutions to [Formula: see text] dimensional resonant nonlinear Schrödinger equation (RNLSE) that explains the behavior of waves with the effect of group velocity dispersion and resonant nonlinearities in the optical fiber. The soliton solutions in single and combined forms like dark, singular, and dark-singular in mixed form are extracted by means of two innovative integration norms namely extended sinh-Gordon equation expansion and [Formula: see text]-expansion function methods. Moreover, kink and closed form solutions are also observed under different constraint conditions. By choosing the suitable selection of the parameters, three dimensional, two dimensional, and contour plots are sketched. The obtained outcomes show that the applied computational strategies are direct, efficient, concise and can be implemented in more complex phenomena with the assistant of symbolic computations.

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