In-Plane Bending of a U-Shaped Circular Tube With End Constraints

1970 ◽  
Vol 92 (4) ◽  
pp. 792-796 ◽  
Author(s):  
Henry J. Thailer ◽  
David H. Cheng
Keyword(s):  
General Solution ◽  
Potential Energy ◽  
Circular Tube ◽  
Total Potential Energy ◽  
Center Line ◽  
Bending Moments ◽  
Series Form ◽  
Total Potential ◽  
In Series ◽  
Plane Bending

A general solution is presented for a thin, curved, circular tube containing rigid end constraints, subjected to in-plane bending moments. Inextensibility of the meridional center line is assumed. The displacements are expanded in series form and the equations of equilibrium are guaranteed by minimizing the total potential energy. The minimization is achieved in the manner of Rayleigh-Ritz. Analytical results are compared with published experimental results and existing axisymmetric theory.

In-Plane Bending of Curved Circular Tubes

1968 ◽  
Vol 90 (4) ◽  
pp. 666-670 ◽  
Author(s):  
D. H. Cheng ◽  
H. J. Thailer
Keyword(s):  
Experimental Data ◽  
General Solution ◽  
Compatibility Condition ◽  
Circular Tube ◽  
Series Expansions ◽  
Center Line ◽  
Complementary Energy ◽  
Circular Tubes ◽  
Binomial Expansion ◽  
Plane Bending

A general solution is presented for a thin, curved circular tube under in-plane bending. It includes the solution given by Clark and Reissner as a particular case in which the ratio of the radius of the tube to the radius of its center line is very small. The series expansions satisfy the equilibrium equation for any radius ratio while the compatibility condition is guaranteed by minimizing the complementary energy. The minimization is achieved in the manner of Raileigh-Ritz whereas the evaluation of integrals are facilitated by the use of binomial expansion. Numerical results correlate well with the experimental data. The solution is more rapidly convergent as compared to the existing analytical methods.

Analysis of a Planar Tensegrity-Based Compliant Mechanism

2010 ◽  
Author(s):  
Youngjin Moon ◽  
Carl D. Crane ◽  
Rodney G. Roberts
Keyword(s):  
Potential Energy ◽  
Stiffness Matrix ◽  
Compliant Mechanism ◽  
Total Potential Energy ◽  
Numerical Examples ◽  
Total Potential ◽  
Moving Body ◽  
In Series ◽  
Spring Constants

This paper presents an analysis of a planar tensegrity-based mechanism. In this study, a moving body is joined to ground by four compliant leg connectors. Each leg connector is comprised of a spring in series with an adjustable length piston. Two problems are solved in this paper. In the first, the values of the four spring constants and free lengths are given and the lengths of the four pistons are determined such that: (1) the top body is positioned and oriented at a desired pose; (2) the top body is at equilibrium while a specified external wrench is applied; and (3) the total potential energy stored in the four springs equals some desired value. In the second problem, the values for the four spring free lengths are given and the values for the four spring constants and the lengths of the four pistons are determined such that conditions (1) and (2) from above are met and also the instantaneous stiffness matrix of the top body equals a specified set of matrix values. The paper formulates the solutions of these two problems. Numerical examples are presented.

Position and Force Analysis of a Planar Tensegrity-Based Compliant Mechanism

2012 ◽  
Vol 4 (1) ◽  
Author(s):  
Youngjin Moon ◽  
Carl D. Crane ◽  
Rodney G. Roberts
Keyword(s):  
Potential Energy ◽  
Stiffness Matrix ◽  
Compliant Mechanism ◽  
Total Potential Energy ◽  
Force Analysis ◽  
Numerical Examples ◽  
Total Potential ◽  
Moving Body ◽  
In Series ◽  
Spring Constants

This paper presents an analysis of a planar tensegrity-based mechanism. In this study, a moving body is joined to ground by four compliant leg connectors. Each leg connector is comprised of a spring in series with an adjustable length piston. Two problems are solved in this paper. In the first, the values of the four spring constants and free lengths are given and the lengths of the four pistons are determined such that (1) the top body is positioned and oriented at a desired pose, (2) the top body is at equilibrium while a specified external wrench is applied, and (3) the total potential energy stored in the four springs equals some desired value. In the second problem, the values for the four spring free lengths are given and the values for the four spring constants and the lengths of the four pistons are determined such that conditions (1) and (2) from above are met and also the instantaneous stiffness matrix of the top body equals a specified set of matrix values. The paper formulates the solutions of these two problems. Numerical examples are presented.

A simplified formulation of adhesion problems with elastic plates

2009 ◽  
Vol 465 (2107) ◽  
pp. 2217-2230 ◽  
Author(s):  
Carmel Majidi ◽  
George G. Adams
Keyword(s):  
Potential Energy ◽  
Contact Area ◽  
Contact Region ◽  
Bending Moment ◽  
Total Potential Energy ◽  
Work Of Adhesion ◽  
Contact Radius ◽  
Algebraic Complexity ◽  
Elastic Plates ◽  
Total Potential

The solution of adhesion problems with elastic plates generally involves solving a boundary-value problem with an assumed contact area. The contact region is then found by minimizing the total potential energy with respect to the contact area (i.e. the contact radius for the axisymmetric case). Such a procedure can be extremely long and tedious. Here, we show that the inclusion of adhesion is equivalent to specifying a discontinuous internal bending moment at the contact region boundary. The magnitude of this moment discontinuity is related to the work of adhesion and flexural rigidity of the plate. Such a formulation can greatly reduce the algebraic complexity of solving these problems. It is noted that the related plate contact problems without adhesion can also be solved by minimizing the total potential energy. However, it has long been recognized that it is mathematically more efficient to find the contact area by specifying a continuous internal bending moment at the boundary of the contact region. Thus, our moment discontinuity method can be considered to be a generalization of that procedure which is applicable for problems with adhesion.

An Optimization Method for the Static Balancing of Manipulators Using Springs

2020 ◽  
Author(s):  
Jieyu Wang ◽  
Xianwen Kong
Keyword(s):  
Potential Energy ◽  
Objective Function ◽  
Multiple Solutions ◽  
Optimization Method ◽  
Total Potential Energy ◽  
Static Balancing ◽  
Attachment Point ◽  
Total Potential

Abstract This paper discusses a novel optimization method to design statically balanced manipulators. Only springs are used to balance the manipulators composed of revolute (R) joints. Since the total potential energy of the system is constant when statically balanced, the sum of squared differences between the two potential energy when giving different random values of joint variables is set as the objective function. Then the optimization tool of MATLAB is used to obtain the spring attachment points. The results show that for a 1-link manipulator mounted on an R joint, in addition to attaching the spring right above the R joint, the attachment point can have offset. It also indicates that an arbitrary spatial manipulator with n link, whose weight cannot be neglected, can be balanced using n springs. Using this method, the static balancing can be readily achieved, with multiple solutions.

Automatic Refinement of FE Shell Models Based on a Local Energy Function

2013 ◽  
Author(s):  
Antonio Carminelli ◽  
Giuseppe Catania
Keyword(s):  
Potential Energy ◽  
Local Density ◽  
Free Vibration Analysis ◽  
Element Model ◽  
Companion Paper ◽  
Total Potential Energy ◽  
Shape Functions ◽  
Total Potential ◽  
Error Functional ◽  
Local Patch

This paper deals with an adaptive refinement technique of a B-spline degenerate shell finite element model, for the free vibration analysis of curved thin and moderately thick-walled structures. The automatic refinement of the solution is based on an error functional related to the density of the total potential energy. The model refinement is generated by locally increasing, in a sub-domain R of a local patch domain, the number of shape functions while maintaining constant the functions polynomial order. The local refinement strategy is described in a companion paper, written by the same authors of this paper and presented in this Conference. A two-step iterative procedure is proposed. In the first step, one or more sub domains to be refined are identified by means of a point-wise error functional based on the system total potential energy local density. In the second step, the number of shape functions to be added is iteratively increased until the difference of the total potential energy, calculated on the sub domain between two iteration, is below a user defined tolerance. A numerical example is presented in order to test the proposed approach. Strengths and limits of the approach are critically discussed.

First-Principles Study on Crystal Configuration and Many-Body Cohesive Energy of Solid Argon

2019 ◽  
Vol 807 ◽  
pp. 135-140
Author(s):  
Xi Jin Fu
Keyword(s):  
Potential Energy ◽  
Interaction Energy ◽  
First Principles ◽  
Total Potential Energy ◽  
Basis Set ◽  
Many Body ◽  
Body Interaction ◽  
Total Potential ◽  
Geometric Configurations ◽  
Solid Argon

Based on the first-principles, using CCSD(T) ab initio calculation method, many-body potential energy of solid argon are accurately calculated with the atomic distance R from 2.0Å to 3.6Å at T=300K, and firstly establish and discuss the face-centered cubic (fcc) atomic crystal configurations of two-, three-, and four-body terms by geometry optimization. The results shows that the total number of (Ar)2 clusters is 903, which belongs to 12 different geometric configurations, the total number of (Ar)3 clusters is 861, which belongs to 25 different geometric configurations, and the total number of (Ar)4 clusters of is 816 which belongs to 27 different geometric configurations. We find that the CCSD(T) with the aug-cc-pVQZ basis set is most accurate and practical by comprehensive consideration. The total potential energy Un reachs saturation at R>2.0Å when the only two-and three-body interaction energy are considered. When R≤2.0Å, the total potential energy Un must consider four-and higher-body interaction energy to achieve saturation. Many-body expansion potential of fcc solid argon is an exchange convergent series.

Energy-free adjustment of gravity equilibrators by adjusting the spring stiffness

2008 ◽  
Vol 222 (9) ◽  
pp. 1839-1846 ◽  
Author(s):  
W D van Dorsser ◽  
R Barents ◽  
B M Wisse ◽  
M Schenk ◽  
J L Herder
Keyword(s):  
Potential Energy ◽  
Total Potential Energy ◽  
Spring Stiffness ◽  
External Energy ◽  
Static Balancing ◽  
Concept Model ◽  
Total Potential ◽  
Novel Variant ◽  
Energy Conserving

Static balancing is a useful concept to reduce the operating effort of mechanisms. Spring mechanisms are used to achieve a constant total potential energy, thus eliminating any preferred position. Quasi-statically, the mechanism, once statically balanced, can be moved virtually without the operating energy. In some cases, it is desirable to adjust the characteristic of the balancer, for instance, due to a change in the payload in a gravity balanced mechanism. The adjustment of current static balancers requires significant operating energy. This paper will present a novel variant to adjust the spring- and linkage-based static balancers without the need for external energy. The variant makes use of the possibility to adjust the spring stiffness in an energy-conserving way by adjusting the number of active coils. The conditions under which it functions properly will be given, and a proof of the concept model will be shown.

Structure électronique de dérivés sulfures. XI. Thiétanne et dérivés

1975 ◽  
Vol 53 (8) ◽  
pp. 1224-1236 ◽  
Author(s):  
Claude Guimon ◽  
Daniel Liotard ◽  
Geneviève Pfister-Guillouzo
Keyword(s):  
Experimental Data ◽  
Potential Energy ◽  
Total Potential Energy ◽  
Geometric Parameters ◽  
The Third ◽  
Total Potential ◽  
Partial Energy ◽  
Chloro Derivatives ◽  
Semi Empirical ◽  
Structure Electronique

The conformations of thietane, thietane sulfoxide, and their 3-chloro derivatives were obtained theoretically by minimization of the energy with respect to geometric parameters using the semi-empirical CNDO/2 method extended to the third period. The results agree well with known experimental data. The respective stabilities of the different conformers are explained by partial energy results obtained by a bicentric partition of the total potential energy of the molecules. [Journal translation]

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