On the Inflation of a Plane Nonlinear Membrane

1974 ◽  
Vol 41 (3) ◽  
pp. 767-771 ◽  
Author(s):  
W. W. Feng ◽  
P. Huang
Keyword(s):  
Potential Energy ◽  
Minimum Potential Energy ◽  
Equilibrium Equations ◽  
Energy Principle ◽  
Strain Energy Density Function ◽  
Total Potential ◽  
Minimum Potential ◽  
Minimum Potential Energy Principle ◽  
Admissible Functions ◽  
Nonlinear Membrane

The deformed configurations of an inflated flat nonlinear membrane are obtained by the minimum potential energy principle. The deformed configurations of the membrane are assumed to be represented by a series of geometric admissible functions with unknown coefficients. The unknown coefficients that minimize the total potential energy of the deformed membrane are determined by Fletcher and Powell’s [1] method. The strain-energy-density function for the numerical calculations is assumed to have the Mooney form. The results for a particular case when the Mooney membrane reduces to the neo-Hookean membrane, agree with the previous results obtained by numerical integration of the corresponding equilibrium equations.

A Global Extremum Principle in Mixed Form for Equilibrium Analysis With Elastic/Stiffening Materials (a Generalized Minimum Potential Energy Principle)

1994 ◽  
Vol 61 (4) ◽  
pp. 914-918 ◽  
Author(s):  
J. E. Taylor
Keyword(s):  
Potential Energy ◽  
Problem Formulation ◽  
Extremum Problem ◽  
Equilibrium Analysis ◽  
Minimum Potential Energy ◽  
Problem Statement ◽  
Energy Principle ◽  
Potential Energy Principle ◽  
Minimum Potential ◽  
Minimum Potential Energy Principle

An extremum problem formulation is presented for the equilibrium mechanics of continuum systems made of a generalized form of elastic/stiffening material. Properties of the material are represented via a series composition of elastic/locking constituents. This construction provides a means to incorporate a general model for nonlinear composites of stiffening type into a convex problem statement for the global equilibrium analysis. The problem statement is expressed in mixed “stress and deformation” form. Narrower statements such as the classical minimum potential energy principle, and the earlier (Prager) model for elastic/locking material are imbedded within the general formulation. An extremum problem formulation in mixed form for linearly elastic structures is available as a special case as well.

Analysis of Assumed Mooring Arrangement for Maritime Class Ship

1968 ◽  
Vol 5 (03) ◽  
pp. 257-266
Author(s):  
John L. Horton ◽  
Raymond A. Yagle
Keyword(s):  
Wind Tunnel ◽  
Potential Energy ◽  
Great Lakes ◽  
Minimum Potential Energy ◽  
Energy Principle ◽  
Wind Tunnel Tests ◽  
Potential Energy Principle ◽  
Minimum Potential ◽  
Minimum Potential Energy Principle

An assumed but routine mooring arrangement for a standard Great Lakes ship--in this case a Maritime Class vessel--is analyzed to ascertain what wind conditions would be sufficient to establish the sequence necessary to cause parting of one line, followed by parting of second and third lines and, finally, by full failure of the mooring arrangement. Wind-tunnel tests on a model of the ship are reviewed, and application of the minimum potential energy principle used in the analysis is illustrated.

Stability Analysis of Slope with Arbitrary Sliding Surface on Multi Strata Using Minimum Potential Energy Principle

2011 ◽  
Vol 250-253 ◽  
pp. 2588-2591 ◽  
Author(s):  
Shu Jie Wen ◽  
You Li ◽  
Xin Chen
Keyword(s):  
Stability Analysis ◽  
Slope Stability ◽  
Potential Energy ◽  
Safety Factor ◽  
Sliding Surface ◽  
Minimum Potential Energy ◽  
Energy Principle ◽  
Potential Energy Principle ◽  
Minimum Potential ◽  
Minimum Potential Energy Principle

As a rule,the natural slope is not homogeneous,and its sliding surface is arbitrary. However,the common slope stability analysis methods used to assume shape of sliding surface and slope homogeneity,and the calculation process is so complex that accuracy of results is decreasing.In this study,the potential energy function of sliding body is established for slope with arbitrary sliding surface on multi strata.Using minimum potential energy principle, the displacement of sliding body can be got. Then based on Moore - Coulomb criterion and condition of force equilibrium in the sliding direction, the safety factor can be got directly. Case studies show: ①This slope stability analysis methods is valid.② Different definition of safety factor leads to different analysis result.

Research on Ship Part Nesting System Based on Energy Principle and Intelligent Optimization

2013 ◽  
Vol 694-697 ◽  
pp. 2771-2774
Author(s):  
Xiang Qiang Zhong ◽  
Li Dong Liang ◽  
Yan Hong Yang
Keyword(s):  
Potential Energy ◽  
Physical Meaning ◽  
Minimum Potential Energy ◽  
Energy Principle ◽  
Intelligent Optimization ◽  
Potential Energy Principle ◽  
Minimum Potential ◽  
Nesting Problem ◽  
Minimum Potential Energy Principle ◽  
Intersection Test

A nesting system based on minimum potential energy principle and intelligent optimization for ship part nesting problem was proposed. Discussing polygon judgment and separation, intersection test and collision problems of ship parts, a kind of polygon overlap detection method was put forward, and contacting process was analyzed by use of envelope rectangle intersection test algorithm; During analyzing ship part nesting process based on minimum potential energy principle and genetic algorithm fusion, basic physical meaning of nesting problem was explained from mechanics. Throng intelligent ship part nesting system verification, the algorithm is feasible, physical meaning is clear; it can realize ship part nesting.

Implement of Ameliorated ACM Element in Numerical Manifold Space for Tackling Kirchhoff Plate Bending Problems

2014 ◽  
Vol 638-640 ◽  
pp. 1710-1715
Author(s):  
Hong Wei Guo ◽  
Hong Zheng ◽  
Wei Li
Keyword(s):  
Partition Of Unity ◽  
Plate Bending ◽  
Minimum Potential Energy ◽  
Energy Principle ◽  
Displacement Boundary ◽  
Minimum Potential ◽  
Bending Problems ◽  
Minimum Potential Energy Principle ◽  
Numerical Manifold ◽  
Fourth Order Problems

Ab ridging the chasm between the prevalent ly employed continuum methods (e.g. FEM) and discontinuum methods (e.g. DDA) ,the numerical manifold (NNM) ,which utilizes two covers, namely the mathematical cover and physical cover , has evinced various advantages in solving solid mechanic al issues. The forth-order partial elliptic differential equation governing Kirchhoff plate bending makes it arduous to establish the -regular Lagrangian partition of unity ,nevertheless, this study renders a modified conforming ACM manifold element , irrespective of accreting its cover degrees, to resolve the fourth-order problems. In tandem with the forming of the finite element cover system that erected on r ectangular mesh es , a succession of n umerical manifold formulas are derived on grounds of the minimum potential energy principle and the displacement boundary conditions are executed by penalty function methods. The numerical example elucidates that , compared with the orthodox ACM element , the proposed methods bespeak the accuracy and precipitating convergence of the NMM .

Total potential energy minimization method in structural analysis considering material nonlinearity

2017 ◽  
Vol 3 (3) ◽  
pp. 129 ◽  
Author(s):  
Rasim Temür ◽  
Gebrail Bekdaş ◽  
Yusuf Cengiz Toklu
Keyword(s):  
Structural Analysis ◽  
Potential Energy ◽  
Total Potential Energy ◽  
Metaheuristic Algorithms ◽  
Truss Structures ◽  
Minimum Potential Energy ◽  
Minimization Method ◽  
Total Potential ◽  
Tlbo Algorithm ◽  
Minimum Potential

Minimum potential energy principle is the basis of the most of the well-known traditional techniques used in the structural analysis. This principle determines the equilibrium conditions of systems with reference to minimization of the sum of the total potential energy of the structure. In traditional applications, this methodology is formulized by using matrix operations. A methodology has been proposed in the last decades for structural analyses based on the idea of using metaheuristic algorithms to obtain minimum potential energy of the structural system instead of following this classical approach. This new method, called “Total Potential Optimization using Metaheuristic Algorithms (TPO/MA)”, has been applied in this paper to truss structures considering linear and nonlinear behavior of the structural material. The metaheuristic method used in this process is teaching-learning based optimization (TLBO) algorithm. The proposed technique is applied on numerical examples and results are compared with other techniques in order to test the efficiency of the proposed method. According to results obtained, TPO/MA method with TLBO algorithm is a feasible technique for the investigated problem.

Study on the Influence of Thickness and Width on the Post-Buckling Deformation of Cold-Rolled Strip

2014 ◽  
Vol 941-944 ◽  
pp. 1773-1776
Author(s):  
Dong Cheng Wang ◽  
Xue Feng Zhou ◽  
Hong Min Liu
Keyword(s):  
Rolling Process ◽  
Rolled Strip ◽  
Analysis Method ◽  
Minimum Potential Energy ◽  
Energy Principle ◽  
Potential Energy Principle ◽  
Post Buckling ◽  
Minimum Potential ◽  
Cold Rolled ◽  
Minimum Potential Energy Principle

As a consequence of post-buckling due to high residual stresses caused by the cold-rolling process, long free thin strips frequently show excessive wavy surface. In this paper, a new analytical approach by extending a classic post-buckling analysis method based on the minimum potential energy principle is used to study on the influence of strip thickness and width on the post-buckling deformation for the center and edge wave. It is concluded that the thickness of the strip has significant effect on the flatness defects, while the width does not.

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