Derivation of Geometrieal Nonlinear Stiffness Matrix for Space Beam Element

2011 ◽  
Vol 368-373 ◽  
pp. 3106-3112
Author(s):  
Wei Shuo Wang ◽  
Guang Jian Bao
Keyword(s):  
Stiffness Matrix ◽  
Beam Element ◽  
Axial Deformation ◽  
Energy Principle ◽  
Geometrically Nonlinear Analysis ◽  
Minimum Potential ◽  
Stress Matrix ◽  
Minimum Potential Energy Principle ◽  
Space Beam Element ◽  
The Impact

A space beam element is derived for geometrically nonlinear analysis based on the principle of minimum potential energy principle. The impact of high-order nonlinear is considered by introducing the axial deformation into the stiffness matrix. The large displacement matrix is divided into four and the initial stress matrix into three submatrix

The Meticulous Analysis of Skew Beam Based on the Space Skew Beam Element Method

2014 ◽  
Vol 578-579 ◽  
pp. 220-224
Author(s):  
Xiang Feng Xu ◽  
Feng Zhang ◽  
Guang Zhi Qi
Keyword(s):  
Stiffness Matrix ◽  
Beam Element ◽  
Finite Element Models ◽  
Single Beam ◽  
Skew Bridge ◽  
Proposed Model ◽  
Minimum Potential ◽  
Space Beam Element ◽  
Beam Bridge ◽  
Grillage Method

When a skew bridge is analyzed, it is difficult to treat skew boundary conditions with general space beam element in single beam calculation of skew beam bridge. The stiffness of skew bridge cannot be simulated efficiently. In order to improve the accuracy of skew bridge, the stiffness matrix of the space skew beam element is derived based on the principle of minimum potential in this paper, this element is suitable for single beam of skew bridge and grillage method. A corresponding program is completed by Visual C++, the calculated results of different finite element models are compared, so the validity of the proposed model in this paper is validated. This paper can provide reference for plane and space calculation of the skew bridge design.

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.

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 .

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.

A variational method for calculating the longitudinal deformation of a shield tunnel in soft soil caused by grouting under tunnel

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Honggui Di ◽  
Shihao Huang ◽  
Longlong Fu ◽  
Binglong Wang
Keyword(s):  
Variational Method ◽  
Soft Soil ◽  
Shield Tunnel ◽  
Longitudinal Deformation ◽  
Energy Principle ◽  
Content Type ◽  
Minimum Potential ◽  
Minimum Potential Energy Principle ◽  
Case Validation ◽  
High Computational Efficiency

Purpose The paper aims to predict longitudinal deformation of a tunnel caused by grouting under the tunnel bottom in advance according to the grouting parameters, which can ensure the safety of the tunnel structure during the grouting process and also help to design the grouting parameters. Design/methodology/approach The paper adopted the analytical approach for calculating the longitudinal deformation of a shield tunnel caused by grouting under a tunnel, including usage of the Mindlin’s solution, the minimum potential energy principle and case validation. Findings The paper provides a variational method for calculating the longitudinal deformation of a shield tunnel in soft soil caused by grouting under the tunnel, which has high computational efficiency and accuracy. Originality/value This paper fulfils an identified need to study how the longitudinal deformation of a shield tunnel in soft soil caused by grouting under the tunnel can be calculated.

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.

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.

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