Spline Function Method Analysis Nature Frequency of Annular Foundations

2011 ◽  
Vol 128-129 ◽  
pp. 307-313
Author(s):  
Xiu Yun Gao ◽  
Ru Xin Jing ◽  
Jian Hui Song
Keyword(s):  
Function Method ◽  
Spline Function ◽  
Dynamical Equation ◽  
Curve Beam ◽  
Minimum Potential Energy ◽  
Oil Storage ◽  
Nature Frequency ◽  
Minimum Potential ◽  
Method Analysis ◽  
Good Agreement

The foundation style of such construction as liquefied oil storage tank and environmental protected reaction pool is mostly annular foundation. In the paper, the annular foundation will be put on WINKER foundation, and then the annular foundation will be simplified as a curve beam, the cubic B spline functions as displacement functions of curve beam. The dynamical equation and the nature frequency of annular foundation based on the instantaneous principle of minimum potential energy, and put forward Spline Function Method to solve the nature frequency of annular foundation. Numerical examples are provided to demonstrate the simplicity and effectiveness of the present method. The results are in good agreement with experimental data.

A Quasi-Greens Function Method for the Bending Problem of Simply Supported Polygonal Shallow Spherical Shells on Pasternak Foundation

2013 ◽  
Vol 353-356 ◽  
pp. 3215-3219
Author(s):  
Shan Qing Li ◽  
Hong Yuan
Keyword(s):  
Function Method ◽  
Homogeneous Boundary Condition ◽  
Fredholm Integral Equations ◽  
Pasternak Foundation ◽  
Boundary Equation ◽  
Spherical Shells ◽  
Simply Supported ◽  
Suitable Form ◽  
Greens Function ◽  
Good Agreement

The quasi-Greens function method (QGFM) is applied to solve the bending problem of simply supported polygonal shallow spherical shells on Pasternak foundation. A quasi-Greens function is established by using the fundamental solution and the boundary equation of the problem. And the function satisfies the homogeneous boundary condition of the problem. Then the differential equation of the problem is reduced to two simultaneous Fredholm integral equations of the second kind by the Greens formula. The singularity of the kernel of the integral equation is overcome by choosing a suitable form of the normalized boundary equation. The comparison with the ANSYS finite element solution shows a good agreement, and it demonstrates the feasibility and efficiency of the proposed method.

Principles of minimum potential energy and complementary energy

2020 ◽  
pp. 228-248
Author(s):  
Lallit Anand ◽  
Sanjay Govindjee
Keyword(s):  
Boundary Condition ◽  
Potential Energy ◽  
Displacement Field ◽  
Mixed Boundary ◽  
Energy Functional ◽  
The Body ◽  
Minimum Potential Energy ◽  
Complementary Energy ◽  
Minimum Potential ◽  
Potential Energy Functional

With the displacement field taken as the only fundamental unknown field in a mixed-boundary-value problem for linear elastostatics, the principle of minimum potential energy asserts that a potential energy functional, which is defined as the difference between the free energy of the body and the work done by the prescribed surface tractions and the body forces --- assumes a smaller value for the actual solution of the mixed problem than for any other kinematically admissible displacement field which satisfies the displacement boundary condition. This principle provides a weak or variational method for solving mixed boundary-value-problems of elastostatics. In particular, instead of solving the governing Navier form of the partial differential equations of equilibrium, one can search for a displacement field such that the first variation of the potential energy functional vanishes. A similar principle of minimum complementary energy, which is phrased in terms of statically admissible stress fields which satisfy the equilibrium equation and the traction boundary condition, is also discussed. The principles of minimum potential energy and minimum complementary energy can also be applied to derive specialized principles which are particularly well-suited to solving structural problems; in this context the celebrated theorems of Castigliano are discussed.

Optimization for Minimum Potential Energy, Maximum Rigidity and Minimum Deformability

1984 ◽  
pp. 9-87
Author(s):  
Andrej M. Brandt ◽  
Wojciech Dzieniszewski ◽  
Stefan Jendo ◽  
Wojciech Marks ◽  
Stefan Owczarek ◽  
...  
Keyword(s):  
Potential Energy ◽  
Minimum Potential Energy ◽  
Minimum Potential ◽  
Energy Maximum

Numerical algorithm for predicting wheel flange wear in trams – Validation in a curved track

2019 ◽  
Vol 234 (10) ◽  
pp. 1156-1169
Author(s):  
Bartosz Łuczak ◽  
Bartosz Firlik ◽  
Tomasz Staśkiewicz ◽  
Wojciech Sumelka
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Computational Effort ◽  
Wheel Wear ◽  
Curved Track ◽  
Method Accuracy ◽  
Elliptic Contact ◽  
Method Analysis ◽  
Good Agreement ◽  
Element Method

In tram operations, flange wear is predominant due to the low-radius curves and inappropriate technical conditions of the infrastructure; hence, investigations should be focused on the interaction between the wheel flange and the rail gauge corner. Moreover, the calculation methods based on the Hertzian model (elliptic contact patch) provide less accurate results due to the contact occurrence in the wheel flange region. This paper presents a methodology of a finite element method to predict the tram wheel wear in complex motions. The new procedure is based on the Abaqus software and several other sub-procedures written in Python and Fortran. Multibody simulations were used to determine the wheel–rail alignment. In this method, accuracy was chosen at the expense of the computational effort. The main steps are: preparation of models and ride scenarios, multibody simulation for calculating the wheel–rail alignment for different track scenarios and multiple runs of finite element method analysis to determine the wear magnitude. The proposed methodology presents a good agreement with the measurements and can be considered as guidelines for a proper configuration of the flange-designing experimental setup where the influence of the technical conditions of the infrastructure should be introduced adequately.

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.

scholarly journals The wave making resistance prediction of a mini-submarine by using tent function method

2018 ◽  
Vol 177 ◽  
pp. 01003 ◽  
Author(s):  
Aries Sulisetyono ◽  
Ardi Nugroho Yulianto
Keyword(s):  
Water Surface ◽  
Function Method ◽  
The Body ◽  
Source Distribution ◽  
Hull Form ◽  
Operational Conditions ◽  
A Value ◽  
Resistance Prediction ◽  
Havelock Source ◽  
Good Agreement

This paper describes the wave making resistance solution of a mini submarine operating in under water surface with different level depth. The Thin ship theory was adopted to solve the problem for a case of the slenderness body. The source distribution along the centre plane of the body was expressed in Green’s function of Havelock source potential under water surface. The Tent function method was proposed to illustrate the hull form based on offsets data, and to solve the Michell integral problem numerically. Four operational conditions were performed i.e. floating, snorkelling, and diving with 0.5m and 1m under water surface. The computational results for the mini submarine with length of 2m and diameter of 0.25m explained a more deeply operated under water surface cause to decrease a value of wave making resistance for all cases of Froude numbers. While in the diving conditions of 0.5m and 0.1m under the water surface, the wave making resistance were resulted about 64% and 74% less than the case of floating condition respectively. Furthermore, the effect of vertical fin on the body was investigated, where the wave making resistance could increase average 7.2% in snorkelling, 11.4% in 0.5m diving, and in the 1m diving about 9.07% for all Froude numbers. Over all the results of this approach shown a good agreement with the results come from Mitchell code.

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