scholarly journals Accurate Element of Compressive Bar considering the Effect of Displacement

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Lifeng Tang ◽  
Jing Xu ◽  
Hongzhi Wang ◽  
Xinghua Chen
Keyword(s):  
Potential Energy ◽  
Shape Function ◽  
Variation Principle ◽  
Shape Functions ◽  
Governing Equations ◽  
Energy Principle ◽  
Potential Energy Principle ◽  
Total Potential ◽  
Stiffness Matrices ◽  
Function Element

By constructing the compressive bar element and developing the stiffness matrix, most issues about the compressive bar can be solved. In this paper, based on second derivative to the equilibrium differential governing equations, the displacement shape functions are got. And then the finite element formula of compressive bar element is developed by using the potential energy principle and analytical shape function. Based on the total potential energy variation principle, the static and geometrical stiffness matrices are proposed, in which the large deformation of compressive bar is considered. To verify the accurate and validity of the analytical trial function element proposed in this paper, a number of the numerical examples are presented. Comparisons show that the proposed element has high calculation efficiency and rapid speed of convergence.

The Study for the Critical Moment of Arches in the Action of Endmoment Considering Shear Lag

2012 ◽  
Vol 446-449 ◽  
pp. 1380-1383
Author(s):  
Y. J. Chen ◽  
Qi Zhi Luo
Keyword(s):  
Potential Energy ◽  
Deformation Behaviour ◽  
Power Method ◽  
Shear Lag ◽  
Energy Principle ◽  
Potential Energy Principle ◽  
Basic Assumptions ◽  
Total Potential ◽  
Out Of Plane ◽  
Basic Displacement Functions

Based on six basic assumptions and deformation behaviour, the total potential energy of arches are obtained. The basic displacement functions are expressed with spline function. According to minmum potential energy principle, the characteristic equation is deducted. The characteristic value is solved by multiplication power method. An exampleof arches in the action of endmoment is calculated. The critical positive and negtive moment of out-of-plane stability in arches with single sysmetry axis section are studied.

scholarly journals Postbuckling Analysis Of A Rectangular Plate Loaded In Compression

2015 ◽  
Vol 15 (2) ◽  
Author(s):  
Jozef Havran ◽  
Martin Psotný
Keyword(s):  
Rectangular Plate ◽  
User Program ◽  
Nonlinear Fem ◽  
Buckling Mode ◽  
Energy Principle ◽  
Initial Imperfections ◽  
Potential Energy Principle ◽  
Total Potential ◽  
The Stability ◽  
Minimum Total Potential Energy

Abstract The stability analysis of a thin rectangular plate loaded in compression is presented. The nonlinear FEM equations are derived from the minimum total potential energy principle. The peculiarities of the effects of the initial imperfections are investigated using the user program. Special attention is paid to the influence of imperfections on the post-critical buckling mode. The FEM computer program using a 48 DOF element has been used for analysis. Full Newton-Raphson procedure has been applied.

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.

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.

The Variational Principles of Coupled Systems in Fatigue Problem Undergoing Large Range Damage

2016 ◽  
Vol 835 ◽  
pp. 514-520
Author(s):  
Wen Feng Tan
Keyword(s):  
Fatigue Crack ◽  
Crack Initiation ◽  
Potential Energy ◽  
Large Range ◽  
Fatigue Crack Initiation ◽  
Form Solution ◽  
Coupled Systems ◽  
Energy Principle ◽  
Potential Energy Principle ◽  
Crack Initiation Life

The coupled systems of fatigue crack initiation problem undergoing large range damage is defined. The zero different work principle, coupled potential energy principle, coupled complementary energy principle in the coupled system is established. By using of coupled potential energy principle, Closed form solution about predicting fatigue crack initiation life of three-dimensional component which leads to large range damage is derived. Compared with reference [1], the close form solution derived from this some. It is proved that the method is correct. The method adopted in this paper is definite in mechanical concept,it can be widely used in analysis of predicting fatigue crack initiation life of various component which leads to large range damage.

Bending of Sandwich Plates of Variable Thickness

1988 ◽  
Vol 55 (2) ◽  
pp. 419-424 ◽  
Author(s):  
N. Paydar ◽  
C. Libove
Keyword(s):  
Potential Energy ◽  
Variable Thickness ◽  
Middle Surface ◽  
Total Potential Energy ◽  
Sandwich Plates ◽  
Energy Principle ◽  
Total Potential ◽  
Small Deflection ◽  
The Face ◽  
Deflection Theory

A small deflection theory, consisting of differential equations and a total potential energy expression, is presented for determining the stresses and deformations in variable thickness elastic sandwich plates symmetric about a middle surface. The theory takes into account the contribution of the face-sheet membrane forces (by virtue of their slopes) to the transverse shear. A finite-difference formulation of the stationary total potential energy principle is presented along with an illustrative application.

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