Nonlinear Winkler-based beam element with improved displacement shape functions

2013 ◽  
Vol 17 (1) ◽  
pp. 192-201 ◽  
Author(s):  
Suchart Limkatanyu ◽  
Kittisak Kuntiyawichai ◽  
Enrico Spacone ◽  
Minho Kwon
Keyword(s):  
Beam Element ◽  
Shape Functions

Research and Applications of a Plane Embedded Combined Element Model Considering Bond and Slip

2013 ◽  
Vol 275-277 ◽  
pp. 1296-1301
Author(s):  
Ji Wei Wang ◽  
Qin Qin Qiao ◽  
Fei Leng
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Shear Deformation ◽  
Element Model ◽  
Beam Element ◽  
Shape Functions ◽  
Element Analysis ◽  
Bond Slip ◽  
Numerical Examples ◽  
Nodal Force

It is one of the most important issues for finite element analysis of lining structures that how to describe anchor rod reasonably and effectively and simulate the interaction between rod and concrete or rock. Virtual nodes are constructed in concrete/rock element at the ends of anchor rod and bond-slip element is set between virtual nodes and beam element which describes anchor rod. An embedded combined element with bond slip and shear deformation is established through the transformation of nodal force at nodes of bond-slip element to those of concrete/rock element via shape functions. The element is convenient for meshing element because the location and direction of anchor rod are not necessary to be considered. Meanwhile, the element has the advantage of low computing cost. Finally, the validity and efficiency are verified by numerical examples.

scholarly journals A Spinning Finite Beam Element of General Orientation Analyzed With Rayleigh/Timoshenko/Saint-Venant Theory

1994 ◽  
Author(s):  
Thomas J. S. Abrahamsson ◽  
Jan Henrik Sällström
Keyword(s):  
Stiffness Matrix ◽  
Axial Load ◽  
Angular Speed ◽  
Beam Element ◽  
Shape Functions ◽  
Geometric Stiffness ◽  
General Orientation ◽  
Linear Vibrations ◽  
Fixed Axis ◽  
And Performance

Linear vibrations are studied for a straight uniform finite beam element of general orientation spinning at a constant angular speed about a fixed axis in the inertial space. The gyroscopic and circulatory matrices and also the geometric stiffness matrix of the beam element are presented. The effect of the centrifugal static axial load on the bending and torsional dynamic stiffnesses is thereby accounted for. The Rayleigh/Timoshenko/Saint-Venant theory is applied, and polynomial shape functions are used in the construction of the deformation fields. Non-zero off-diagonal elements in the gyroscopic and circulatory matrices indicate coupled bending/shearing/torsional/tensional free and forced modes of a generally oriented spinning beam. Two numerical examples demonstrate the use and performance of the beam element.

scholarly journals Free Vibration and Stability of Axially Functionally Graded Tapered Euler-Bernoulli Beams

2011 ◽  
Vol 18 (5) ◽  
pp. 683-696 ◽  
Author(s):  
Ahmad Shahba ◽  
Reza Attarnejad ◽  
Shahin Hajilar
Keyword(s):  
Modulus Of Elasticity ◽  
Longitudinal Vibration ◽  
Mass Density ◽  
Beam Element ◽  
Functionally Graded ◽  
Shape Functions ◽  
Cross Sectional ◽  
Beam Elements ◽  
Graded Material ◽  
Free Transverse Vibration

Structural analysis of axially functionally graded tapered Euler-Bernoulli beams is studied using finite element method. A beam element is proposed which takes advantage of the shape functions of homogeneous uniform beam elements. The effects of varying cross-sectional dimensions and mechanical properties of the functionally graded material are included in the evaluation of structural matrices. This method could be used for beam elements with any distributions of mass density and modulus of elasticity with arbitrarily varying cross-sectional area. Assuming polynomial distributions of modulus of elasticity and mass density, the competency of the element is examined in stability analysis, free longitudinal vibration and free transverse vibration of double tapered beams with different boundary conditions and the convergence rate of the element is then investigated.

scholarly journals Exact Shape Functions for Timoshenko Beam Element

2017 ◽  
Vol 19 (03) ◽  
pp. 12-20
Author(s):  
Sri Tudjono ◽  
Aylie Han ◽  
Dinh-Kien Nguyen ◽  
Shota Kiryu ◽  
Buntara S. Gan
Keyword(s):  
Timoshenko Beam ◽  
Beam Element ◽  
Shape Functions ◽  
Exact Shape ◽  
Timoshenko Beam Element

scholarly journals SHAPE FUNCTIONS OF THREE-DIMENSIONAL TIMOSHENKO BEAM ELEMENT

2003 ◽  
Vol 259 (2) ◽  
pp. 473-480 ◽  
Author(s):  
A. BAZOUNE ◽  
Y.A. KHULIEF ◽  
N.G. STEPHEN
Keyword(s):  
Timoshenko Beam ◽  
Three Dimensional ◽  
Beam Element ◽  
Shape Functions ◽  
Timoshenko Beam Element

scholarly journals Shape functions for high-order shear deformation beam element

2021 ◽  
Author(s):  
Himanshu Gaur ◽  
Mahmoud Dawood ◽  
Ram Kishore Manchiryal
Keyword(s):  
Boundary Conditions ◽  
Shear Deformation ◽  
Beam Theory ◽  
Order Theory ◽  
Beam Element ◽  
High Order ◽  
Shape Functions ◽  
High Order Theory ◽  
Cubic Polynomial ◽  
Transverse Deflection

In this article, shape functions for higher-order shear deformation beam theory are derived. For the two nodded beam element, transverse deflection is assumed as cubic polynomial. By using equations of equilibrium of high-order theory that are already derived by J. N. Reddy in 1997, equation for slope of high- order theory is found. Finally with the boundary conditions of beam element and assumed kinematics of high-order theory, shape functions are derived.

scholarly journals Derivation of an Efficient Non-Prismatic Thin Curved Beam Element Using Basic Displacement Functions

2012 ◽  
Vol 19 (2) ◽  
pp. 187-204 ◽  
Author(s):  
Ahmad Shahba ◽  
Reza Attarnejad ◽  
Mehran Eslaminia
Keyword(s):  
Special Functions ◽  
Free Vibration Analysis ◽  
Beam Element ◽  
Point Of View ◽  
Curved Beam ◽  
Shape Functions ◽  
Curved Beams ◽  
Curved Beam Element ◽  
Exact Shape ◽  
Basic Displacement Functions

The efficiency and accuracy of the elements proposed by the Finite Element Method (FEM) considerably depend on the interpolating functions, namely shape functions, used to formulate the displacement field within an element. In this paper, a new insight is proposed for derivation of elements from a mechanical point of view. Special functions namely Basic Displacement Functions (BDFs) are introduced which hold pure structural foundations. Following basic principles of structural mechanics, it is shown that exact shape functions for non-prismatic thin curved beams could be derived in terms of BDFs. Performing a limiting study, it is observed that the new curved beam element successfully becomes the straight Euler-Bernoulli beam element. Carrying out numerical examples, it is shown that the element provides exact static deformations. Finally efficiency of the method in free vibration analysis is verified through several examples. The results are in good agreement with those in the literature.

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