NONCONVENTIONAL FINITE ELEMENT MODELS FOR NONLINEAR ANALYSIS OF BEAMS

2011 ◽  
Vol 08 (03) ◽  
pp. 349-368 ◽  
Author(s):  
WOORAM KIM ◽  
J. N. REDDY
Keyword(s):  
Finite Element ◽  
Mixed Models ◽  
Mixed Model ◽  
Mixed Finite Element ◽  
Beam Theory ◽  
Finite Element Models ◽  
Various Boundary Conditions ◽  
Beam Bending ◽  
Displacement Based ◽  
Euler Bernoulli Beam

In this study, mixed finite element models of beam bending are developed to include the membrane forces and shear forces in addition to the bending moments and displacements. Mixed finite element models were developed based on the weighted residual statements of governing equations. The Euler–Bernoulli beam theory (EBT) and the Timoshenko beam theory (TBT) are used. The effectiveness of the new mixed models is evaluated in light of other mixed models to show the advantages. Each newly developed model is examined and compared with other models to verify its performance under various boundary conditions. In the linear analysis, solutions are compared with available analytical solutions and solutions of existing models. In the nonlinear case, direct and Newton–Raphson methods are used to solve the nonlinear equations. The converged solutions are compared with available solutions of the displacement models. Post-processed data of the mixed model developed herein shows better accuracy than the conventional displacement-based model.

Modeling and Finite Element Analysis of Drill Bit Vibrations

1989 ◽  
Vol 111 (2) ◽  
pp. 148-155 ◽  
Author(s):  
O. Tekinalp ◽  
A. G. Ulsoy
Keyword(s):  
Finite Element ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Helix Angle ◽  
Drill Bit ◽  
Element Analysis ◽  
Cross Sectional ◽  
Various Boundary Conditions ◽  
Drill Bits ◽  
Euler Bernoulli Beam

Drill bit vibrations are modeled using the Euler-Bernoulli beam theory. The model includes the most important properties of drill bits and of the drilling operation. These are: the drill bit cross sectional geometry, the drill helix angle, rotational speed of the drill bit, the thrust force, torque, and cutting forces generated during drilling. Equations of motion are derived in an inertial frame and then transformed to a rotating fluted frame for convenience in the solution. The transformed equations are discretized using finite element techniques. The finite element code developed is capable of solving the eigenvalue problem for various boundary conditions and drill cross sectional geometries. Finite element solutions are compared to known analytical, numerical, and experimental results from the literature and good agreement is obtained.

Fatigue Life Prediction of Drill-String Subjected to Random Loadings

2014 ◽  
Author(s):  
Jiahao Zheng ◽  
Hongyuan Qiu ◽  
Jianming Yang ◽  
Stephen Butt
Keyword(s):  
Fatigue Life ◽  
Time History ◽  
Beam Theory ◽  
Drill String ◽  
Finite Element Models ◽  
Bernoulli Beam ◽  
Stress Cycles ◽  
Rainflow Counting ◽  
Euler Bernoulli Beam ◽  
Random Nature

Based on linear damage accumulation law, this paper investigates the fatigue problem of drill-strings in time domain. Rainflow algorithms are developed to count the stress cycles. The stress within the drill-string is calculated with finite element models which is developed using Euler-Bernoulli beam theory. Both deterministic and random excitations to the drill-string system are taken into account. With this model, the stress time history in random nature at any location of the drill-string can be obtained by solving the random dynamic model of the drill-string. Then the random time history is analyzed using rainflow counting method. The fatigue life of the drill-string under both deterministic and random excitations can therefore be predicted.

Matrix Method for Buckling Analysis of Frames Based on Hencky Bar-Chain Model

2019 ◽  
Vol 19 (08) ◽  
pp. 1950093 ◽  
Author(s):  
W. H. Pan ◽  
C. M. Wang ◽  
H. Zhang
Keyword(s):  
Matrix Method ◽  
Structural Changes ◽  
Beam Theory ◽  
Buckling Analysis ◽  
Chain Model ◽  
Bernoulli Beam ◽  
Various Boundary Conditions ◽  
End Restraint ◽  
Euler Bernoulli Beam ◽  
General Frames

Presented herein is a matrix method for buckling analysis of general frames based on the Hencky bar-chain model comprising of rigid segments connected by hinges with elastic rotational springs. Unlike the conventional matrix method of structural analysis based on the Euler–Bernoulli beam theory, the Hencky bar-chain model (HBM) matrix method allows one to readily handle the localized changes in end restraint conditions or localized structural changes (such as local damage or local stiffening) by simply tweaking the spring stiffnesses. The developed HBM matrix method was applied to solve some illustrative example problems to demonstrate its versatility in solving the buckling problem of beams and frames with various boundary conditions and local changes. It is hoped that this easy-to-code HBM matrix method will be useful to engineers in solving frame buckling problems.

Modelling of Rotating Twisted Blades as 1D Continuum

2016 ◽  
Vol 821 ◽  
pp. 183-190
Author(s):  
Jan Brůha ◽  
Drahomír Rychecký
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Beam Theory ◽  
Parameter Tuning ◽  
Finite Element Models ◽  
Cross Sectional ◽  
One Dimensional ◽  
Rayleigh Beam ◽  
Twisted Blade ◽  
Sectional Parameters

Presented paper deals with modelling of a twisted blade with rhombic shroud as one-dimensional continuum by means of Rayleigh beam finite elements with varying cross-sectional parameters along the finite elements. The blade is clamped into a rotating rigid disk and the shroud is considered to be a rigid body. Since the finite element models based on the Rayleigh beam theory tend to slightly overestimate natural frequencies and underestimate deflections in comparison with finite element models including shear deformation effects, parameter tuning of the blade is performed.

Developing a beam formulation for semi-crystalline two-way shape memory polymers

2020 ◽  
Vol 31 (12) ◽  
pp. 1465-1476
Author(s):  
Mohammad-Ali Maleki-Bigdeli ◽  
Majid Baniassadi ◽  
Kui Wang ◽  
Mostafa Baghani
Keyword(s):  
Finite Element ◽  
Shape Memory ◽  
Shape Memory Polymer ◽  
Beam Theory ◽  
Shape Memory Polymers ◽  
Bernoulli Beam ◽  
Von Karman ◽  
Von Kármán ◽  
Euler Bernoulli Beam ◽  
Beam Theories

In this research, the bending of a two-way shape memory polymer beam is examined implementing a one-dimensional phenomenological macroscopic constitutive model into Euler–Bernoulli and von-Karman beam theories. Since bending loading is a fundamental problem in engineering applications, a combination of bending problem and two-way shape memory effect capable of switching between two temporary shapes can be used in different applications, for example, thermally activated sensors and actuators. Shape memory polymers as a branch of soft materials can undergo large deformation. Hence, Euler–Bernoulli beam theory does not apply to the bending of a shape memory polymer beam where moderate rotations may occur. To overcome this limitation, von-Karman beam theory accounting for the mid-plane stretching as well as moderate rotations can be employed. To investigate the difference between the two beam theories, the deflection and rotating angles of a shape memory polymer cantilever beam are analyzed under small and moderate deflections and rotations. A semi-analytical approach is used to inspect Euler–Bernoulli beam theory, while finite-element method is employed to study von-Karman beam theory. In the following, a smart structure is analyzed using a prepared user-defined subroutine, VUMAT, in finite-element package, ABAQUS/EXPLICIT. Utilizing generated user-defined subroutine, smart structures composed of shape memory polymer material can be analyzed under complex loading circumstances through the two-way shape memory effect.

Analysis of bimorph piezoelectric beam energy harvesters using Timoshenko and Euler–Bernoulli beam theory

2012 ◽  
Vol 24 (2) ◽  
pp. 226-239 ◽  
Author(s):  
Gang Wang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Slenderness Ratio ◽  
Beam Theory ◽  
Bernoulli Beam ◽  
Energy Harvesters ◽  
Bernoulli Beam Theory ◽  
Spectral Finite Element ◽  
Euler Bernoulli Beam ◽  
Element Method

Single-degree-of-freedom lumped parameter model, conventional finite element method, and distributed parameter model have been developed to design, analyze, and predict the performance of piezoelectric energy harvesters with reasonable accuracy. In this article, a spectral finite element method for bimorph piezoelectric beam energy harvesters is developed based on the Timoshenko beam theory and the Euler–Bernoulli beam theory. Linear piezoelectric constitutive and linear elastic stress/strain models are assumed. Both beam theories are considered in order to examine the validation and applicability of each beam theory for a range of harvester sizes. Using spectral finite element method, a minimum number of elements is required because accurate shape functions are derived using the coupled electromechanical governing equations. Numerical simulations are conducted and validated using existing experimental data from the literature. In addition, parametric studies are carried out to predict the performance of a range of harvester sizes using each beam theory. It is concluded that the Euler–Bernoulli beam theory is sufficient enough to predict the performance of slender piezoelectric beams (slenderness ratio > 20, that is, length over thickness ratio > 20). In contrast, the Timoshenko beam theory, including the effects of shear deformation and rotary inertia, must be used for short piezoelectric beams (slenderness ratio < 5).

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