Curvature-Based Finite Element Method for Euler-Bernoulli Beams

2007 ◽  
Author(s):  
Y. L. Kuo ◽  
W. L. Cleghorn
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Degrees Of Freedom ◽  
Transverse Displacement ◽  
Bernoulli Beam ◽  
Numerical Examples ◽  
Displacement Based ◽  
Curvature Distribution ◽  
Euler Bernoulli Beam ◽  
Element Method

This paper presents a new method called the curvature-based finite element method to solve Euler-Bernoulli beam problems. An approximated curvature distribution is selected first, and then the approximated transverse displacement is determined by double integrations. Four numerical examples demonstrate the validity of the method, and the results show that the errors are smaller than those generated by a conventional method, the displacement-based finite element method, for comparison based on the same number of degrees of freedom.

STRESS-BASED FINITE ELEMENT METHOD FOR EULER-BERNOULLI BEAMS

2006 ◽  
Vol 30 (1) ◽  
pp. 1-6 ◽  
Author(s):  
Y.L. Kuo ◽  
W.L. Cleghorn ◽  
K. Behdinan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Degrees Of Freedom ◽  
Transverse Displacement ◽  
Bending Stress ◽  
Numerical Examples ◽  
A New Technique ◽  
Displacement Based ◽  
Element Method

This paper presents a new technique, which can apply the stress-based finite element method to Euler-Bernoulli beams. An approximated bending stress distribution is selected, and then the approximated transverse displacement is determined by twice integration. Due to the satisfaction of compatibility, the integration constants are determined by the boundary conditions related to transverse displacement and rotation. To compare with the displacement-based finite element method, this technique provides the continuities of not only transverse displacement and rotation but also stress at nodes. Besides, the boundary conditions related to stress are satisfied. Two numerical examples demonstrate the validity of this technique. The results show that the errors are smaller than those generated by the displacement-based finite element method for the same number of degrees of freedom.

Accuracy Enhancement of Flexible Fourbar Mechanisms via the Curvature-Based Finite Element Method

2008 ◽  
Author(s):  
Y. L. Kuo ◽  
W. L. Cleghorn
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Great Reduction ◽  
Degrees Of Freedom ◽  
Solid Mechanics ◽  
Accuracy Enhancement ◽  
Displacement Based ◽  
Curvature Distribution ◽  
High Degree ◽  
Element Method

The paper investigates accuracy enhancement of flexible four-bar mechanisms via the curvature-based finite element method. Conventionally, the displacement-based method is usually applied to solid mechanics, and it needs more elements or high-degree polynomials to obtain highly accurate solutions. The curvature-based method assumes a polynomial to approximate a curvature distribution, and the expressions are investigated to obtain the displacement and rotation distributions. During the process, the boundary conditions associated with displacement, rotation, and curvature are imposed, which leads the great reduction of the number of degrees of freedom which are required. The numerical results demonstrate that the errors obtained by applying the curvature-based method are much smaller than those by applying the displacement-based method, based on the comparison of the same number of degrees of freedom.

scholarly journals Stress evaluation in displacement-based 2D nonlocal finite element method

2018 ◽  
Vol 5 (1) ◽  
pp. 136-145 ◽  
Author(s):  
Aurora Angela Pisano ◽  
Paolo Fuschi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stress Field ◽  
Nonlocal Elasticity ◽  
Integration Technique ◽  
Stress Evaluation ◽  
Numerical Examples ◽  
Spurious Oscillations ◽  
Displacement Based ◽  
Element Method

Abstract The evaluation of the stress field within a nonlocal version of the displacement-based finite element method is addressed. With the aid of two numerical examples it is shown as some spurious oscillations of the computed nonlocal stresses arise at sections (or zones) of macroscopic inhomogeneity of the examined structures. It is also shown how the above drawback, which renders the stress numerical solution unreliable, can be viewed as the so-called locking in FEM, a subject debated in the early seventies. It is proved that a well known remedy for locking, i.e. the reduced integration technique, can be successfully applied also in the nonlocal elasticity context.

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).

Application of Extended Finite Element Method (XFEM) to Stress Intensity Factor Calculations

2015 ◽  
Author(s):  
Do-Jun Shim ◽  
Mohammed Uddin ◽  
Sureshkumar Kalyanam ◽  
Frederick Brust ◽  
Bruce Young
Keyword(s):  
Finite Element Method ◽  
Stress Intensity Factor ◽  
Finite Element ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Degrees Of Freedom ◽  
Extended Finite Element Method ◽  
Partition Of Unity ◽  
Extended Finite Element ◽  
Element Method

The extended finite element method (XFEM) is an extension of the conventional finite element method based on the concept of partition of unity. In this method, the presence of a crack is ensured by the special enriched functions in conjunction with additional degrees of freedom. This approach also removes the requirement for explicitly defining the crack front or specifying the virtual crack extension direction when evaluating the contour integral. In this paper, stress intensity factors (SIF) for various crack types in plates and pipes were calculated using the XFEM embedded in ABAQUS. These results were compared against handbook solutions, results from conventional finite element method, and results obtained from finite element alternating method (FEAM). Based on these results, applicability of the ABAQUS XFEM to stress intensity factor calculations was investigated. Discussions are provided on the advantages and limitations of the XFEM.

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