Effective Convergence Checks for Verifying Finite Element Stresses at Two-Dimensional Stress Concentrations

2016 ◽  
Vol 1 (4) ◽  
Author(s):  
G. B. Sinclair ◽  
J. R. Beisheim ◽  
P. J. Roache
Keyword(s):  
Finite Element ◽  
Error Estimation ◽  
Accurate Determination ◽  
Benchmark Problems ◽  
Two Dimensional ◽  
Stress Concentrations ◽  
Element Analysis ◽  
Stress Risers ◽  
Stress Concentration Factors

The accurate determination of stresses at two-dimensional (2D) stress risers is both an important and a challenging problem in engineering. Finite element analysis (FEA) has become the method of choice in making such determinations when new configurations with unknown stress concentrations are encountered in practice. For such FEA to be useful, discretization errors in peak stresses have to be sufficiently controlled. Convergence checks and companion error estimates offer a means of exerting such control. Here, we report some new convergence checks to this end. These checks are designed to promote conservative error estimation. They are applied to seven benchmark problems that have exact solutions for their peak stresses. Associated stress concentration factors span a range that is larger than that normally experienced in engineering. Error levels in the FEA of these peak stresses are classified in accordance with: 1–5%, satisfactory; 1/5–1%, good; and <1/5%, excellent. The present convergence checks result in 91 error assessments for the benchmark problems. For these 91, errors are assessed as being at the same level as true exact errors on 83 occasions and one level worse for the other 8. Thus, stress error estimation is largely accurate (91%) and otherwise modestly conservative (9%).

On the Generation of Tuned Test Problems for Stress Concentrations

2021 ◽  
Author(s):  
Glenn Sinclair ◽  
Ajay A Kardak
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Stress Concentration ◽  
Precise Determination ◽  
Test Problems ◽  
Stress Concentrations ◽  
Element Analysis ◽  
Concentration Factors ◽  
Stress Concentration Factors

Abstract When stress concentration factors are not available in handbooks, finite element analysis has become the predominant method for determining their values. For such determinations, there is a need to know if they have sufficient accuracy. Tuned Test Problems can provide a way of assessing the accuracy of stress concentration factors found with finite elements. Here we offer a means of constructing such test problems for stress concentrations within boundaries that have local constant radii of curvature. These problems are tuned to their originating applications by sharing the same global geometries and having slightly higher peak stresses. They also have exact solutions, thereby enabling a precise determination of the errors incurred in their finite element analysis.

Effective Convergence Checks for Verifying Finite Element Stresses at Three-Dimensional Stress Concentrations

2018 ◽  
Vol 3 (3) ◽  
Author(s):  
J. R. Beisheim ◽  
G. B. Sinclair ◽  
P. J. Roache
Keyword(s):  
Finite Element ◽  
Error Estimation ◽  
A Posteriori Error Estimates ◽  
Three Dimensional ◽  
Posteriori Error ◽  
Test Problems ◽  
A Posteriori ◽  
Stress Concentrations ◽  
Element Analysis ◽  
A Posteriori Error

Current computational capabilities facilitate the application of finite element analysis (FEA) to three-dimensional geometries to determine peak stresses. The three-dimensional stress concentrations so quantified are useful in practice provided the discretization error attending their determination with finite elements has been sufficiently controlled. Here, we provide some convergence checks and companion a posteriori error estimates that can be used to verify such three-dimensional FEA, and thus enable engineers to control discretization errors. These checks are designed to promote conservative error estimation. They are applied to twelve three-dimensional test problems that have exact solutions for their peak stresses. Error levels in the FEA of these peak stresses are classified in accordance with: 1–5%, satisfactory; 1/5–1%, good; and <1/5%, excellent. The present convergence checks result in 111 error assessments for the test problems. For these 111, errors are assessed as being at the same level as true exact errors on 99 occasions, one level worse for the other 12. Hence, stress error estimation that is largely reasonably accurate (89%), and otherwise modestly conservative (11%).

Determination of Stress Concentration Around an Oblique Hole by a Finite-Element Technique

1983 ◽  
Vol 105 (2) ◽  
pp. 206-212 ◽  
Author(s):  
Hua-Ping Li ◽  
F. Ellyin
Keyword(s):  
Finite Element ◽  
Stress Concentration ◽  
Maximum Stress ◽  
Plate Thickness ◽  
Two Dimensional ◽  
Element Analysis ◽  
The Finite Element Analysis ◽  
Parametric Studies ◽  
Element Technique

A plate weakened by an oblique penetration of a circular cylindrical hole has been investigated. The stress concentration around the hole is determined by a finite-element method. The results are compared with experimental data and other analytical works. Parametric studies of effects of angle of inclination, plate thickness, and width are performed. The maximum stress concentration factor (SCF) obtained from the finite-element analysis is higher than experimental results, and this deviation increases with the increase of angle of skewness. The major reason for this difference is attributed to the shear-action between layers parallel to the plate surface which cannot be directly included in the two-dimensional elements. An empirical formula is derived which accounts for the shear-action and renders the finite-element predictions in line with experimentally observed data.

Determination of Stiffness Properties of Single-Ply Cord-Rubber Composites

1988 ◽  
Vol 16 (2) ◽  
pp. 118-126 ◽  
Author(s):  
S. Parhizgar ◽  
E. M. Weissman ◽  
C. S. Chen
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Accurate Determination ◽  
Rubber Composites ◽  
Element Analysis ◽  
Stiffness Properties ◽  
The Finite Element Analysis ◽  
Adequate Accuracy ◽  
Accuracy Determination

Abstract Accurate determination of stiffness properties of cord-rubber composites is a key to successful finite element analysis of tires. The Halpin-Tsai and similar equations which are used to determine stiffness properties of cord-rubber single plies from the stiffness properties of cord and rubber do not provide adequate accuracy. Determination of these properties from strains directly measured by the Moire technique is more appropriate. In this paper the disadvantages of Halpin-Tsai and similar equations as well as the advantages of the Moire technique for cord-rubber composites are discussed. The stiffness properties obtained using the above different methods are compared. These stiffness properties are then used in the finite element analysis of a two-ply cord-rubber strip. The results of the finite element analyses are compared with experimental data.

On the determination of boundary stresses in finite elements

1987 ◽  
Vol 22 (2) ◽  
pp. 87-96 ◽  
Author(s):  
J Smart
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Finite Elements ◽  
The Body ◽  
Surface Element ◽  
Single Element ◽  
Two Dimensional ◽  
Element Analysis ◽  
Nodal Displacements

A new method for determining the stresses in a finite element analysis on the surface of a body is proposed. The body is meshed using standard quadratic isoparametric elements and the nodal displacements determined in the normal way. The stresses are then determined within any surface element by letting the quadratic become a cubic element, applying the corner nodal displacements and known boundary stresses as penalty functions, and then performing a finite element analysis on the single element. The solution then yields a further set of displacements from which the stresses can be determined. The method is applied to various two-dimensional bodies and the improvements in the predicted boundary stresses shown.

Determination of Charge Coefficient of Piezoelectric Films Using a Combined Finite Element Model and Dynamic Loading Technique

2020 ◽  
Vol 835 ◽  
pp. 229-242
Author(s):  
Oboso P. Bernard ◽  
Nagih M. Shaalan ◽  
Mohab Hossam ◽  
Mohsen A. Hassan
Keyword(s):  
Finite Element ◽  
Dynamic Loading ◽  
Material Properties ◽  
Accurate Determination ◽  
Substrate Material ◽  
Experimental Results ◽  
Piezoelectric Composite ◽  
Piezoelectric Film ◽  
Piezoelectric Charge

Accurate determination of piezoelectric properties such as piezoelectric charge coefficients (d33) is an essential step in the design process of sensors and actuators using piezoelectric effect. In this study, a cost-effective and accurate method based on dynamic loading technique was proposed to determine the piezoelectric charge coefficient d33. Finite element analysis (FEA) model was developed in order to estimate d33 and validate the obtained values with experimental results. The experiment was conducted on a piezoelectric disc with a known d33 value. The effect of measuring boundary conditions, substrate material properties and specimen geometry on measured d33 value were conducted. The experimental results reveal that the determined d33 coefficient by this technique is accurate as it falls within the manufactures tolerance specifications of PZT-5A piezoelectric film d33. Further, obtained simulation results on fibre reinforced and particle reinforced piezoelectric composite were found to be similar to those that have been obtained using more advanced techniques. FE-results showed that the measured d33 coefficients depend on measuring boundary condition, piezoelectric film thickness, and substrate material properties. This method was proved to be suitable for determination of d33 coefficient effectively for piezoelectric samples of any arbitrary geometry without compromising on the accuracy of measured d33.

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