This study aims to determining the strain gauge location points in the problems of stress concentration, and it includes both experimental and numerical results. Strain gauges were proposed to be positioned to corresponding locations on beam and blocks to related node of elements of finite element models. Linear and nonlinear cases were studied. Cantilever beam problem was selected as the linear case to approve the approach and conforming contact problem was selected as the nonlinear case. An identical mesh structure was prepared for the finite element and the experimental models. The finite element analysis was carried out with ANSYS. It was shown that the results of the experimental and the numerical studies were in good agreement.

The finite element method is one of the efficient and well-known numerical methods for various engineering problems. For the last 30 years it has been used for the solution of many types of problems. Finite element results are validated with either analytical solution or experimental studies. Many experimental researches have been carried out in many areas.

Wei and Zhao [

Briscoe and Chateauminois [

Kanehara and Fujioka [

Cordey and Gautier [

In those studies, strain gauges were placed on highly stressed zones but it was not discussed if the strain gauges were at the ideal position. According to deviation in placement of the gauges there may be a difference between the experimental and the numerical analysis results. In addition, strain gauges have never been used in contact regions. In this paper, an approach is suggested to obtain more accurate results for contact region from comparison of finite element and experimental results. Thus, strain gauge locations on real model are selected as corresponding points at finite element model which are nodes of element. Cantilever beam problem is considered for the linear case to approve the approach. Conforming contact problem is considered for the nonlinear case with stress concentration. An identical mesh structure is prepared for finite element and experimental models. Strain gauges are located at positions on beam and blocks, corresponding to nodes of elements in the finite element models. The results from the experiment are then compared with finite element analysis.

An aluminum beam was fixed at one end and point load was applied to the other end for beam problem case. In the conforming contact case, two aluminum blocks were machined with different dimensions. The smaller block was placed on the other block and loading was applied to the top of the upper block.

Strain gauges were centered and bonded to positions on the beam and blocks corresponding to the nodes of the elements of the finite element models. Strain gauge measurements were performed with data logger. Measured output voltages were transferred to the strain value as

This case involves the bending of a rectangular cross-section aluminum beam as shown in Figure

Mechanical properties of the aluminum alloy block.

Orientation | Elastic modulus |
Yield stress |
Ultimate tensile stress |
---|---|---|---|

Longitudinal | 105 | 365 | 436 |

Application of strain gauges.

Dimensions of the cantilever beam in millimeters.

Load is applied to the beam as a point load at the end of the beam by the increment of 0.5 kg from 0.5 to 5 kg and measurements were read from the strain gauge indicator.

Two aluminum alloy blocks were manufactured to the geometry shown in Figure

Dimensions of the aluminum blocks in millimeters.

After the application of strain gauges as illustrated in Figure

Strain gauge applications.

60 tons capacity MFL hydraulic machine.

Three-dimensional finite element analysis was performed. The strain values were determined at nodal points of corresponding finite element.

The beam was modeled with the finite element software ANSYS. SOLID186 [

Finite element mesh and loading and boundary conditions of the beam.

A model of the contacting blocks was developed using ANSYS. A small grid size was used to get acceptable finite element result. The mesh, as illustrated in Figure

Finite element model and loading and boundary conditions of blocks.

Finite element model

Loading and boundary conditions

Strain variation along

Almost the same values of strain are observed for the experimental and the numerical cases. For this linear case with stress concentration free condition, stress varies smoothly and linearly. Hence the deviation of strain gauge position will not affect the results significantly.

In the nonlinear case, strain is changed in

Gauge 7

Gauge 11

Upper block

Lower block

The case study for conforming contact also includes stress concentrations at the locations where the peripheral of small block contacts with the larger one. The attention is concentrated to these locations: sudden stress variation is observed at these concentration points. Hence, the use of strain gauges at incorrect locations will yield some errors. The amount of possible error with small deviations of location is searched in Figure

Comparison of

The suggested approach gives a better comparison with the results of finite elements and experimental studies. While the linear case results are identical due to linearity of the problem; the accuracy of nonlinear case results is very high. For the nonlinear case and existence of stress concentration, strain measurement and placement of strain gauges require more attention due to rapid change of the stress value. Any dislocation of strain gauge is shown to yield an error of up to 10%.

The authors declare that there is no conflict of interests regarding the publication of this paper.