Finite Element Modelling as a Teaching Aid

Development, Calibration & Verification of Finite Element Models of Laboratory Structures to Aid Teaching in Structural Engineering Luke Molloy1 & Paul Archbold2 1

Athlone Institute of Technology A00107448@student.ait.ie

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Athlone Institute of Technology parchbold@ait.ie Abstract

Interactive, reusable learning objects are being developed to aid the teaching of structural engineering modules within the Department of Civil, Construction & Mineral Engineering.

Further, laboratory practicals are an established means of teaching and are commonly used throughout the existing programme delivery modes, while the use of finite element models to simulate loading and structural responses is studied in higher level programmes. This paper describes the development, calibration and verification of FE models, which can be used to simulate the loading and response in two laboratory practicals currently undertaken by undergraduate students. These simulations will be incorporated into reusable learning objects to aid the teaching of the relevant engineering principles and to better prepare students for the actual laboratory practical sessions.

Keywords: finite element, simulation, laboratory, structural engineering, reusable learning object

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Introduction

As part of the teaching and learning strategy for modules in civil engineering programmes in AIT, innovative and interactive methods of teaching are being developed to promote student engagement and to cater for a broader range of learning styles, while also facilitating greater accessibility to class content. Currently students undertake laboratory practicals to further understand theory in the area of structural engineering. In order to further integrate the learning from the laboratory practicals into the theoretical classes and vice-versa, finite element models of two common laboratory structures were developed. This facilitates the study of the mechanical behavior of these structures to validate assumptions made in class in relation to material behavior. Further, they can be used to better prepare the students for carrying out the practical work once they enter the laboratory. In order for these finite element models to have validity, they were calibrated and verified through comparison with actual experimental data recorded in the laboratory. It is envisaged that these numerical simulations will also form the basis of reusable learning objects currently being developed for use in teaching aspects of structural engineering. This paper describes the development, calibration and verification of these finite element models.

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Elastic Beam Apparatus

The purpose of the elastic beam apparatus is to illustrate the concept of bending stress distribution in an elastic beam structure. The experiment is based upon applying an incremental point load at midspan of a t-shaped aluminium beam and recording the strain distribution through the section using 9 electrical resistance strain gauges. Figure 1 shows the experimental configuration for the apparatus.

A finite element model of the beam was developed in ANSYS using shell elements, as shown in Figure 2. This model was then subjected to incremental loads to replicate the laboratory loading regime. The predicted strain values from the FE model were then compared to measured values from experimental data and these formed the basis of calibration of the model. A model updating procedure was employed, which determined that the Young’s Modulus of the material was the most sensitive input parameter and this was then optimized to minimize the error between the measured and predicted results. Following optimization the magnitude of this error reduced from approximately 12% to less than 2% over 10 load increments, indicating excellent agreement between the numerical model and the actual beam apparatus.

Figure 1. Elastic Beam Apparatus

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Figure 2. FE Model of Elastic Beam

Three-hinged Arch

The three-hinged arch apparatus is used to explain the determination of horizontal and vertical reaction forces in an arch structure. The arch is subjected to vertical loads from a rolling weight. An FE model was developed to represent the arch structure as shown in Figure 4. This model was calibrated through comparison of horizontal reactions at the base of the arch following a transient analysis, which simulated each of the load positions. Following calibration, the error between the predicted and measured values reduced to within 1% at for all load steps.

Figure 3. Three-hinged arch apparatus

Figure 4. FE Model of three-hinged arch

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Incorporation of FE Simulations into Reusable Learning Objects

Once both models had been updated and verified, they were suitable for use in developing reusable learning objects for teaching the respective structural principles and for preparing the students for the laboratory practical work. They could also be used after the practicals to provide follow-up support to students writing laboratory reports. Various outputs from the simulatiosn are useful in this regard.

Firstly, tabulated numerical values corresponding to the parameters recorded during labs can be provided as a means of checking measured values. Secondly, video animations can be incorporated to illustrate changing response s due to changes in load position or magnitude. Thirdly, the threedimensional models can simply be used to illustrate the test specimens and laboratory set-up. All of the above are currently being incorporated into reusable learning objects, which should be available shortly.

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Conclusions

Finite element models have been developed for two commonly used laboratory apparatus. These models have been calibrated and verified through comparison of both measured and predicted responses. Both models are capable of simulating all load conditions applied through the normal laboratory practical procedures and can illustrate the structural response accurately. These simulations will be incorporated into reusable learning objects for teaching structural engineering topics to

undergraduate students.