title: Modelling Buckling and Post-buckling Behaviours of Corrugated Paperboard Structures

authors: Kueh, Celia Swee Li

subjects: buckling

abstract: The buckling and post-buckling behaviours of corrugated paperboard packaging structures are the focus of this study. The motivations for this study are to improve understanding of post-buckling behaviour to better predict packaging performance and investigate reasons for the discrepancy between experimental and predicted results reported in literature.

The research questions posed consider how post-buckling behaviour of corrugated paperboard panels are affected by varying in-plane boundary conditions and using multi-term out-of-plane displacement functions in analytical Galerkin’s method models with symmetric and / or anti-symmetric geometric imperfections. The panels of varying in-plane boundary conditions and geometric imperfections were also modelled by the Finite Element (FE) method. The material properties of corrugated paperboard obtained by different methods were compared, involving materials testing methods (edge compression, four-point bending and sonic vibration frequency tests) and equivalent single-layered and detailed geometric material models. Comparisons between experimental and predicted panel buckling results consider what boundary conditions best resemble experimental conditions and which displacement modes are dominant.
Difference of in-plane boundary conditions were not the likely source of discrepancy between post-buckling behaviour in models and experiments. Instead, shortcomings in the equivalent single-layered material models used were thought to be the most significant source of discrepancy in the post-buckling results.
The number of modes in the displacement function of the analytical Galerkin’s models influences the post-buckling results. A nine-term symmetric mode model with fundamental geometric imperfection had an increased panel central deflection of 16% at a load ratio of 1.8 times the critical load, compared to the single-term solution. Interactions between symmetric and anti-symmetric displacement modes were observed only for panels with both symmetric and anti-symmetric geometric imperfections, thought to be due to changes in the in-plane stress distribution. 
Equivalent single-layered material models for corrugated paperboard did not give sufficient agreement in effective in-plane elastic moduli compared with materials tests indicating this modelling approach is inadequate for predicting the post-buckling behaviour. Detailed geometric or alternative homogenisation material models for corrugated paperboard accounting for changes in humidity, viscoelastic and plastic behaviour, and transverse shear deformation should be considered for future studies. 
The equivalent single-layered analytical Galerkin’s models, and equivalent and detailed geometric FE models show that the in-plane boundary conditions case for which loaded edges are subjected to uniform displacement and unloaded edges are free of constraints, had the least disagreement with the panel buckling experiments in this study. Possible sources of the discrepancy were investigated, involving panel imperfection and material properties. The fundamental displacement mode was most dominant in the experimental results, but only four non-zero modes were given by fitting panel deflections into a Fourier series using the collocation method, due to limited deflection measurement points. The least squares method for estimating the experimental critical load had slightly better agreement than Southwell’s method in comparisons with analytical and FE model predictions, but caused difficulties with convergence in some cases. The in-plane and flexural material properties from the frequency testing of corrugated paperboard were scaled to consider their impact on the analytical post-buckling model results. Calibration of the material properties from frequency tests to suit prediction of post-buckling behaviour may be possible if it can be justified in further experiments.

text: Modelling Buckling and Post-buckling Behaviours of Corrugated Paperboard Structures The buckling and post-buckling behaviours of corrugated paperboard packaging structures are the focus of this study. The motivations for this study are to improve understanding of post-buckling behaviour to better predict packaging performance and investigate reasons for the discrepancy between experimental and predicted results reported in literature.

The research questions posed consider how post-buckling behaviour of corrugated paperboard panels are affected by varying in-plane boundary conditions and using multi-term out-of-plane displacement functions in analytical Galerkin’s method models with symmetric and / or anti-symmetric geometric imperfections. The panels of varying in-plane boundary conditions and geometric imperfections were also modelled by the Finite Element (FE) method. The material properties of corrugated paperboard obtained by different methods were compared, involving materials testing methods (edge compression, four-point bending and sonic vibration frequency tests) and equivalent single-layered and detailed geometric material models. Comparisons between experimental and predicted panel buckling results consider what boundary conditions best resemble experimental conditions and which displacement modes are dominant.
Difference of in-plane boundary conditions were not the likely source of discrepancy between post-buckling behaviour in models and experiments. Instead, shortcomings in the equivalent single-layered material models used were thought to be the most significant source of discrepancy in the post-buckling results.
The number of modes in the displacement function of the analytical Galerkin’s models influences the post-buckling results. A nine-term symmetric mode model with fundamental geometric imperfection had an increased panel central deflection of 16% at a load ratio of 1.8 times the critical load, compared to the single-term solution. Interactions between symmetric and anti-symmetric displacement modes were observed only for panels with both symmetric and anti-symmetric geometric imperfections, thought to be due to changes in the in-plane stress distribution. 
Equivalent single-layered material models for corrugated paperboard did not give sufficient agreement in effective in-plane elastic moduli compared with materials tests indicating this modelling approach is inadequate for predicting the post-buckling behaviour. Detailed geometric or alternative homogenisation material models for corrugated paperboard accounting for changes in humidity, viscoelastic and plastic behaviour, and transverse shear deformation should be considered for future studies. 
The equivalent single-layered analytical Galerkin’s models, and equivalent and detailed geometric FE models show that the in-plane boundary conditions case for which loaded edges are subjected to uniform displacement and unloaded edges are free of constraints, had the least disagreement with the panel buckling experiments in this study. Possible sources of the discrepancy were investigated, involving panel imperfection and material properties. The fundamental displacement mode was most dominant in the experimental results, but only four non-zero modes were given by fitting panel deflections into a Fourier series using the collocation method, due to limited deflection measurement points. The least squares method for estimating the experimental critical load had slightly better agreement than Southwell’s method in comparisons with analytical and FE model predictions, but caused difficulties with convergence in some cases. The in-plane and flexural material properties from the frequency testing of corrugated paperboard were scaled to consider their impact on the analytical post-buckling model results. Calibration of the material properties from frequency tests to suit prediction of post-buckling behaviour may be possible if it can be justified in further experiments.

year: 2012

title: The effectiveness of Problem-Based Learning (PBL) online on students’ creative and critical thinking in physics at tertiary level in Malaysia

authors: Sulaiman, Fauziah

subjects: Problem-Based Learning

abstract: The purpose of this study was to investigate whether student performance in creative thinking could be enhanced through Problem Based Learning delivered online (referred to as PBL online) and critical thinking. Students’ perceptions and adoptions of PBL learning and online learning also were studied. The PBL online model was adopted from the McMaster’s Model, and comprised three major steps: (i) problem posing; (ii) information searching; and (iii) discussion and application of knowledge in solving problems. PBL is operationally defined here as an instructional strategy which focuses on problem solving. Students are faced with real issues which they have to solve through information searching and group discussion online. In this study, students were given physics problems to solve as part of their Modern Physics course. The phases involved were (i) overview of the topic of the lesson; (ii) problem encounter; (iii) problem definition; (iv) exploration; (v) solution; and (vi) reflection. All of these phases were done through the University’s Learning Management System (LMS), which thus acts as the online delivery tool. This study employed a quasi-experimental design based on mixed between-within-subjects repeated measures. The independent variable was the instruction method, either PBL online (experimental) or Traditional method online (control), and the dependent variables were performance in creative and critical thinking. The Torrance Test of Creative Thinking (TTCT) and the Watson Glaser Critical Thinking (WGCT) were used to measure the respective dependent variables. In the TTCT, there are four criteria used to evaluate creative thinking: (i) fluency; (ii) flexibility; (iii) originality; and (v) elaboration. For the critical thinking, five criteria were used: (i) making an inference; (ii) making an assumption; (iii) deduction; (iv) making an interpretation; and also (v) evaluation argument. Additionally, students’ perceptions and adoptions of PBL, as well as online learning, were captured through this study. A total of 102 students from the School of Science and Technology (SST) and the School of Education and Social Development were the subjects of the study. The SST students were science physics students (N = 61), and the SESD students were pre-service science teachers (N = 41). Results of the Mann-Whitney U test and also Independent Sample t-Test showed that there was significant difference in creative thinking in overall for both SST and SESD cohorts in favour of the PBL group. In addition, when the analysis was focussed on the two cohorts (i.e., SST and SESD), there were statistically significant differences observed for flexibility, originality and elaboration also in favour of the PBL group. However, results from the same analyses showed there was, in general, no significance difference for critical thinking for both cohorts. Further analysis identified statistically significant differences for making an inference (in favour of the PBL group) and assumption (in favour of the Traditional group). For the SST students, there were statistically significant differences in making an inference and evaluation argument criteria, in favour of the PBL group. Nevertheless, there were statistically significant differences for assumption, in favour of the Traditional group. No statistically significant differences were noted in any criterion for the SESD group. Students’ perceptions of PBL and willingness to adopt it were positive, even though they reported feeling confused at the beginning of the learning process. PBL was also reported as taking more time and requiring more effort. Nevertheless, students reported managing to build their capacity for self-directed learning and improving soft skills (i.e., communication, managing their learning timetable, finding relevant and valuable knowledge online, etc.). In the case of online learning, the students felt that they had learned how to get much more information online, and how to critique such information. Students’ readiness to use online learning was encouraging, and it provided at least basic experience on courses delivered through online learning. However, the Internet access needs to be adequate to ensure that online learning operates satisfactorily. Important findings were derived from this study. First, the results from this study suggest that PBL online enhances of Malaysian tertiary students’ creative thinking for both science physics students and pre-service science teachers. Second, PBL online also is capable of having a positive impact on students’ critical thinking for certain criteria, but this would be fostered by a whole programme approach rather than delivery via a single course. Third, students’ acceptance and perceptions of PBL and online learning were positive and encouraging, this despite encountering some issues technical during the intervention.

text: The effectiveness of Problem-Based Learning (PBL) online on students’ creative and critical thinking in physics at tertiary level in Malaysia The purpose of this study was to investigate whether student performance in creative thinking could be enhanced through Problem Based Learning delivered online (referred to as PBL online) and critical thinking. Students’ perceptions and adoptions of PBL learning and online learning also were studied. The PBL online model was adopted from the McMaster’s Model, and comprised three major steps: (i) problem posing; (ii) information searching; and (iii) discussion and application of knowledge in solving problems. PBL is operationally defined here as an instructional strategy which focuses on problem solving. Students are faced with real issues which they have to solve through information searching and group discussion online. In this study, students were given physics problems to solve as part of their Modern Physics course. The phases involved were (i) overview of the topic of the lesson; (ii) problem encounter; (iii) problem definition; (iv) exploration; (v) solution; and (vi) reflection. All of these phases were done through the University’s Learning Management System (LMS), which thus acts as the online delivery tool. This study employed a quasi-experimental design based on mixed between-within-subjects repeated measures. The independent variable was the instruction method, either PBL online (experimental) or Traditional method online (control), and the dependent variables were performance in creative and critical thinking. The Torrance Test of Creative Thinking (TTCT) and the Watson Glaser Critical Thinking (WGCT) were used to measure the respective dependent variables. In the TTCT, there are four criteria used to evaluate creative thinking: (i) fluency; (ii) flexibility; (iii) originality; and (v) elaboration. For the critical thinking, five criteria were used: (i) making an inference; (ii) making an assumption; (iii) deduction; (iv) making an interpretation; and also (v) evaluation argument. Additionally, students’ perceptions and adoptions of PBL, as well as online learning, were captured through this study. A total of 102 students from the School of Science and Technology (SST) and the School of Education and Social Development were the subjects of the study. The SST students were science physics students (N = 61), and the SESD students were pre-service science teachers (N = 41). Results of the Mann-Whitney U test and also Independent Sample t-Test showed that there was significant difference in creative thinking in overall for both SST and SESD cohorts in favour of the PBL group. In addition, when the analysis was focussed on the two cohorts (i.e., SST and SESD), there were statistically significant differences observed for flexibility, originality and elaboration also in favour of the PBL group. However, results from the same analyses showed there was, in general, no significance difference for critical thinking for both cohorts. Further analysis identified statistically significant differences for making an inference (in favour of the PBL group) and assumption (in favour of the Traditional group). For the SST students, there were statistically significant differences in making an inference and evaluation argument criteria, in favour of the PBL group. Nevertheless, there were statistically significant differences for assumption, in favour of the Traditional group. No statistically significant differences were noted in any criterion for the SESD group. Students’ perceptions of PBL and willingness to adopt it were positive, even though they reported feeling confused at the beginning of the learning process. PBL was also reported as taking more time and requiring more effort. Nevertheless, students reported managing to build their capacity for self-directed learning and improving soft skills (i.e., communication, managing their learning timetable, finding relevant and valuable knowledge online, etc.). In the case of online learning, the students felt that they had learned how to get much more information online, and how to critique such information. Students’ readiness to use online learning was encouraging, and it provided at least basic experience on courses delivered through online learning. However, the Internet access needs to be adequate to ensure that online learning operates satisfactorily. Important findings were derived from this study. First, the results from this study suggest that PBL online enhances of Malaysian tertiary students’ creative thinking for both science physics students and pre-service science teachers. Second, PBL online also is capable of having a positive impact on students’ critical thinking for certain criteria, but this would be fostered by a whole programme approach rather than delivery via a single course. Third, students’ acceptance and perceptions of PBL and online learning were positive and encouraging, this despite encountering some issues technical during the intervention.

year: 2011

title: Maori goddesses in literature. Part 2: 1900-1940

authors: Yates-Smith, Aroha

subjects: Atua wāhine

abstract: Many contemporary Māori are familiar with atua wāhine, Māori goddesses, through accounts that have been passed on to them by word of mouth. Few, however, have had an opportunity to consult accounts of atua wāhine that date from the early period of Māori-Pākehā contact. Those who wish to do so may have considerable difficulty in sifting through all of the written materials for the information they seek. For this reason, this paper provides a review of the literature pertaining to atua wāhine from 1900 to 1940, together with a commentary on the sources to which reference is made. A review of literature on atua wāhine from 1880 – 1900 appeared in the first issue of this Journal. The period 1940 towards 2000 will be reviewed in the next issue.

text: Maori goddesses in literature. Part 2: 1900-1940 Many contemporary Māori are familiar with atua wāhine, Māori goddesses, through accounts that have been passed on to them by word of mouth. Few, however, have had an opportunity to consult accounts of atua wāhine that date from the early period of Māori-Pākehā contact. Those who wish to do so may have considerable difficulty in sifting through all of the written materials for the information they seek. For this reason, this paper provides a review of the literature pertaining to atua wāhine from 1900 to 1940, together with a commentary on the sources to which reference is made. A review of literature on atua wāhine from 1880 – 1900 appeared in the first issue of this Journal. The period 1940 towards 2000 will be reviewed in the next issue.

year: 2001-02