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: Portfolio pointers: Preparing and presenting high quality teaching portfolios

authors: Spiller, Dorothy

abstract: This goal of this project was to develop a set of guidelines for creating teaching portfolios for the Tertiary Teaching Excellence Awards or for other purposes. It includes key pointers to “getting started”, collecting evidence, interrogating practice, editing, and protecting the unique “voice” of the nominee and their student body.

The guidelines consist of general principles and practical examples from both successful academic developers and award recipients and some examples from award-winning portfolios to illustrate good practice.

text: Portfolio pointers: Preparing and presenting high quality teaching portfolios This goal of this project was to develop a set of guidelines for creating teaching portfolios for the Tertiary Teaching Excellence Awards or for other purposes. It includes key pointers to “getting started”, collecting evidence, interrogating practice, editing, and protecting the unique “voice” of the nominee and their student body.

The guidelines consist of general principles and practical examples from both successful academic developers and award recipients and some examples from award-winning portfolios to illustrate good practice.

year: 2011-03

title: Waitomo District: Demographic profile 1986-2031

authors: Jackson, Natalie

abstract: This report outlines the demographic changes that have occurred in Waitomo Region, as well as what trends are expected in the future.

text: Waitomo District: Demographic profile 1986-2031 This report outlines the demographic changes that have occurred in Waitomo Region, as well as what trends are expected in the future.

year: 2014