Extension of paperboard modelling with Föppl–von Karman terms for improved stress state under suction pressure

Mikko Salo, Jarno Jokinen, Matti Vilkko, Mikko Kanerva — Tue, 01 Oct 2024 00:00:00 +0300

A practical method for solving the bending stiffness of a thin orthotropic plate based on measured deflection and known loading was studied. The target application was paperboard manufacturing and related process control. Here, finite element (FE) method was used to create virtual paperboard and its deflection data. The accuracy of the linear Kirchhoff plate model used in the practical method was tested against the FE model with known load and material properties. It was found that in the case of significant deflections, the linear Kirchoff model was not accurate. The non-linear Föppl--von Kàrmàn model takes into account the occurring membrane stresses and extends on the Kirchhoff model, allowing for larger deflection. The non-linear Föppl--von Kàrmàn model was found to successfully describe the simulated situation and could be used to better solve for the paperboard's bending stiffness values over two axes.

Estimating quantiles in acceptance criteria for structural components

Matti Pajari, Lasse Makkonen — Thu, 17 Oct 2024 00:00:00 +0300

The probabilistic foundations of methods to control the characteristic properties of structural materials, expressed as p-quantiles, are discussed. We argue that the acceptance criteria in the quality control should be based on quantile estimators complying with the definition of the quantile. We introduce the distribution-free concept of definition-based quantile estimator. For normal distribution, an application of different types of estimators, as well as some attribute methods and mixed methods presently used, are illustrated by operating characteristic curves. We recommend the prediction method by which the subjective limit values of the mixed methods are eliminated, information from the sample will be used more effectively than in the attribute methods, and the questions about the proper confidence level or a “known” variation coefficient need not be considered. However, the direct application of the prediction method results in stricter quality control than that presently used. Therefore, we recommend adopting p’ > p in such a way that if the predicted p’-quantile estimate is equal to or higher than the lower lilmit L, the required value of the p-quantile, the lot is accepted in the quality control. If the present quality level is appropriate, the value of p’ can be chosen in such a way that the present level is maintained. If not, necessary modifications are possible simply by adjusting p’.

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Extension of paperboard modelling with Föppl–von Karman terms for improved stress state under suction pressure

Estimating quantiles in acceptance criteria for structural components