Positivity of the clamped plate under tension

• Applicant: Dr. Sascha Eichmann
• Subject Area: Mathematics
• Term: from 2021 to 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 497258768

We examine a mathematical model designed to describe the behaviour of a clamped plate under mechanical tension. This model predicts the bending of the plate, if a force is applied to it. Central is the question of so called positivity preserving. This is the question, whether an upward force will yield upward bending. New in our consideration is the parameter of mechanical tension.From our recent examinations we know, that such positiv bending occurs, if the tension is high enough. More precisely one has to choose this tension in dependence of the force and the plate. We like to continue this research by examining the following questions:1) Can positivity preserving be lost, once it has occured? In other words: If we already have positivity preserving for one specific value of tension, can downward bending occur, if the tension is increased?2) Are there optimal plates? I.e. are there plates, satisfying such a positivity preserving property for smallest possible tensions?3) If we modify our model, can we still expect similar results?

• DFG Programme: Research Grants