Higher-order exponential integrators for constrained semi-linear parabolic problems

This paper provides an introduction to exponential integrators for constrained parabolic systems. In addition, building on existing results, schemes with an expected order of convergence of three and four are established and numerically tested on parabolic problems with nonlinear dynamic boundary conditions. The simulations reinforce the subjected error behaviour

Those who trust government and others are more likely to comply with stay at home orders

In recent months, the majority of the US population has been subject to stay at home and social distancing orders to help prevent the spread of COVID-19. In new research which analyses cellphone data, Daniel A. N. Goldstein and Johannes Wiedemann find that people’s sense of trust in government and others is related to their compliance with going along with preventative measures like stay at home orders. They write that this link is fueled by partisanship and social capital: people are more likely to trust preventative policies if they have high levels of social capital or if the measures are implemented by officials who are from the party they support

In-situ quantification of manufacturing-induced strains in fiber metal laminates with strain gages

The predominant use of FBG sensors to characterize the residual stress state in composite materials to date does not permit absolute strain measurements. The reason for this is the loss of the connection between the sensor and laminate during phase transitions of the resin. Thus, points of significant changes in the measurement signal (e.g. bonding temperature) need to be used for the residual stress evaluation. For fiber metal laminates (FML) however, strain gages applied to the metal layer allow absolute strain measurements since the metal behaves purely elastic over the entire manufacturing process. Hence, residual stresses in the metal layer of an FML are quantified directly. Despite the sensors being applied to the metal layer, it is shown that the cure state of the resin can still be analyzed by changes in the coefficient of thermal expansion. Thus, the effects of different modifications to the cure cycle are assessed in terms of residual stress reduction. It is shown that assuming the bonding temperature to be equal to the stress-free temperature results in a conservative estimation of the residual stress state. The strain gage signal is shown to be in good agreement with FBG sensor data during a combined experiment

Experimental determination of Lamb wave dispersion diagrams over large frequency ranges in fiber metal laminates

Fiber metal laminates (FML) are of high interest for lightweight structures as they combine the advantageous material properties of metals and fiber-reinforced polymers. However, low-velocity impacts can lead to complex internal damage. Therefore, structural health monitoring with guided ultrasonic waves (GUW) is a methodology to identify such damage. Numerical simulations form the basis for corresponding investigations, but experimental validation of dispersion diagrams over a wide frequency range is hardly found in the literature. In this work the dispersive relation of GUWs is experimentally determined for an FML made of carbon fiber-reinforced polymer and steel. For this purpose, multi-frequency excitation signals are used to generate GUWs and the resulting wave field is measured via laser scanning vibrometry. The data are processed by means of a non-uniform discrete 2d Fourier transform and analyzed in the frequency-wavenumber domain. The experimental data are in excellent agreement with data from a numerical solution of the analytical framework. In conclusion, this work presents a highly automatable method to experimentally determine dispersion diagrams of GUWs in FML over large frequency ranges with high accuracy