Modelling the Heating Process in the Transient and Steady State of an In Situ Tape-Laying Machine Head

As the use of composite materials increases, the search for suitable automated processes gains relevance for guaranteeing production quality by ensuring the uniformity of the process, minimizing the amount of scrap generated, and reducing the time and energy consumption. Limitations on production by traditional means such as hand lay-up, vacuum bagging, and in-autoclave methods tend not to be as efficient when the size and shape complexity of the part being produced increases, motivating the search for alternative processes such as automated tape laying (ATL). This work aims to describe the process of modelling and simulating a composite ATL with in situ consolidation by characterizing the machine elements and using the finite differences method in conjunction with energy balances in order to create a digital twin of the process for further control design. The modelling approach implemented is able to follow the process dynamics when changes are made to the heating element and to predict the composite material temperature response, making it suitable for use as a digital twin of a production process using an ATL machine.

The Succession of Heat and Mass Driven Natural Convection Regimes Along a Vertical Impermeable Wall

This paper presents the analysis of the natural convection process that takes place near a vertical plane wall embedded in a constant temperature and linearly mass stratified fluid (the Prandtl number and the Smith number are smaller than 1.0, while the Lewis number is greater than 1.0). The wall has a constant temperature, while the flux of a certain constituent is constant at this boundary. The scale analysis and the finite differences method are used as techniques of work. The scale analysis proves the existence, at equilibrium, of heat and/or mass driven convection regimes along the wall. The finite differences method is used solve the governing equations and to verify the scale analysis results using two particular parameters sets.

On the efficiency of coupled discrete-continuum modelling analyses of cemented materials

Computational load of discrete element modelling (DEM) simulations is known to increase with the number of particles. To improve the computational efficiency hybrid methods using continuous elements in the far-field, have been developed to decrease the number of discrete particles required for the model. In the present work, the performance of using such coupling methods is investigated. In particular, the coupled wall method, known as the “wall-zone” method when coupling DEM and the continuum Finite Differences Method (FDM) using the Itasca commercial codes PFC and FLAC respectively, is here analysed. To determine the accuracy and the efficiency of such a coupling approach, 3-point bending tests of cemented materials are simulated numerically. To validate the coupling accuracy first the elastic response of the beam is considered. The advantage of employing such a coupling method is then investigated by loading the beam until failure. Finally, comparing the results between DEM, DEM-FDM coupled and FDM models, the advantages and disadvantages of each method are outlined.

Modelling the Heating Process at Transient and Steady State of an In Situ Tape Laying Machine Head

As use of composite materials increases, the search for suitable automated processes gains relevance to guarantee production quality by ensuring uniformity of the process, minimizing the amount of generated scrap and reducing time and energy consumption. Limitations on production by traditional means such as hand lay-up, vacuum bagging and in-autoclave methods, tend not to be as efficient when the size and shape complexity of the part being produced increases, motivating the search for alternative processes such as the Automated Tape Laying (ATL). This work aims to describe the process of modelling and simulating a composite ATL with in situ consolidation by characterizing the machine elements, using the finite differences method in conjunction with energy balances, in order to create a digital twin of the process for further control design. The modelling approach implemented is able to follow the process dynamics when changes to the heating element are imposed as well as to predict the composite material temperature response, making it suitable to work as a digital twin of a production process using an ATL machine.

Two Complementary Signaling Pathways Depict Eukaryotic Chemotaxis: A Mechanochemical Coupling Model

Many eukaryotic cells, including neutrophils and Dictyostelium cells, are able to undergo correlated random migration in the absence of directional cues while reacting to shallow gradients of chemoattractants with exquisite precision. Although progress has been made with regard to molecular identities, it remains elusive how molecular mechanics are integrated with cell mechanics to initiate and manipulate cell motility. Here, we propose a two dimensional (2D) cell migration model wherein a multilayered dynamic seesaw mechanism is accompanied by a mechanical strain-based inhibition mechanism. In biology, these two mechanisms can be mapped onto the biochemical feedback between phosphoinositides (PIs) and Rho GTPase and the mechanical interplay between filamin A (FLNa) and FilGAP. Cell migration and the accompanying morphological changes are demonstrated in numerical simulations using a particle-spring model, and the diffusion in the cell membrane are simulations using a one dimensional (1D) finite differences method (FDM). The fine balance established between endogenous signaling and a mechanically governed inactivation scheme ensures the endogenous cycle of self-organizing pseudopods, accounting for the correlated random migration. Furthermore, this model cell manifests directional and adaptable responses to shallow graded signaling, depending on the overwhelming effect of the graded stimuli guidance on strain-based inhibition. Finally, the model cell becomes trapped within an obstacle-ridden spatial region, manifesting a shuttle run for local explorations and can chemotactically “escape”, illustrating again the balance required in the complementary signaling pathways.

Modelling the Heating Process at Transient and Steady State of an In Situ Tape Laying Machine Head

As use of composite materials increases, the search for suitable automated processes gains relevance to guarantee production quality by ensuring uniformity of the process, minimizing the amount of generated scrap and reducing time and energy consumption. Limitations on production by traditional means such as hand lay-up, vacuum bagging and in-autoclave methods, tend not to be as efficient when the size and shape complexity of the part being produced increases, motivating the search for alternative processes such as the Automated Tape Laying (ATL). This work aims to describe the process of modelling and simulating a composite ATL with in situ consolidation by characterizing the machine elements, using the finite differences method in conjunction with energy balances, in order to create a digital twin of the process for further control design. The modelling approach implemented is able to follow the process dynamics when changes to the heating element are imposed as well as to predict the composite material temperature response, making it suitable to work as a digital twin of a production process using an ATL machine.

Some Dynamical Models Involving Fractional-Order Derivatives with the Mittag-Leffler Type Kernels and Their Applications Based upon the Legendre Spectral Collocation Method

Fractional derivative models involving generalized Mittag-Leffler kernels and opposing models are investigated. We first replace the classical derivative with the GMLK in order to obtain the new fractional-order models (GMLK) with the three parameters that are investigated. We utilize a spectral collocation method based on Legendre’s polynomials for evaluating the numerical solutions of the pr. We then construct a scheme for the fractional-order models by using the spectral method involving the Legendre polynomials. In the first model, we directly obtain a set of nonlinear algebraic equations, which can be approximated by the Newton-Raphson method. For the second model, we also need to use the finite differences method to obtain the set of nonlinear algebraic equations, which are also approximated as in the first model. The accuracy of the results is verified in the first model by comparing it with our analytical solution. In the second and third models, the residual error functions are calculated. In all cases, the results are found to be in agreement. The method is a powerful hybrid technique of numerical and analytical approach that is applicable for partial differential equations with multi-order of fractional derivatives involving GMLK with three parameters.

The Behavior of Electromagnetic Wave Propagation in Photonic Crystals with or without a Defect

In this study, the electromagnetic wave propagation behavior of two-dimensional photonic crystal plates with a defect is investigated. For this purpose, the partial differential equation for the electromagnetic wave propagation in various photonic crystal plates containing a defect or not is obtained by using Maxwell’s equations. The defect is also defined in the electromagnetic wave propagation equation appropriately. In order to solve the electromagnetic wave propagation equation, the finite differences method is used. The material property parameters of the photonic crystal plates are determined with respect to the defects. Accordingly, the effects of material property parameters on electromagnetic wave propagation frequencies, phase velocities, and group velocities are examined. The effects of the size and position of the defects on the electromagnetic wave propagation frequencies are also discussed. The highest electromagnetic wave propagation fundamental frequency value obtained from the analyses performed is 1.198 Hz. This fundamental frequency value is obtained for the electromagnetic wave propagation in the t-shaped photonic crystal plate. Electromagnetic field distribution maps for the fundamental frequencies of the photonic crystal plates whose electromagnetic wave propagation behaviors are examined are obtained with the ANSYS package program based on the finite differences time-domain (FDTD) method.