Least Square Finite Element Model for Analysis of Multilayered Composite Plates under Arbitrary Boundary Conditions

Laminated composites are widely used in many engineering industries such as aircraft, spacecraft, boat hulls, racing car bodies, and storage tanks. We analyze the 3D deformations of a multilayered, linear elastic, anisotropic rectangular plate subjected to arbitrary boundary conditions on one edge and simply supported on other edge. The rectangular laminate consists of anisotropic and homogeneous laminae of arbitrary thicknesses. This study presents the elastic analysis of laminated composite plates subjected to sinusoidal mechanical loading under arbitrary boundary conditions. Least square finite element solutions for displacements and stresses are investigated using a mathematical model, called a state-space model, which allows us to simultaneously solve for these field variables in the composite structure’s domain and ensure that continuity conditions are satisfied at layer interfaces. The governing equations are derived from this model using a numerical technique called the least-squares finite element method (LSFEM). These LSFEMs seek to minimize the squares of the governing equations and the associated side conditions residuals over the computational domain. The model is comprised of layerwise variables such as displacements, out-of-plane stresses, and in- plane strains, treated as independent variables. Numerical results are presented to demonstrate the response of the laminated composite plates under various arbitrary boundary conditions using LSFEM and compared with the 3D elasticity solution available in the literature.

Numerical Study of the Transition Between Reentrant Jet and Twin Vortex Flow Regimes in Ventilated Cavitation

Contrary to natural cavitation,ventilated cavitation is controllable and is not harmful.It is particularly used to reduce the drag of the hydraulic vehicles.The ventilated cavitation is characterized by various gas regimes.The mechanisms of ventilated cavitation are investigated in the present work with CFD based on a 2D solver.The attention is especially focused on the transition between the reentrant jet and twin vortex regimes.The results confirmthat the product of ventilated cavitation number and Froude number is lower than 1(σcFr<1)in the twin vortex regime,while it is higher than 1(σcFr>1)in the reentrant jet regime,as reported in the literature.Further analysis shows that ventilated cavitation is significantly influenced by the natural cavitation number.

End-to-end differentiable learning of turbulence models from indirect observations

The emerging push of the differentiable programming paradigm in scientific computing is conducive to training deep learning turbulence models using indirect observations.This paper demonstrates the viability of this approach and presents an end-to-end differentiable framework for training deep neural networks to learn eddy viscosity models from indirect observations derived from the velocity and pressure fields.The framework consists of a Reynolds-averaged Navier–Stokes(RANS)solver and a neuralnetwork-represented turbulence model,each accompanied by its derivative computations.For computing the sensitivities of the indirect observations to the Reynolds stress field,we use the continuous adjoint equations for the RANS equations,while the gradient of the neural network is obtained via its built-in automatic differentiation capability.We demonstrate the ability of this approach to learn the true underlying turbulence closure when one exists by training models using synthetic velocity data from linear and nonlinear closures.We also train a linear eddy viscosity model using synthetic velocity measurements from direct numerical simulations of the Navier–Stokes equations for which no true underlying linear closure exists.The trained deep-neural-network turbulence model showed predictive capability on similar flows.

A laser extinction based sensor for simultaneous droplet size and vapor measurement

Multiphase flows involving liquid droplets in association with gas flow occur in many industrial and sci- entific applications. Recent work has demonstrated the feasibility of using optical techniques based on laser extinction to simultaneously measure vapor concentration and temperature and droplet size and loading. This work introduces the theoretical background for the optimal design of such laser extinction techniques, termed WMLE （wavelength-multiplexed laser extinction）. This paper focuses on the devel- opment of WMLE and presents a systematic methodology to guide the selection of suitable wavelengths and optimize the performance of WMLE for specific applications. WMLE utilizing wavelengths from 0.5 to 10 ixm is illustrated for droplet size and vapor concentration measurements in an example of water spray, and is found to enable unique and sensitive Sauter mean diameter measurement in the range of ~1-15 ~m along with accurate vapor detection. A vapor detection strategy based on differential absorp- tion is developed to extend accurate measurement to a significantly wider range of droplet loading and vapor concentration as compared to strategies based on direct fixed-wavelength absorption. Expected performance of the sensor is modeled for an evaporating spray. This work is expected to lay the ground- work for implementing optical sensors based on WMLE in a variety of research and industrial applications involving multi-phase flows.

Frame Invariance and Scalability of Neural Operators for Partial Differential Equations

Partial differential equations(PDEs)play a dominant role in themathematicalmodeling ofmany complex dynamical processes.Solving these PDEs often requires prohibitively high computational costs,especially when multiple evaluations must be made for different parameters or conditions.After training,neural operators can provide PDEs solutions significantly faster than traditional PDE solvers.In this work,invariance properties and computational complexity of two neural operators are examined for transport PDE of a scalar quantity.Neural operator based on graph kernel network(GKN)operates on graph-structured data to incorporate nonlocal dependencies.Here we propose a modified formulation of GKN to achieve frame invariance.Vector cloud neural network(VCNN)is an alternate neural operator with embedded frame invariance which operates on point cloud data.GKN-based neural operator demonstrates slightly better predictive performance compared to VCNN.However,GKN requires an excessively high computational cost that increases quadratically with the increasing number of discretized objects as compared to a linear increase for VCNN.

Seeing permeability from images： fast prediction with convolutional neural networks

Fast prediction of permeability directly from images enabled by image recognition neural networks is a novel pore-scale modeling method that has a great potential. This article presents a framework that includes (1) generation of porous media samples,(2) computation of permeability via fluid dynamics simulations,(3) training of convolutional neural networks (CNN) with simulated data, and (4) validations against simulations. Comparison of machine learning results and the ground truths suggests excellent predictive performance across a wide range of porosities and pore geometries, especially for those with dilated pores. Owning to such heterogeneity, the permeability cannot be estimated using the conventional Kozeny–Carman approach. Computational time was reduced by several orders of magnitude compared to fluid dynamic simulations. We found that, by including physical parameters that are known to affect permeability into the neural network, the physics-informed CNN generated better results than regular CNN. However, improvements vary with implemented heterogeneity.

Recent progress in augmenting turbulence models with physics-informed machine learning

In view of the long stagnation in traditional turbulence modeling,researchers have attempted using machine learning to augment turbulence models.This paper presents some of the recent progresses in our group on augmenting turbulence models with physics-informed machine learning.We also discuss our works on ensemble-based field inversion to provide training data for constructing machine learning models.Future and on-going research efforts are introduced.

Investigation on the Reduction of Center of Mass Oscillations of Flexible Flapping Fins

Nature has been a source of inspiration for developing advanced autonomous aerial and underwater vehicles. The bodies with flapping appendages produce Center of Mass （COM） oscillations as the flapping fins generate forces oscillatory in nature. The vehicles with larger COM oscillations pose the problems of control and maneuverability and this paper discusses the effect of flexibility and other operating parameters such as heaving, pitching amplitudes and operating frequency on COM oscillations. A detailed theoretical investigation has been carried out to predict the optimal operating parameters along with the fin stiffness to reduce the COM oscillations for a given Self-Propelled Speed （SPS）. Experiments have been performed to validate the theoretical results. It has been observed that the flexible fins operating at larger frequencies produce lower COM oscillations compared to stiffer fins operating at lower frequencies for a given mean thrust/SPS, and that the trailing edge amplitude along with the deformation pattern play a role in the generation of COM oscillations.