Determining the law of ice deformation

Verified simulation of the stationary polymer fluid flows in the channel with elliptical cross-section

A number of statements of inverse problems of rational and optimal design of composite structures are considered. The problem of maintenance of a momentless state of a composite shell with respect to parameters’ choice of reinforcement is solved. The problem of optimum design of composite pressure vessels is investigated.

https://iopscience.iop.org/article/10.1088/1742-6596/1715/1/012034/pdf

On analytical and numerical solutions of inverse problems of the mechanics of composites

Generative adversarial networks (GANs) have shown their potential for data generation. However, this type of generative model often suffers from oscillating training processes and mode collapse, among other issues. To mitigate these, this work proposes a generalization of both mean square error (mse) GAN and Wasserstein GAN (WGAN) with gradient penalty, referred to as VGAN. Within the framework of conditional WGAN with gradient penalty, VGAN resorts to the Vapnik V-matrix-based criterion that generalizes mse. Also, a novel early stopping-like strategy is proposed that keeps track during training of the most suitable model. A comprehensive set of experiments on a fault-diagnosis task for an industrial robot where the generative model is used as a data augmentation tool for dealing with imbalance datasets is presented. The statistical analysis of the results shows that the proposed model outperforms nine other models, including vanilla GAN, conditional WGAN with and without conventional regularization, and synthetic minority oversampling technique, a classic data augmentation technique.

VGAN: Generalizing MSE GAN and WGAN-GP for Robot Fault Diagnosis

The paper is devoted to the application of the least-squares collocation method for solving the two- and one-dimensional problems in the mechanics of deformable solids. Calculation results of the deflections of isotropic and orthotropic elastic plates within the framework of various theories are presented. This paper shows that approximate solutions obtained by the hp-version of the least-squares collocation method converge with a high order and agree with analytical solutions of test problems with a high degree of accuracy. Numerical and mathematical modeling of three-point bending of composite beams was carried out taking into account nonlinear stress-strain relationships, multi-modulus behavior, and incipient fracture. It was found that the simulation results are in good agreement with the results of mechanical tests of three-point bending of composite beams.

The least-squares collocation method in the mechanics of deformable solids

This paper reports new hand p-versions of the least squares collocation method of high-order accuracy proposed and implemented for solving boundary value problems for the biharmonic equation in irregular and multiply-connected domains. This paper shows that approximate solutions obtained by the least squares collocation method converge with high order and agree with analytical solutions of test problems with high degree of accuracy. There has been a comparison made for the results achieved in this study and results of other authors who used finite difference and spectral methods.

The least squares collocation method for the biharmonic equation in irregular and multiply-connected domains

This paper describes new versions of the least-squares collocation method for solving differential and integral equations. A p-version of the method has been proposed and implemented to solve nonlinear systems of partial differential equations. The stationary Navier-Stokes equations are used as an example. A hp-version of the method has been implemented for the numerical solution of the Fredholm integral equations of the second kind in the one-and two-dimensional cases. This paper shows that approximate solutions obtained by various versions of the least-squares collocation method converge with a high order and agree with analytical solutions of test problems with a high degree of accuracy.

https://iopscience.iop.org/article/10.1088/1742-6596/1715/1/012031/pdf

Vasily Belyaev

Papers

Determining the law of ice deformation

The least squares collocation method for the biharmonic equation in irregular and multiply-connected domains

Verified simulation of the stationary polymer fluid flows in the channel with elliptical cross-section

New versions of the least-squares collocation method for solving differential and integral equations

The least-squares collocation method in the mechanics of deformable solids