Semi-Infinite Structure Analysis with Bimodular Materials with Infinite Element

The modulus of elasticity of some materials changes under tensile and compressive states is simulated by constructing a typical material nonlinearity in a numerical analysis in this paper. The meshless Finite Block Method (FBM) has been developed to deal with 3D semi-infinite structures in the bimodular materials in this paper. The Lagrange polynomial interpolation is utilized to construct the meshless shape function with the mapping technique to transform the irregular finite domain or semi-infinite physical solids into a normalized domain. A shear modulus strategy is developed to present the nonlinear characteristics of bimodular material. In order to verify the efficiency and accuracy of FBM, the numerical results are compared with both analytical and numerical solutions provided by Finite Element Method (FEM) in four examples.

A ROBUST OPERATIONAL MATRIX OF NONSINGULAR DERIVATIVE TO SOLVE FRACTIONAL VARIABLE-ORDER DIFFERENTIAL EQUATIONS

Currently, a study has come out with a novel class of differential operators using fractional-order and variable-order fractal Atangana–Baleanu derivative, which in turn, became the source of inspiration for new class of differential equations. The aim of this paper is to apply the operation matrix to get numerical solutions to this new class of differential equations and help us help us to simplify the problem and transform it into a system of an algebraic equation. This method is applied to solve two types, linear and nonlinear of fractal differential equations. Some numerical examples are given to display the simplicity and accuracy of the proposed technique and compare it with the predictor–corrector and mixture two-step Lagrange polynomial and the fundamental theorem of fractional calculus methods.

An extension of Lagrange interpolation to approximate derivative, integral and bivariate function

Lagrange interpolation is the effective method to approximate an arbitrary function by a polynomial. But there is a need to estimate derivative and integral given a set of points. Although it is possible to make Lagrange interpolation first, which produces Lagrange polynomial; after that we take derivative or integral on such polynomial. However this approach does not result out the best estimation of derivative and integral. This research proposes a different approach that makes approximation of derivative and integral based on point data first, which in turn applies Lagrange interpolation into the approximation. Moreover, the research also proposes an extension of Lagrange interpolation to bivariate function, in which interpolation polynomial is converted as two-variable polynomial.

Evaluation of Stress Distribution of Isotropic, Composite, and FG Beams with Different Geometries in Nonlinear Regime via Carrera-Unified Formulation and Lagrange Polynomial Expansions

In this study, the geometrically nonlinear behaviour caused by large displacements and rotations in the cross sections of thin-walled composite beams subjected to axial loading is investigated. Newton–Raphson scheme and an arc length method are used in the solution of nonlinear equations by finite element method to determine the mechanical effect. The Carrera-Unified formulation (CUF) is used to solve nonlinear, low or high order kinematic refined structure theories for finite beam elements. In the study, displacement area and stress distributions of composite structures with different angles and functionally graded (FG) structures are presented for Lagrange polynomial expansions. The results show the accuracy and computational efficiency of the method used and give confidence for new research.

A Fractional Order Hepatitis C Mathematical Model with Mittag-Leffler Kernel

In this paper, a mathematical fractional order Hepatitis C virus (HCV) spread model is presented for an analytical and numerical study. The model is a fractional order extension of the classical model. The paper includes the existence, singularity, Hyers-Ulam stability, and numerical solutions. Our numerical results are based on the Lagrange polynomial interpolation. We observe that the model of fractional order has the same behavior of the solutions as the integer order existing model.

Synthesis of Regulators of the Drying Plant Control System Based on Statistical Data

In the article a method to carry out a synthesis of regulators of the drying plant control system is considered based on the integration of known statistical data by the Lagrange polynomial. An algorithm to correct the parameters of regulators in problematic modes of operation of the drying plant is proposed. It is shown that the control system developed and implemented on the PLC provides stable control of temperature and humidity during the drying of materials

Modification of the Algorithm for Selecting a Variable Parameter of the Gaussian Interpolation Function

The paper presents an algorithm for selecting the optimal value of the variable parameter α of the Gaussian interpolation function to obtain the smallest possible error when interpolating the tabular data. The results of the algorithm are checked on a sample of elementary mathematical functions. For comparison, the interpolation data of the Lagrange polynomial are given. The paper presents the results of Gaussian interpolation at different α, conclusions are made about the need to applying the algorithm for selecting of its optimal value.