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5 results on '"complete basis function"'

1. The Improved Interpolating Complex Variable Element-Free Galerkin Method for Two-Dimensional Elastic Problems.

Author

Deng, Yajie and Dai, Ying

Abstract

An improved interpolating complex variable element-frees Galerkin (IICVEFG) method for the two-dimensional elastic problems is developed. This method is based on the improved interpolating complex variable moving least-squares (IICVMLS) method and the integral form of the elastic problems. In the IICVEFG method, the proposed shape function has the interpolating feature. Therefore, the essential boundary conditions can be exerted directly. Additionally, the unnecessary terms in the discrete matrices are removed, which results in a set of concise formulas. This method is verified by analyzing three elastic examples under different constraints and loads. The numerical results show that the IICVEFG method is superior in precision and efficiency to other non-interpolating meshless methods. [ABSTRACT FROM AUTHOR]

Published
2022
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2. Analysis of Elastic–Plastic Problems Using the Improved Interpolating Complex Variable Element Free Galerkin Method

Author

Yajie Deng, Xingkeng Shen, Jixiao Tao, and Ying Dai

Subjects
elastic–plastic problem, complex variable meshless method, interpolating shape function, singular weight function, complete basis function, Mathematics, QA1-939
Abstract

A numerical model for the two-dimensional nonlinear elastic–plastic problem is proposed based on the improved interpolating complex variable element free Galerkin (IICVEFG) method and the incremental tangent stiffness matrix method. The viability of the proposed model is verified through three elastic–plastic examples. The numerical analyses show that the IICVEFG method has good convergence. The solutions using the IICVEFG method are consistent with the solutions obtained from the finite element method using the ABAQUS program. Moreover, the IICVEFG method shows greater computing precision and efficiency than the non-interpolating meshless methods.

Published
2021
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4. Numerical Computation, Data Analysis and Software in Mathematics and Engineering.

Author

Cheng, Yumin and Cheng, Yumin

Subjects
Information technology industries, ANSYS CFX, BP neural network, Beijing, COVID-19, Helmholtz equation, alkali-activated slag ceramsite compound insulation block, basement structure, car-following model, cold-roll forming, complete basis function, complex variable meshless method, construction site management, control signal, convection-diffusion-reaction problem, convolutional neural network, crack propagation, cubic spline function, cumulative chord, data analysis, deep learning, defects, dimension splitting generalized interpolating element-free Galerkin method, dimension splitting method, dimension splitting-interpolating moving least squares (DS-IMLS) method, driver's predictive effect, dual-horizon, dynamic response characteristics, elastic-plastic problem, electronic throttle angle, finite element method, heavy haul, hydrogel network, improved element-free Galerkin method, improved interpolating element-free Galerkin (IEFG) method, improved moving least-squares approximation, indoor thermal environment, infrared temperature measurement, interpolating shape function, leased price, longitudinal strain, mathematical model, mechanical property, meshless method, multi-grid, n/a, optimal estimation of flux difference integral, penalty method, peridynamics, personnel health monitoring, potential problem, railway tunnel, residential land, self-avoiding walk, singular weight function, smart helmet, stability analysis, strong wind, temperature error compensation, the lattice hydrodynamic model, thermal and mechanical performances, total leased area, traffic flow, two-dimensional lattice hydrodynamic model, variable horizon, visual angle model
Abstract

Summary: The present book contains 14 articles that were accepted for publication in the Special Issue "Numerical Computation, Data Analysis and Software in Mathematics and Engineering" of the MDPI journal Mathematics. The topics of these articles include the aspects of the meshless method, numerical simulation, mathematical models, deep learning and data analysis. Meshless methods, such as the improved element-free Galerkin method, the dimension-splitting, interpolating, moving, least-squares method, the dimension-splitting, generalized, interpolating, element-free Galerkin method and the improved interpolating, complex variable, element-free Galerkin method, are presented. Some complicated problems, such as tge cold roll-forming process, ceramsite compound insulation block, crack propagation and heavy-haul railway tunnel with defects, are numerically analyzed. Mathematical models, such as the lattice hydrodynamic model, extended car-following model and smart helmet-based PLS-BPNN error compensation model, are proposed. The use of the deep learning approach to predict the mechanical properties of single-network hydrogel is presented, and data analysis for land leasing is discussed. This book will be interesting and useful for those working in the meshless method, numerical simulation, mathematical model, deep learning and data analysis fields.

5. Analysis of Elastic–Plastic Problems Using the Improved Interpolating Complex Variable Element Free Galerkin Method.

Author

Deng, Yajie, Shen, Xingkeng, Tao, Jixiao, and Dai, Ying

Subjects
*COMPLEX variables, *GALERKIN methods, *FINITE element method, *NEWTON-Raphson method, *NUMERICAL analysis
Abstract

A numerical model for the two-dimensional nonlinear elastic–plastic problem is proposed based on the improved interpolating complex variable element free Galerkin (IICVEFG) method and the incremental tangent stiffness matrix method. The viability of the proposed model is verified through three elastic–plastic examples. The numerical analyses show that the IICVEFG method has good convergence. The solutions using the IICVEFG method are consistent with the solutions obtained from the finite element method using the ABAQUS program. Moreover, the IICVEFG method shows greater computing precision and efficiency than the non-interpolating meshless methods. [ABSTRACT FROM AUTHOR]

Published
2021
Full Text
View/download PDF

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