Название: Application of Numerical Methods in Engineering Problems using MATLAB
Автор: M.S.H. Al-Furjan, M. Rabani Bidgoli, R. Kolahchi, A. Farrokhian, M.R. Bayati
Издательство: CRC Press
Год: 2023
Страниц: 297
Язык: английский
Формат: pdf (true)
Размер: 10.2 MB

Application of Numerical Methods in Engineering Problems Using MATLAB presents an analysis of structures using numerical methods and mathematical modeling. This structural analysis also includes beam, plate, and pipe elements, and examines deflection and frequency or buckling loads. The various engineering theories of beams/plates/shells are comprehensively presented, and the relationships between stress and strain, and the governing equations of the structure are extracted. To solve governing equations with numerical methods, there are two general types, including methods based on derivatives or integrals. Derivative-based methods have the advantage of flexibility in modeling boundary conditions, low analysis time, and a very high degree of accuracy. Therefore, the book explains numerical methods based on derivatives, especially the differential quadrature method.

In Chapter 1, various theories for beams, plates, and shells, such as classical, frst order, third order, Reddy, and sinusoidal, are presented. In Chapter 2, various solutions methods for example analytical methods (Galerkin and Navier) and derivative based numerical methods for space domain such as differential quadrature, harmonic differential quadrature, discrete singular convolution, and differential cubature as well as numerical methods for time domain, such as Newmark, Poincare–Lindstedt, multiple scale, and the second-order three-time scale expansion, are presented. The governing equations for various examples are derived based on energy method and Hamilton’s principle in Chapters 3 through 14. The analytical and numerical solutions are presented for static and dynamic solutions of the beams, plates, and shells in Chapters 3 through 5, 6 through 10 and 11 through 14, respectively. The key fndings of this book are the basic relations and deriving the governing equations for beams, plates, and shells, as well as the mathematical modeling and mechanical analysis of them.

Features:

Examines the application of numerical methods to obtain the deflection, frequency, and buckling loads.
Discusses the application of numerical methods for solving motion equations.
Includes numerous practical and applicable examples throughout.




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