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Finite Element Formulations
for Statics and Dynamics of Plane Structures (with Matlab)
Yassin, A. Y. M., et al (2018). Finite Element Formulations for Statics and Dynamics of Plane Structures (with Matlab). Malaysian Society for Numerical Methods. Perak, Malaysia.
This book has evolved from a series of lecture notes of the first author refined over the period of ten years with the co-authors. It revolves around frame structural analysis, both statics and dynamics. In Chapter 1, the book begins with the basic concepts of numerical methods before introducing the concept of Galerkin weighted residual method towards the end. Chapter 2 focuses on bar finite element. The formulation of beam element is discussed in Chapter 3. Chapter 4 discusses the concept of space orientation and the assembly of elements for plane structures (truss and frame). Chapter 5 discusses two classes of eigenvalue problems; free vibration and buckling of structures. Chapter 6 details the formulation of forced vibration of bar, beam and plane frame. In this final chapter, time discretization by finite difference method is introduced.
2D Finite Element Formulations
for Heat, Solid and Fluid (with Matlab)
Yassin, A. Y. M., et al (2020). 2D Finite Element Formulations for Heat, Solid and Fluid (with Matlab). Malaysian Society for Numerical Methods. Perak, Malaysia.
This book is can be considered as an extension to the previous publication (Finite Element Formulations for Statics and Dynamics of Frame Structures) as it dwells on two-dimensional formulation of continuums. Also, the discussion has been extended to nonlinear formulation to cater for the nonlinearity of Navier-Stokes equations. However, in ensuring it to be self-contained, the discussions on the basic concept of numerical methods from the previous publication have been combined, shortened and included in the introduction chapter of this book (Chapter 1). The book is still prepared based on the similar approach that a topic always begins with the derivation of the partial differential equation/s of the problem and followed by the discretization into matrix forms using Galerkin Weighted Residual method hence FEM. At the end of a chapter, worked example and Matlab source code are provided.