Introduction to the Finite Element Method and Implementation with MATLAB®

Connecting theory with numerical techniques using MATLAB®, this practical textbook equips students with the tools required to solve finite element problems. This hands-on guide covers a wide range of engineering problems through nine well-structured chapters including solid mechanics, heat transfer and fluid dynamics; equilibrium, steady state and transient; and 1-D, 2-D and 3-D problems. Engineering problems are discussed using case study examples, which are solved using a systematic approach, both by examining the steps manually and by implementing a complete MATLAB®code. This topical coverage is supplemented by discourse on meshing with a detailed explanation and implementation of 2-D meshing algorithms. Introducing theory and numerical techniques alongside comprehensive examples this text increases engagement and provides students with the confidence needed to implement their own computer codes to solve given problems.

Preface; 1. Introduction; 2. Mathematical preliminaries; 3. Numerical analysis methods; 4. General procedure of FEA for linear static analysis: 1-D problems; 5. FEA for multi-dimensional scalar field problems; 6. Mesh generation; 7. FEA for multi-dimensional vector field problems; 8. Structural elements; 9. FEA for linear time-dependent analysis; Index.

Dr. Gang Li is a professor and D. W. Reynolds Emerging Scholar of Mechanical Engineering at Clemson University. He was an awardee of the National Science Foundation Early Career Award. He is an Associate Editor of the Journal of Computational Electronics and has been serving on the ASME Committee on Computing in Applied Mechanics since 2007. Dr. Li's scholarly articles on computational mechanics and finite element method frequently appear in International Journal for Numerical Methods in Engineering, Computer Methods in Applied Mechanics and Engineering, and Journal of Applied Physics.