A pragmatic introduction to the finite element method for thermal & stress analysis: With the Matlab toolkit SOFEA

This textbook provides an accessible and self-contained description of the Galerkin finite element method for the two important models of continuum mechanics, transient heat conduction and elastodynamics, from formulation of the governing equations to implementation in Matlab. The coverage follows an intuitive approach: the salient features of each initial boundary value problem are reviewed, including a thorough description of the boundary conditions, the method of weighted residuals is applied to derive the discrete equations, and clear examples are introduced to illustrate the method.

Model of a Taut Wire. The Method of Galerkin. Statics and Dynamics Examples for the Wire Model. Boundary Conditions for the Model of a Taut Wire. Model of Heat Conduction. Galerkin Method for the Model of Heat Conduction. Steady-State Heat Conduction Solutions. Transient Heat Conduction Solutions. Expanding the Library of Element Types. Discretization Error, Error Control, and Convergence. Model of Elastodynamics. Galerkin Formulation for Elastodynamics. Finite Elements for True 3-D Problems. Analyzing the Stresses. Plane Strain, Plane Stress, and Axisymmetric Models. Consistency + Stability = Convergence.