Fundamentals of Finite Element Analysis Linear Finite Element Analysis pdf.
This text grew out of a set of notes, originally created for a graduate class on Finite Element (FE) analysis of structures that I teach in the Civil and Environmental Engineering department of Virginia Tech. The book attempts to provide an understanding or the salient features of linear FE analysis, beginning with the mathematics describing an actual physical problem and continuing with the introduction of the FE approximation and the calculation of pertinent arrays and vectors.
The mathematical description of various physical problems in this book (primarily elasticity and heat conduction) employs the “strong form–weak form” paradigm. Given a physical problem, the strong form (governing differential equations and boundary conditions) is established. Then, a weak form is obtained, into which the finite element approximation is subsequently introduced. I believe the strong form–weak form paradigm is a more efficient way of teaching the method than, for example, variational principles, because it is fairly straightforward and also more powerful from a teaching point of view. For example, the derivation of the weak form for solid and structural mechanics provides a formal proof of the principle of virtual work.
The book contains a total of 19 chapters and 4 appendices.
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