Introduction to Finite Element Methods

The textbook at hand offers an introduction to Finite Element Methods from an engineering point of view comprising the basic principles of virtual work, derivations of displacement-based, mixed and hybrid element formulations for 1-D and 2-D membrane as well as bending structures and heat conduction. Different element geometries, including triangular elements and the isoparametric concept, and related numerical integration schemes, are presented. The element matrices and load vectors are derived in detail, the assembly at the system level is discussed with respect to fulfillment of boundary conditions and numerical efficiency. Evaluation of errors and investigations concerning the quality of the elements complete the work flow.

The textbook offers an introduction to the Finite Element Method from an engineering point of view Heat conduction as well as linear-elastic plane stress and bending structures are addressed The textbook provides background to different methodological approaches and sophisticated element technologies

Autorentext

Dieter Dinkler is Professor emeritus of Structural Analysis at Technische Universität Braunschweig. Ursula Kowalsky is Associate Professor of Structural Analysis at Technische Universität Braunschweig.

Inhalt
Introduction.- Discretization of the Work Equation.- Structure and Solution of the System of Equations.- Heat Conduction.- Membrane Structures.- Bending Structures.- Triangular Elements - Description of Geometry.- Triangular Elements to Describe Heat Conduction.- Triangular Elements for Membrane Structures.- Triangular Elements for Kirchhoff Plates.- Numerical Integration.- Isoparametric Elements.- Hybrid Finite Elements.- Hybrid-Mixed Plane Stress Elements.- Hybrid-Mixed Euler-Bernoulli Beam Elements.- Hybrid-Mixed Kirchhoff Plate Elements.- Hybrid Triangular Plate Elements.- Hybrid-Mixed Triangular Plate Elements.- Discrete Kirchhoff-Teory Element.- Benchmark Concerning Triangular Plate Elements.- Timoshenko Beam Elements.- Plate Elements Including Shear Deformations.- Error Estimations.- Quality of Elements.- References.- Index.