A first course in the finite element method /
Daryl L. Logan
- 3rd ed.
- Bangalore : Thomson Learning, 2002.
- xvi, 696 pages : illustrations ; 25 cm
Brief History -- Introduction to Matrix Notation -- Role of the Computer -- General Steps of the Finite Element Method -- Applications of the Finite Element Method -- Advantages of the Finite Element Method -- Computer Programs for the Finite Element Method -- Definition of the Stiffness Matrix -- Derivation of the Stiffness Matrix for a Spring Element -- Example of a Spring Assemblage -- Assembling the Total Stiffness Matrix by Superposition (Direct Stiffness Method) -- Boundary Conditions -- Potential Energy Approach to Derive Spring Element Equations -- Development of Truss Equations -- Derivation of the Stiffness Matrix for a Bar Element in Local Coordinates -- Selecting Approximation Functions for Displacements -- Transformation of Vectors in Two Dimensions -- Global Stiffness Matrix -- Computation of Stress for a Bar in the x-y Plane -- Solution of a Plane Truss -- Transformation Matrix and Stiffness Matrix for a Bar in Three-Dimensional Space -- Use of Symmetry in Structure -- Inclined, or Skewed, Supports -- Potential Energy Approach to Derive Bar Element Equations -- Comparison of Finite Element Solution to Exact Solution for Bar -- Galerkin's Residual Method and Its Application to a One-Dimensional Bar -- Development of Beam Equations -- Beam Stiffness -- Example of Assemblage of Beam Stiffness Matrices -- Examples of Beam Analysis Using the Direct Stiffness Method -- Distributed Loading -- Comparison of the Finite Element Solution to the Exact Solution for a Beam -- Beam Element with Nodal Hinge.