Essentials of the finite element method: for mechanical and structural engineers

1.6.1. Step 1. Discretize or Model the Structure1.6.2. Step 2. Define the Element Properties; 1.6.3. Step 3. Assemble the Element Structural Matrices; 1.6.4. Step 4. Apply the Loads; 1.6.5. Step 5. Define Boundary Conditions; 1.6.6. Step 6. Solve the System of Linear Algebraic Equations; 1.6.7. Step 7. Calculate Stresses; 1.7. What About the Available Software Packages?; 1.8. Physical Principles in the Finite Element Method; 1.9. From the Element Equation to the Structure Equation; 1.10. Computer-Aided Learning of the Finite Element Method; 1.10.1. Introduction to CALFEM.

General purpose commandsMatrix functions; Material functions; Element functions; 1.10.2. Spring elements; Input variable; Stiffness matrix; Section force; 1.10.3. Bar Elements for Two-Dimensional Analysis; Input variables; Stiffness matrix; Section force; 1.10.4. Bar Elements for Three-Dimensional Analysis; Input variables; Stiffness matrix; Section force; 1.10.5. Beam Elements for Two-Dimensional Analysis; Input variables; Stiffness matrix; Section force; 1.10.6. Beam Elements for Three-Dimensional Analysis; Input variables; Stiffness matrix; Section force; 1.10.7. System Functions.

1.10.8. Statement Functions1.10.9. Graphic Functions; 1.10.10. Working Environment in ANSYS; References; Chapter 2: Mathematical Background; 2.1. Vectors; 2.1.1. Definition of Vector; 2.1.2. Scalar Product; 2.1.3. Vector Product; 2.1.4. Rotation of Coordinate System; 2.1.5. The Vector Differential Operator (Gradient); 2.1.6. Greens Theorem; 2.2. Coordinate Systems; 2.2.1. Rectangular (or Cartesian) Coordinate System; 2.2.2. Cylindrical Coordinate System; 2.2.3. Spherical Coordinate System; 2.2.4. Component Transformation.

Fundamental coverage, analytic mathematics, and up-to-date software applications are hard to find in a single text on the finite element method (FEM). Dimitrios Pavlou's Essentials of the Finite Element Method: For Structural and Mechanical Engineers makes the search easier by providing a comprehensive but concise text for those new to FEM, or just in need of a refresher on the essentials. Essentials of the Finite Element Method explains the basics of FEM, then relates these basics to a number of practical engineering applications. Specific topics covered include linear spring elements, bar.