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This new book, resulting from the author's 22 years of teaching finite element analysis to undergraduate and graduate students, intends to strike an appropriate balance between the theory and application of the FEM. Utilizing a unique combination of live MATHEMATICA® and MATLAB® implementations, the book enables students to see behind the equations, "inside the black box", to fully understand the methods being presented and the solutions produced.
Steps in a Finite Element Solution. Interpolation Functions. Integration by Parts. Numerical Integration Using Gauss Quadrature. Mapped Elements. Governing Equations. General Form of Finite Element Equations. Tetrahedral Element. Mapped Solid Elements. Stress Calculations. Static Condensation. Substructuring. The Patch Test and Incompatible Elements. Computer Implementation - fe2Quad. Equations of Elasticity in Cylindrical Coordinates. Axisymmetric Analysis. Unsymmetrical Loading. Problems. Euler-Bernoulli Beam Theory (EBT). Mixed Beam Element Based on EBT. Timoshenko Beam Theory (TBT). Displacement Based Element for Timoshenko Beam6. Shear Locking in Displacement Based Elements for Timoshenko Beam. Mixed Beam Element Based on Timoshenko Beam Theory. A Four Field Timoshenko Beam Element. Timoshenko Beam Element Using Linked Interpolation. Problems. Multifield Formulations for Analysis of Elastic Solids. Governing Equations. Displacement Formulation. Stress Formulation. Mixed Formulation. Assumed Stress Field For Mixed Formulation. Analysis of Nearly Incompressible Solids. Kirchhoff Plate Theory. Rectangular Kirchhoff Plate Elements. Triangular Kirchhoff Plate Elements. Mixed Formulation for Kirchhoff Plates. Mindlin Plate Theory. Displacement Based Finite Elements for Mindlin Plates. Nonlinear differential equation. Solution Procedures for Nonlinear Problems. Linearization and Directional Derivative. Analysis of Axially Loaded Bars. Nonlinear Analysis of Trusses. Material Nonlinearity in General Solids. Basic Continuum Mechanics Concepts. Governing Differential Equations and Weak Froms. Linearization of Weak Form. General Form of Element Tangent Matrices. Constitutive Equations. Computations For a Planar Analysis. Deformation Dependent Loading. Linearized Buckling Analysis. Appendix: Double contraction of tensors. Problems. Contact Problems. A Simple Normal Contact Example.