Introductory Finite Element MethodAlthough there are many books on the finite element method (FEM) on the market, very few present its basic formulation in a simple, unified manner. Furthermore, many of the available texts address either only structure-related problems or only fluid or heat-flow problems, and those that explore both do so at an advanced level. Introductory Finite Element Method examines both structural analysis and flow (heat and fluid) applications in a presentation specifically designed for upper-level undergraduate and beginning graduate students, both within and outside of the engineering disciplines. It includes a chapter on variational calculus, clearly presented to show how the functionals for structural analysis and flow problems are formulated. The authors provide both one- and two-dimensional finite element codes and a wide range of examples and exercises. The exercises include some simpler ones to solve by hand calculation-this allows readers to understand the theory and assimilate the details of the steps in formulating computer implementations of the method. Anyone interested in learning to solve boundary value problems numerically deserves a straightforward and practical introduction to the powerful FEM. Its clear, simplified presentation and attention to both flow and structural problems make Introductory Finite Element Method the ideal gateway to using the FEM in a variety of applications. |
Contents
Principles and Laws | 7 |
Steps in the Finite Element Method | 13 |
TwoDimensional Problems | 41 |
Summary | 47 |
OneDimensional Stress Deformation | 53 |
Principle of Minimum Potential Energy | 61 |
Integration | 75 |
Boundary Conditions | 82 |
Boundary Conditions | 261 |
ThreeDimensional Formulation | 284 |
Comparisons of Numerical Predictions and Closed Form Solutions | 309 |
Review and Comments | 327 |
1888888 | 345 |
Static Condensation | 354 |
References | 360 |
Stream Function Formulation | 371 |
Strains and Stresses | 88 |
Formulation by Galerkins Method | 92 |
Bounds | 112 |
References | 120 |
Problems | 135 |
TimeDependent Problems | 144 |
OneDimensional Consolidation | 162 |
Problems | 169 |
References | 175 |
Users Guide for Code DFTC1DFE | 184 |
Users Guide for Field2D | 195 |
BeamColumn | 219 |
Problems | 228 |
References | 237 |
References | 248 |
Thermal or Heat Flow Problem | 377 |
Electromagnetic Problems | 384 |
References | 392 |
Finite Element Formulation | 400 |
Computer Code | 418 |
Problems | 428 |
References | 436 |
Computer Code | 447 |
Transformation of Coordinates | 455 |
Solution of Beam | 459 |
Comparisons of the Methods | 469 |
Solution Procedure | 475 |
References | 482 |
Other editions - View all
Common terms and phrases
a₁ a₂ approximation function assemblage equations assumed axial b₁ b₂ beam bending beam-column boundary conditions Chapter closed form solution coefficient column computed consider consolidation coordinate system deformation degrees of freedom denotes Desai differential discretized dxdy dy dy dy elements Figure Example expressed finite element analysis finite element formulation finite element method flow problem fluid head Gaussian elimination given global coordinate governing equation heat flow Hence hybrid input integration interelement compatibility interpolation functions k₁ kg/cm² load vector local coordinates M₁ mesh N₁ N₂ natural boundary conditions Node number NSLC obtain one-dimensional pore water pressure potential energy potential flow primary unknown procedure quadrilateral element respectively shear stresses shown in Figure solve Step stiffness matrix strain surface traction T₁ T₂ temperature torsion triangular element two-dimensional v₁ values variation velocity w₁ warping function x₁ Y₁ Young's modulus zero эт