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. |
Other editions - View all
Common terms and phrases
approximation function assemblage equations assumed axial beam bending beam-column Chapter closed form solution coefficient column components computer code consider coordinate system defined deformation degrees of freedom denotes Derive Element Equations Desai discretized elastic elements Figure equation and natural evaluated exact solution Example expressed finite element analysis finite element formulation finite element method flow problem fluid head Galerkin’s method Gaussian elimination given global coordinate governing equation heat flow Hence hybrid integration interelement compatibility interpolation functions load vector local coordinates material properties mesh natural boundary conditions nodal displacements node numbers nodes nondimensional obtain one-dimensional plane strain plane stress plate polynomial expansion potential energy potential flow primary unknown procedure quadrilateral element quantities residual respectively seepage shear stresses shown in Figure solve Step stiffness matrix strain Substitution surface traction temperature triangular element two-dimensional variation variational calculus vector of nodal velocity warping function yields zero