Boundary and Finite Elements: Theory and ProblemsSince the development of the finite element method, engineering students have come to rely upon it almost exclusively. Consequently, they eventually leave school and enter the field with little or no experience in alternative methods of solving structural mechanics problems. As powerful and versatile as the finite element method is, a working knowledge of the various approximate methods not only gives structural engineers more options in their problem-solving efforts, it also imparts an understanding of the development and evolution of techniques that ultimately led to the finite element method. Focusing on the practical aspects of the techniques rather than delving deep into the mathematics, Boundary and Finite Elements Theory and Problems brings together the techniques most useful in solving structural mechanics problems, including various approximate methods, the finite element method, and the boundary element method. The author presents the material in a reader-friendly, question-and-answer format, filled with illustrations, exercises and fully worked examples. Thorough, accessible, and practical, Boundary and Finite Elements Theory and Problems is well suited as a text for engineering-oriented courses in approximate methods, the boundary element method, and the finite element method. It also serves as an outstanding reference for engineers working in structural mechanics. |
Contents
Preface vii | 1 |
RayleighRitz method | 31 |
Weighted residual methods | 67 |
The finite difference method | 103 |
The finite element method | 137 |
The boundary element method | 273 |
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Common terms and phrases
A₁ a²w a²w assume ax² axial element beam Betti's theorem body force boundary conditions boundary element method coefficients collocation collocation method constant cos² cross section degrees of freedom Derive differential equation Dirac delta function displacement displacement vector domain dx dy dx² dy² element stiffness expression Find the deflection finite element method finite-difference fundamental solution Galerkin Galerkin method Gaussian quadrature global stiffness governing equation Hence indicial notation isoparametric Jacobian L₁ L₂ loaded as shown N₁ N₂ nodal nodes obtained plate potential energy problem q₁ Rayleigh-Ritz method satisfy shape functions shown in Fig simply supported Solving stiffness matrix strain energy Substituting eq total potential truss u₁ uniformly distributed load variation w₁ w₂ weighted residual x₁ Y₁ zero αξ ΕΙ ηπ Μπ ΣΣ дп дх ду