The Finite Element Method: Linear Static and Dynamic Finite Element AnalysisThis text is geared toward assisting engineering and physical science students in cultivating comprehensive skills in linear static and dynamic finite element methodology. Based on courses taught at Stanford University and the California Institute of Technology, it ranges from fundamental concepts to practical computer implementations. Additional sections touch upon the frontiers of research, making the book of potential interest to more experienced analysts and researchers working in the finite element field. In addition to its examination of numerous standard aspects of the finite element method, the volume includes many unique components, including a comprehensive presentation and analysis of algorithms of time-dependent phenomena, plus beam, plate, and shell theories derived directly from three-dimensional elasticity theory. It also contains a systematic treatment of "weak," or variational, formulations for diverse classes of initial/boundary-value problems. Directed toward students without in-depth mathematical training, the text incorporates introductory material on the mathematical theory of finite elements and many important mathematical results, making it an ideal primer for more advanced works on this subject. |
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accuracy algorithm analysis approximation array assume bilinear boundary conditions calculations computed Consider constant constraint ratio convergence coordinates defined degrees of freedom denote derivatives diagonal displacement DLEARN dn+1 dynamic eigenvalues eigenvectors elasticity element stiffness equation exact example Exercise Figure Finite Element Analysis Finite Element Method formulation four-node Galerkin Gauss Gaussian quadrature global heat conduction heat equation heterosis incompressible International Journal interpolation Journal for Numerical Lagrange Lanczos algorithm Lanczos vectors linear load-time function mesh Methods in Engineering Newmark Nint nodal node numbers Note Numerical Methods one-point orthogonal plane strain plate polynomial pressure modes procedure quadrilateral reduced integration selective integration serendipity shape functions shear solution space spurious modes stability step strain subroutine symmetric T. J. R. Hughes theorem trapezoidal rule triangle weak formulation zero ξη ξι