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 timedependent phenomena, plus beam, plate, and shell theories derived directly from threedimensional elasticity theory. It also contains a systematic treatment of "weak," or variational, formulations for diverse classes of initial/boundaryvalue problems. Directed toward students without indepth 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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One of the best books ever written and presented in the FEA history. The reader needs substantial mathematical background to digest the contents. Once understood, the concepts will never leave you. Simply the best !!
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accuracy algorithm analysis approximation array assume bending bilinear boundary conditions boundaryvalue problem calculations Chapter computed Consider constant constraint ratio convergence coordinates defined definition degrees of freedom denote derivatives diagonal displacement DLEARN dynamic eigenvalues eigenvectors elastic element stiffness employed equation error exact example Exercise Figure Finite Element Analysis Finite Element Method formulation fournode quadrilateral Galerkin Gauss Gaussian quadrature global heat conduction heat equation heterosis incompressible International Journal interpolation isoparametric Journal for Numerical Lagrange Lanczos algorithm Lanczos vectors linear loadtime function mass matrix mesh Methods in Engineering nodal node numbers Note onepoint orthogonal plane strain plate polynomial positivedefinite pressure modes procedure Program quadratic quadrilateral reduced integration satisfy selective integration serendipity shape functions solution space spurious modes stability step stiffness matrix stress SUBROUTINE symmetric T. J. R. Hughes theorem trapezoidal rule triangle values weak formulation zero