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Introduction and Discrete Problems
OneDimensional Boundary Value Problems
9 other sections not shown
algebraic equations approximate solution assembly basic boundary value problem centroid components Consider constant constraints convergence coordinates corresponding derived variables determined differential equation discretization discussed displacements dr dz dVol dx dy dy dx eigenvalue problem eigenvectors elastic Elemental formulation elemental matrices elemental stiffness matrix equilibrium essential boundary essential boundary conditions Euler algorithm evaluated exact solution example expressed FIGURE Finite Element Analysis finite element method finite element model follows Galerkin Galerkin method Gauss points Gauss quadrature given by Eq global stiffness matrix indicated in Fig integration interelement interpolation functions iteration linear algebraic linearly interpolated natural boundary conditions nodal values nodes normal obtained one-dimensional potential energy Q8 elements quadratically interpolated Rayleigh quotient region Repeat Exercise Ritz Ritz method satisfied segment set of equations shear stress shown in Fig solve step symmetric torsion two-dimensional typical weak formulation yields zero