A method of obtaining exact finite element stiffnesses directly from governing differential equations is explained; another method which uses the column analogy is indicated. These can both be modified by matrix manipulation to allow for relaxed restraint conditions. Exact stiffness matrices are given for the straight prismatic beam, the beam-column (or tie), the vibrating beam-column (or tie), the tapered beam and the annular slab. They are compared briefly with matrices obtained from simple polynomial approximations. Further exact finite elements are possible; they minimize convergence problems and their wider usage is advocated.
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