The classical finite strip method can treat linearly elastic prismatic folded plate structures if the structure is simply supported at the ends, if restraints such as bents and diaphragms exert no longitudinal restraint, and if longitudinal loads are in equilibrium. Because it uses a series of longitudinal basis functions which decouple, permitting the solution of a series of relatively small harmonic stiffnesses instead of a larger, combined one, the method is very efficient. Many solutions have been proposed to eliminate the above restrictions. Some of these permit non-simple end supports, but none employ a decoupled harmonic series for general folded plate structures; furthermore, none can treat longitudinally loads and restraints. The extended classical finite snip method proposed in the current study is not restricted in this fashion. It can treat arbitrary end support conditions, arbitrary longitudinal loads and restraints, and uses a decoupled harmonic series. Longitudinal loads and restraints are modelled by expanding the harmonic series of the classical method to include a longitudinal rigid body motion of the strips as well as a uniform longitudinal displacement of each joint. When longitudinal loads are not in equilibrium on each joint, it is shown that the classical finite strip method cannot be used. Care must in particular be exercised for some unsymmetrical prestressing tendons for which the classical method can predict incorrect results. Arbitrary end support conditions are included by means of a Lagrange multiplier procedure, according to which the boundary conditions are stated and added into the potential energy functional. The expanded harmonic series discussed above is used, and acceleration techniques are outlined for improving convergence. For several large-scale examples, results yielded by the extended method, by curved beam theory, and by a finite element program are compared, illustrating that the extended method provides highly accurate values in an efficient manner.
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