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A simple and systematic choice of admissible functions, which are the eigenfunctions of the closest, simple problem extracted from the one considered, is proposed. The extracted problem must be "less-constrained" than the original one; in other words it must be a problem where some constraints or other complications (e.g. added masses) are eliminated. Elastic constraints replace the eliminated rigid ones. The convergence is also analyzed. This approach has practical applications when it is possible to extract a problem with eigenfunctions expressed in closed form. It also allows a very simple calculation of the potential energy of the system. Solutions for several cases involving beams are given in order to show the power of the method. Application of the method to circular plates and shells is also addressed.
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