EIGENVALUE SOLUTIONS FOR EULER-BERNOULLI BEAMS ON TWO-PARAMETER FOUNDATIONS USING STODOLA-VIANELLO ITERATION METHOD AND POLYNOMIAL BASIS FUNCTIONS
Abstract
The critical buckling load determination of axially compressed simply supported Euler-Bernoulli beams rested on two-parameter foundations (EBBo2PF) of Filonenko-Borodich, Pasternak or Vlasov is important for their analysis and design. This work uses the Stodola-Vianello iteration method to formulate the governing domain equation, and constructs a fourth degree polynomial shape function that satisfies the simply supported ends. By substitution of the derived polynomial basis function in the Stodola-Vianello iterations and use of boundary conditions, the four constants of integration in the algebraic formulation are calculated. The requirement for convergence of the iteration at the first iteration is used to establish the buckling equation, whose roots yield the eigenvalue from which the critical buckling load is derived. The critical buckling load expression is found to depend upon the two beam-foundation parameters  and ; and presented in tabulated forms for given values of the foundation parameters. The critical buckling load solution obtained in this study showed insignificant difference of less than 0.075% from the previously reported solution by Anghel and Mares for all values of the foundation parameters. It is further found that when the second foundation parameter b2 vanishes the buckling load becomes identical to the critical buckling load for Euler-Bernoulli beams on Winkler foundations, EBBoWF.
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KEYWORDS Euler-Bernoulli beam on two-parameter foundation, eigenvalue, critical buckling load, characteristic buckling equation Stodola-Vianello iteration method.
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