INELASTIC ANALYSIS OF FLEXIBLE BARS USING SIMPLIFIED NONLINEAR EQUIVALENT SYSTEMS

The research here deals with the inelastic analysis of flexible bars of any arbitrary variation in their moment of inertial along their length, that are subjected to complicated loading conditions. Since the material of such flexible members is permitted to be stressed well beyond its elastic limit, practically all the way to failure, their modulus of elasticity along their length will also vary. Therefore, the already complicated nonlinear analysis of such members must also take into consideration the actual variation of their modulus of elasticity along their length when large deflections and rotations are calculated. The analysis and mathematical formulation of this problem is based on the method of the equivalent systems which was developed by the first author of this research. This method permits the replacement of the initial nonlinear problem with complicated moment of inertia variations and loading conditions with an equivalent simpler nonlinear system of constant stiffness E1I1, that has the same length, elastic line, and boundary conditions, as the initial nonlinear system. The constant stiffness nonlinear equivalent system will be loaded with a few concentrated equivalent loads. The solution of the constant stiffness equivalent nonlinear system may be obtained by using either one of the following two ways: (a) By using simpler nonlinear analysis if such analysis is readily obtainable, or (b) by deriving a pseudolinear equivalent system of constant stiffness and applying linear analysis. The choice of method would largely depend upon individual preference, but utilization of equivalent pseudolinear systems coupled with pseudolinear analysis, was proven to be the most convenient. The method is considered to be general and it can be applied to many types of flexible beam problems. Exact, as well as accurate approximate solutions are obtained, and the results are compared.