A study on an efficient numerical analysis of the curved structural elements

In this study, in-plane loaded and perpendicularly loaded to plane curved rods with variable geometric properties along the axis, barrel vaults and axisymmetric structural elements subjected to static and dynamic loads are theoretically investigated. The materials of the structural elements are assumed to be homogeneous, isotropic, elastic or linear viscoelastic. The governing equations of such structural elements under static loads have been summarized. The obtained canonical form of the first order ordinary differential equations has been solved by Complementary Functions Method (CFM). Also, the transient analysis of in-plane loaded curved rods under the various dynamic loads has been analyzed in the Laplace domain. Furthermore, in the viscoelastic material case, the Kelvin model is employed. According to the correspondence principle, material constants are replaced with their complex counterparts in the Laplace domain. The solution obtained are transformed to the time domain using the modified Durbin's inverse numerical Laplace transformed method. For the suggested models, the computer programs with the static and dynamic analysis of the planar curved structural elements are coded in Mathematica and Fortran. Verification of the computer programs are performed by comparing the results of the present methods with the other numerical methods and analytical solutions. The procedures have been proved to be highly accurate and efficient compared to various other numerical methods available in the literatures. Key Words: Two-Point Boundary Value Problems, Complementary Function Method (CFM), Inverse Laplace Transforms.