Nonlinear structural analysis technique based on flexibility method by Pade approximants

This work proposes an improved numerical methodology based on the flexibility method to study the geometric nonlinearity of space cable structures. The proposed approach makes use of the Pade approximation to enhance the performance of computation. The transformation to the Pade arrangement is particularly successful in quickly speeding up convergence and obtaining the solution when working with complex structures that demonstrate geometrically nonlinear properties. In contrast to previous approaches, the suggested method directly solves the problem by formulating an algebraic system of nonlinear equations using the Pade approximation. To arrive at an analytical solution, some of the most well-established methods that make use of iterative techniques include dynamic relaxation, finite element analysis, and minimum total potential energy. A comprehensive evaluation of the proposed technique's precision and reliability was conducted using six different numerical examples. The recommended method's accuracy, consistency, and computational efficiency are shown by carefully comparing the results with those of techniques that have been around for a long time. This work contributes to the advancement of numerical approaches for the analysis of complex structural behavior by providing a reliable and efficient alternative. Moreover, this work is beneficial for both academics and professionals working in the field.