Meshfree analysis of structures modeled as extensible slender rods

The analysis of members that can be modeled as extensible elastic slender rods is investigated. A meshfree formulation using a Local Radial Point Interpolation Method (LRPIM) is developed that utilizes radial basis functions in curvilinear coordinates. This approach bypasses the need to utilize more conventional element meshes and significantly reduces the number of equations needed for the numerical solution. The slender rod formulation presented allows for tension variation, axial stretch, incremental loading and distributed load variation along the rod. It is well suited for nonlinear problems that involve large deflections and rigid rotations. The position and tangent vectors are expressed using Hermite-type approximations, and radial basis functions, while the interpolation of tension variation and distributed loads are described using polynomials. The solution procedure of weighted residuals Galerkin weak formulation combined with an incremental iterative numerical scheme is introduced to address the incremental loading and large deflection issues for static and quasi-static problems. The implementation of the analytical formulation and the numerical procedure are illustrated using three nonlinear problems. The first two examples provide insight into the validity, accuracy, and efficiency of the methodology. The third example presents the case of a moving boundary condition problem which models a cable entangled by fishing boat-trawling equipment.