Numerical Modeling of Change of Shape of Flexible Bars

Flexible bars experiencing large displacements and small strains during loading are investigated. The purpose of the study: numerical analysis of the stress-strain state of flexible bars, taking into account geometric nonlinearity in a three-dimensional formulation. The displacement-based finite element method is used as the mathematical framework. The process of shape changing of the bar was modeled by incremental loading in combination with the restructuring of the geometry of the model, taking into account the resulting displacements. The bar was modeled using rectilinear beam finite elements connected at adjacent nodes by linear and rotational combined elements with variable stiffness. To conduct computational experiments, macros in the APDL language, embedded in the ANSYS Mechanical software, were written and verified. Numerical experiments were performed using finite element models with elastic hinges and without hinges. Based on the results obtained, it is established that the proposed direct incremental algorithm for solving geometrically nonlinear problems of structural mechanics is absolutely convergent. The developed method of defining the stiffness of rotational springs can be used in modeling spatial unstable frames.