The Use of the Finite Element Method for the Calculation of Spatial Rod Systems in Consideration the Large Displacements

摘要

The paper presents a methodology for the analytical calculation of systems with unilateral constraints.This technique is based on the Finite Element Method in the form of a classical mixed method.The approach to the formation of a system of resolving equations for spatial rod systems with large displacements of nodes is described in detail.The following conditions are used for this: static equilibrium equations for all nodes of the system,the kinematic conditions that describe the nodal displacements and the conditions of continuity.In the first step,the calculation is performed in a linear setting.In the transition to the solution of the problem in a non-linear formulation,the resulting solution on the non-deformable scheme is used as the initial approximation.Further calculation is carried out in the form of an iterative process based on the stepwise loading procedure and do the calculation in a linear setting at each step,taking into account the new geometry of the system achieved in the previous step.