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

International Multi-Conference on Industrial Engineering and Modern technologies

Voronkova, G.V.^1 ; Potapova, E.O.^1

Volgograd State Technical University, 28, Avenue V.I. Lenin, Volgograd

400005, Russia^1

关键词: Analytical calculation;    Initial approximation;    Iterative process;    Kinematic condition;    Large displacements;    Nodal displacement;    Static equilibrium equations;    Unilateral constraints;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/463/3/032099/pdf
DOI  :  10.1088/1757-899X/463/3/032099

来源: IOP

【 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.