Numerical simulation of the shaping process of a regular-rod hexagonal lattice under discrete kinematic action

Introduction. The problem of studying the process of transformation of a regular rod system from an initial flat state to an arched shape under controlled kinematic action is based on solving a geometrically nonlinear problem of structural mechanics. There is practically no information in the literature on the mathematical modelling of transformable hinge-rod systems, taking into account the shape change, in this regard, the relevant direction is related to the development of engineering techniques for calculating geometrically variable structures using the finite element method.

Materials and methods. This paper presents a technique for finite element modelling of the shape of a regular hexagonal rod lattice using elastic hinges in the nodal joints of beam elements and applying the procedure of incremental kinematic action on contour nodes. Two models of nodal joints are considered: conventional (connecting the displacements and angles of rotation of the nodes of the lattice elements with the corresponding nodes of the joint pads) and with elastic hinges.

Results. A feature of the proposed model of nodal joints of beam end elements is the introduction of six combined elements with different values of linear and rotational stiffness coefficients. Comparative results of computational experiments for lattice models with elastic hinges and without elastic hinges are presented. The simulation results are presented in the form of graphs of the dependence of the “boom” of lifting on the number of transformation steps for various stiffness values of rotary springs.

Conclusions. The proposed direct incremental algorithm for solving a geometrically nonlinear problem is absolutely convergent. Based on the simulation results of the hexagonal lattice shaping process, the hinge-rod joint structure can be designed. The considered transformation of the hexagonal lattice is of particular interest as a 3D art project in the field of architecture and design.

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