Solving geometrically nonlinear tasks of the statics of hinged-rod systems basing on finite element method in the form of classical mixed method

Abstract

The most widely used numerical method used in linear calculation of building structures is finite element method in traditional form of displacements. Different software is developed on its basis. Though it is only possible to check the certainty of these numerical solutions, especially of non-linear tasks of engineering structures’ deformation by the coincidence of the results obtained by two different methods. The authors solved geometrically nonlinear task of the static deformation of a flat hinged-rod system consisting of five linear elastic rods undergoing great tension-compression strains. The solution was obtained basing on the finite element method in the form of classical mixed method developed by the authors. The set of all equilibrium states of the system, both stable and unstable, and all the limit points were found. The certainty of the solution was approved by the coincidence of the results obtained by other authors basing on traditional finite element method in displacements.

Numerical Simulation of the Process of Directed Transformation of a Regular Hinge-Rod System

“…A separate category consists of hinge-rod -sized transformable space structures, the disclosure of which occurs automatically in zero gravity [1]. Works [2,3] are devoted to the problem of finite element analysis of the stress-strain state of hinge-rod systems taking into account large displacements. In particular, in [2] a two-rod instantaneously kinematically variable is considered, the design scheme of which is behavior of the in a geometrically nonlinear formulation, the authors have developed an algorithm based on a step-by-step loading scheme and the formation at each step of a mixed system of equations in the form of the displacement method and the force method.…”

“…The configuration of this corresponding to . In order to verify the algorithm proposed in [2,3] we will perform the calculation of the two-rod for the initial position , , A and configuration of the system in the position , , A patterns of vertical displacement distribution A u y and longitudinal forces N in rods, derived using a nonlinear solver of the software package ANSYS Mechanical. Comparing these data with the results of [2], we establish that the value of A u y max corresponding to the calculation of an both calculations -m. when geometrically nonlinear calculation of in position 0 the results are similar [2].…”