Calculation of flexible arches for large deflections

Authors: Druzyak S.V.
Published in issue: #10(75)/2022
DOI: 10.18698/2541-8009-2022-10-828
Category: Mechanics | Chapter: Mechanics of Deformable Solid Body
Keywords: parameter continuation method, nonlinear deformation, boundary value problem, codimension, limit point, bifurcation point, elastic characteristic, slamming, control parameter
Published: 09.11.2022

The method of constructing the elastic characteristic of a rod structure at all stages of the nonlinear deformation process is considered. Using a rod model reflecting the linear-elastic properties of the material, the boundary value problem for the system of nonlinear differential equations depending on the parameter is solved. The iterative method of continuation over the parameter is chosen as the method for solving the nonlinear problem. The solution is a predictor-corrector scheme. The predictor stage consists in extrapolation of the solution by means of the Lagrange polynomials and the corrector stage is the specification of the results obtained by extrapolation by means of the modified Newton method. The comparison of the results obtained by the author's program with the results of solving the problem in the ANSYS Mechanical APDL finite-element complex is shown.

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