Theoretical prediction of cross-sectional deformation of circular thin-walled tube in large elastic-plastic deformation stage under lateral compression

The present paper focusing on the most important energy absorbing system of the circular thin-walled tubes or shells under lateral compression between two rigid plates, which is also a basic mechanical issue, studies the cross-sectional deformation in terms of the compressive force applying to the tube in the large elastic-plastic deformation stage during the lateral compressive process by both theoretical as well as finite element analysis (FEA) methods. Firstly a FEA simulation for the thin-walled tube's lateral compressive process between two parallel plates is carried out to analyze the mechanical response and deformation characteristics, and then it is validated by tube's lateral compressive experiment using digital image processing technology. Following the simulation results, some assumptions are proposed for theoretical derivation. Secondly focusing on the large elastic-plastic deformation stage (Stage II, in this paper), the compressive deformation of thin-walled tubes is divided into elastic and plastic regions according to the von Mises yield criterion. In elastic region the linear strain-displacement relations of shell theory and Hooke's stress-strain relations are employed, and in plastic region the nonlinear large strain-displacement relations of doubly-curved shell theory and the power hardening rule are employed. Then considering both geometric and material nonlinearities, the equilibrium equation, which is a complicate integral equation with the variable upper limit, is derived using the principle of virtual work. It is solved by expanding the integrand as a set of polynomials power series. Then the predicted cross-sectional deformation in terms of the compressive force can be obtained by the iterative method. Finally some lateral compressive simulations involving various tubes with different geometric parameters are carried out, and the theoretical model is validated by comparison of the cross-sectional profiles predicted by theoretical model with those obtained by the simulations as well as other methods. At the same time, the applicable conditions of this model are discussed. This paper will play a positive role in studying the cross-sectional deformation for various shells under lateral compression in different application areas.

Automated summary

This paper focuses on studying the cross-sectional deformation of circular thin-walled tubes or shells under lateral compression between two rigid plates, which is an important mechanical issue. The study is conducted through both theoretical and finite element analysis methods, where a FEA simulation and experimental validation are carried out to analyze the mechanical response and deformation characteristics of the tubes. The study proposes assumptions for theoretical derivation and divides the compressive deformation of the tubes into elastic and plastic regions. By considering both geometric and material nonlinearities, an equilibrium equation is derived, and the predicted cross-sectional deformation in terms of the compressive force is obtained. The theoretical model is validated through simulations and comparisons with other methods. The research is important for studying the cross-sectional deformation of shells under lateral compression in various application areas.