Abstract
The homotopy perturbation method (HPM) with an auxiliary term was applied to obtain approximate analytical solutions of polymer cushioning packaging system. The second-order solution of the equation of motion was obtained and compared with the numerical simulation solution solved by the Runge-Kutta algorithm. The results showed the high accuracy of this modified HPM with convenient calculation.
Highlights
Dropping is an unavoidable situation for a packaged product while delivered, which is investigated by many researchers [1–3]
In order to avoid some restrictions of perturbation method, some other methods are developed, including the variational iteration method (VIM) [5], the homotopy analysis method (HAM) [6], He’s max-min method, and the homotopy perturbation method (HPM) [7– 11]
Different parameters may lead to the different accuracy of the HPM solution
Summary
Dropping is an unavoidable situation for a packaged product while delivered, which is investigated by many researchers [1–3]. Among the methods for analytical solution, the perturbation method [4] is one of the most well-known approaches, and it is based on the existence of small parameters which are not commonly existed in many nonlinear problems. Noor [19] modified the HPM with an auxiliary term which makes the HPM more flexible In recent studies, He [20] summarized the modification of the HPM by introducing an auxiliary term, and Duffing equation was used as an example to illustrate the solution procedure. This paper investigated for the first time the applicability and the validity of the modified HPM for EPS polymer cushioning packaging system. In order to show the accuracy of this method, some specific parameters were used in the constitutive equation based on real situation, and solutions of the modified HPM and Runge-Kutta method were compared
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