Straight Beams Rested on Nonlinear Elastic Foundations – Part 2 (Numerical Solutions, Results and Evaluation)

Abstract:

This paper presents numerical solutions of straight plane beam structures rested on an elastic (Winkler's) foundation. It is a continuation of our previous work (see Part 1 of this article) focused on practical applications and solutions including nonlinearities in the foundation (i.e. bilateral linear, bilateral linear + cubic, bilateral linear + cubic + quintic approximations and unilateral approximation for dependencies of reaction forces on deflection in the foundation). For solutions of nonlinear problems of mechanics (i.e. differential 4^th-order equations), the Finite Difference Method (i.e. the Central Difference Method) is applied in combination with the Newton (Newton–Raphson) Method. Finally, in one example, linear and nonlinear approaches are solved, evaluated and compared. In some cases, there are evident major differences between the linear and nonlinear solutions.

• Periodical: Applied Mechanics and Materials (Volume 684)
• Pages: 21-29
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.684.21
• Online since: October 2014
• Authors: Šárka Michenková, Karel Frydrýšek*, Marek Nikodým
• Keywords: Beam, Elastic Foundation, Finite Difference Method (Central Differences), Newton–Raphson Method, Nonlinearity, Programming, Results

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