Snežana Vulović, Miroslav Živković, Nenad Grujović, Marko Topalović (DOI: 10.24874/jsscm.2025.19.01.07)

 

Abstract

 

This paper presents a method for improving the numerical analysis of contact problems using a penalty formulation. Since contact phenomena are inherently nonlinear, particularly in the case of large deformations, an incremental solution strategy is required. Conventional Newton-Raphson algorithms often face convergence problems when many nodes make contact simultaneously. To overcome this limitation, we propose an automatic load step adjustment strategy based on a prediction-correction algorithm that limits the number of nodes that make contact per increment. The method is implemented in the finite element software PAK and tested on a reference pipe bending problem. The results show that the adaptive procedure reduces the number of increments required for convergence while maintaining the accuracy of the solution. This approach improves computational efficiency and robustness in finite element simulations of complex contact problems and provides a practical framework for addressing nonlinearities associated with friction and large deformations.

 

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