Zonal method for contact interaction modeling in the semi-analytical finite element method
DOI:
https://doi.org/10.32347/2410-2547.2026.116.75-83Keywords:
semi-analytical finite element method, contact joint, non-axisymmetric contact, zonal method, iterative algorithm, contact zones, contact modelingAbstract
This paper presents a comprehensive investigation of contact interaction modeling capabilities within the Semi-Analytical Finite Element Method for prismatic structures. The classical SAFEM formulation assumes material property invariance along the longitudinal coordinate, which leads to the appearance of non-physical tensile stresses in contact opening zones. To address this issue, a zonal method is proposed, based on partitioning the longitudinal axis into zones and iteratively determining the distribution of elastic moduli depending on the presence or absence of contact in each zone.
Particular attention is given to the modification of the stiffness matrix assembly procedure, where integration along the longitudinal coordinate for contact elements is performed zonally using different elastic moduli. In contact zones, the full material modulus is applied, while in opening zones a significantly reduced modulus is used to simulate the absence of interaction. The modulus distribution is determined iteratively by solving the problem, computing gaps at zone centers, and updating material properties until convergence is achieved.
Verification of the method was carried out on a benchmark problem of a flange connection of two plates, with results compared against calculations performed in the LIRA-SAPR software package. The results demonstrated high agreement between the zonal method and the three-dimensional FEM formulation: the discrepancy in displacements does not exceed 2.4%, and in stresses — 1.04%. At the same time, the computational efficiency of the zonal method is significantly higher due to the reduced problem dimensionality and the possibility of parallelizing calculations for different expansion terms.
The obtained results confirm the feasibility and effectiveness of the zonal method for modeling contact interaction in prismatic structures. This approach allows for accurate representation of opening zones while maintaining high computational efficiency, making the method suitable for a broad class of engineering problems, including flange connections, multilayer composites, and other cases of unilateral contact.
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