Keywords: finite element method, semi-infinite domain, single-layer modelling, structural periodicity, static analysis, eigenvalue analysis, modal superposition, computation efficiency.

This paper presents an efficient finite element methodology for the static analysis of semi-infinite structures, addressing the common issue in structural engineering where the region under analysis is significantly smaller than its surrounding medium. By dividing the domain into proportionally dimensioned layers of elements and maintaining a consistent or proportional stiffness matrix between layers, the proposed method utilises the finite element analysis of only a single layer for predicting the static response of the entire domain invoking the concept of periodicity. Employing eigenvalue analysis, the method examines the relationship between nodal deflection across different layers and mechanical behaviours including the transient and steady-state response. This facilitates the extraction of recurrent modes, which then characterise the overall static response through modal superposition. The methodology is notably efficient in managing the extensive degrees of freedom typically associated with semi-infinite domains, even when employing a fine mesh at the loaded end to enhance the capturing of local effects. The validity of this method is demonstrated through the analysis of a sample problem involving a hole in an infinite plate, with results consistently verifying the accuracy. Furthermore, a foundation problem is examined, underscoring the broader applicability of the proposed method in infrastructural contexts.

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