Non-smooth dynamic analysis of curved bridges considering the earthquake-induced end-pounding

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Curved beam bridges are widely used to accommodate the needs of complex transportation networks. However, these bridges are characterized by a complex dynamic response under earthquake excitation, and it is common to observe pounding-induced damages at the interfaces between adjacent beams or between the beam and the abutment after high-intensity earthquakes. The identification of pounding occurrences is a challenging task and highly dependent on the computational strategy used. The present paper addresses this problem by proposing and analyzing the suitability of an innovative non-smooth approach to solve the rigid bodies’ dynamic response and contact interactions problem of curved beam bridges subjected to seismic ground motions. To this end, the dynamic equations of motions, including the pounding effects, are first formulated with the introduction of the Lagrange multipliers approach. The unilateral constraints are converted into a linear complementarity problem (LCP) formulation related to the velocity and impulse in the normal and transverse directions. The proposed algorithm of the differential equations in LCP form is successively implemented in Matlab to identify the collision and motion states by accessing the stepwise acceleration time history. A two-span curved beam bridge with an intermediate pier and two adjacent abutments under a single ground motion record is considered for case study purposes to investigate the suitability of the proposed procedure. The accuracy of the proposed method is verified by comparison with finite element (FE) analysis. The analysis results include the bridge’s displacement time history and the motion states of all observed pounding occurrences. Finally, three validation methods, including the LCP relationship, the geometric relationship, and the momentum theorem, are evaluated to examine the validity of the proposed method. The results show that the proposed non-smooth dynamic formulation represents a new rigorous approach to identify and analyze the complex problem of end-pounding occurrence in curved bridges.