Seismic analysis and optimization of concrete bridge under the moving train utilizing numerical methods and adaptive improved harmony search algorithm

Abstract In this paper, the simultaneous actions of moving force and seismic load on the dynamic displacement and optimization of the concrete bridge are studied. The sinusoidal shear deformation beam theory is employed for the modelling of the concrete bridge mathematically. The structural damping of the concrete bridge is assumed by the Kelvin–Voigt theory. Utilizing the method of energy and Hamilton’s law, the equations of motion are obtained. Three mixed numerical methods, including the integral quadrature, harmonic differential quadrature method, and Newmark technique, are presented for the numerical outcomes of the differential equations. Utilizing adaptive improved harmony search, improved harmony search, harmony search, and global harmony search algorithms, the optimization process of the concrete bridge is examined. The mentioned algorithm is improved adaptively by utilizing dynamic deflection. The harmony memory is corrected at first and second adjustments, respectively, based on emotional bandwidth and step size randomly. The optimum conditions of the concrete bridge are evaluated with various harmony existing search methods. The role of multiple parameters, including the velocity and acceleration of moving load, length and thickness of bridge, boundary conditions, and the amplitude of carrying load, in the dynamic displacement of the bridge is studied. The numerical results indicate that with increasing the velocity and acceleration of the moving train, the dynamic displacement of the concrete bridge increases. In addition, with increasing the length of the bridge, the time of maximum deflection (i.e. when the train is in the middle of the bridge) is increased. It is concluded for the concrete bridge under the seismic load that the optimum values of the bridge’s length and thickness are decreased (about 24%) and increased (about 21%), respectively. The optimum values of amplitude, velocity, and acceleration of moving train are decreased, respectively, about 34%, 33%, and 29% in the case of the concrete bridge under the earthquake load. In addition, the optimum length of the concrete bridge is decreased significantly, with increasing the moving load amplitude, velocity, and acceleration. Graphical Abstract Graphical Abstract A schematic figure of concrete bridge subjected to the earthquake ground motion and moving load.