Exploring dynamic response in a three-layer dome with non-homogeneous elastic core under a concentrated impact at its apex

The dynamics of a three-layer dome with a discrete-symmetric lightweight reinforced with ribs under a concentrated impact on its top was studied. The study explores the behavior of a three-layer dome, uniquely designed with discrete, symmetrically placed, lightweight ribs for reinforcement, when subjected to a concentrated impact at its apex. The supporting layers of the dome are made with different thicknesses. Each supporting layer of the dome differs in thickness, offering a complex structure for analysis. In the analysis of the elements of the elastic structure, the Timoshenko model of the theory of shells and rods was used under independent static and kinematic hypotheses for each layer. According to the Hamilton–Ostrogradsky variational principle, the equations of motion of asymmetric three-layer hemispherical shells with a discrete-symmetric lightweight rib-reinforced aggregate under axisymmetric local impulse loading were obtained. An appropriate finite element model of the shell was created, which reflects the relationship between the potential energy of deformations in the body and the potential of applied forces. A detailed finite element model was developed to capture the interplay between the dome’s deformation energy and the force applied, facilitating a nuanced exploration of the dome’s dynamic response. The numerical results of the study of the dynamics of a three-layer elastic structure with asymmetric thickness based on the finite element method were obtained The influence of geometrical and physical–mechanical parameters of asymmetric layers of a spherical dome on its dynamic behavior during a concentrated impact on its top was studied and new mechanical effects were investigated. Through numerical analysis, the dome’s asymmetrical layer thickness and the physical and mechanical characteristics of these layers were examined to determine how they influence the dome’s reaction to concentrated impacts. This investigation reveals novel mechanical behaviors and underscores the significance of geometrical and material properties in the dome’s dynamic performance