In this paper, the numerical micromodulus is derived for the plane stress problem to develop a new insight into the application of bond-based peridynamics. Considering the nonlocal property of peridynamics, the numerical micromodulus coupled with influence function provides a reasonable description of the long-range force effect. Through several numerical applications, the effectiveness of the numerical modulus coupled with various influence functions to simulate deformation and failure is analyzed. In addition, a load increment algorithm based on fictitious density is developed specifically for quasi-static problems. It is indicated that the introduction of the influence function can enhance the accuracy in deformation and failure simulation, which is valuable for the advancement and application of numerical micromoduli. Through a comprehensive trade-off between simulation accuracy and stability, the numerical micromodulus coupled with the exponential influence function proves to be the more effective option for brittle material.

The dynamic behavior of three-layer composite beams, consisting of concrete slabs and steel beams, is influenced by the structural configuration of each layer as well as the shear connectors. The interlayer shear stiffness in three-layer composite beams governs their global dynamic behavior, while interlayer slippage-induced localized vibration effects represent a key limiting factor in practical applications. Based on the dynamic test results of steel–concrete double-layer composite beams, the feasibility of a finite element solid model for composite beams, which accounts for interlayer shear connectors and beam body characteristics, has been validated. Utilizing identical modeling parameters, an analytical model for the inherent vibration characteristics of three-layer steel–concrete composite beams has been developed. This study encompasses two types of composite beams: concrete–steel–concrete (CSC) and concrete–concrete–steel (CCS). Numerical simulations and theoretical analysis systematically investigated the effects of interface shear connector arrangements and structural geometric parameters on dynamic performance. Research indicates that the natural frequency of steel–concrete three-layer composite beams exhibits a distinct two-stage increasing trend with the enhancement in interlayer shear stiffness. For CSC-type simply supported composite beams, the fundamental vertical vibration frequency increases by 37.82% when achieving full shear connection at both interfaces compared to the unconnected state, while two-equal-span continuous beams show a 38.06% improvement. However, significant differences remain between the fully shear-connected state and theoretical rigid-bonding condition, with frequency discrepancies of 24.69% for simply supported beams and 24.07% for continuous beams. Notably, CCS-type simply supported beams display a 12.07% frequency increase with full concrete-to-concrete connection, exceeding even the theoretical rigid-bonding frequency value. Longitudinal connector arrangement non-uniformity significantly impacts dynamic characteristics, while the transverse arrangement has minimal influence. Among structural parameters, steel flange plate thickness has the most significant effect, followed by concrete slab width and thickness, with steel web thickness having the least impact. Based on the observation that the first-order vertical vibration frequency of three-layer composite beams exhibits a two-stage decreasing trend with an increase in the span-to-depth ratio, it is recommended that the span-to-depth ratio of three-layer steel–concrete composite beams should not be less than 10.