This study investigates the low-velocity impact response of sandwich plates with a low mass ratio. The top face sheet is modeled as an orthotropic plate on an elastic foundation, representing the compliant core, while a linear contact law describes the interaction with the impactor. Analytical expressions for the impact force and plate deflection are derived as functions of time and a characteristic parameter that depends on both the plate and impactor properties. The proposed methodology involves a two-stage optimization. First, the impact force is maximized under a prescribed deflection constraint using a Lagrange operator combined with gradient-based optimization. Second, the characteristic parameter is optimized through an inverse least-squares approach, using a reference study from the literature as a target. This combined forward-inverse framework provides a systematic and analytically tractable method for tailoring the impact response of sandwich plates. The approach highlights the interplay between material properties, geometric configuration, and impact conditions, offering potential applications in the design of lightweight protective structures, aerospace panels, and other energy-absorbing systems.
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