Impact resistance performance and optimal design of a sandwich beam with a negative stiffness core

Numerical analyses were carried out to investigate the response of a sandwich beam with a negative stiffness (NS) core under quasistatic compression and low-velocity impact at the center. By varying the thicknesses of face sheets and interlayers and the lengths of segments, a parametric study on the impact resistance of the sandwich beam is conducted. The maximal deflection of the top face sheet and the strain energy stored in the NS beam were recorded at the moment when the impactor's velocity decreased to zero. Based on the impact simulation, a multi-objective optimization problem on the beam configuration was set up to find out the most efficient anti-deformation design at the impact velocity of 2500 mm/s. To solve the problem with the surrogate model method, an optimal Latin hypercube sampling (OLHS) technique and a two-phase differential evolution (ToPDE) algorithm were utilized to generate calculation points in the design space, respectively. Then different surrogate models including the RSM model, the Kriging model and the RBF model, were compared to give the best approximation of the original problem. In the end, the genetic algorithm (GA) dealing with discrete optimization problems was employed to obtain the optimum solutions. Results indicate that different parts of the NS beam dominate the resistance to deformation under different levels of impact intensity. The largest portion of the strain energy is stored in the four curved plates. In the obtained optimization solution, the longest segment is near the two ends and the flat plates near the top are thicker, which is instructive to the beam design on improving impact resistance.