In this study we consider numerical solutions of transient problems in elastic and viscoelastic composite strips. The wide variability and complexity of the expressions makes for overly cumbersome analytic inversion of the Laplace transformed solutions, so we accomplish the inversion numerically, via the DAC algorithm. The DAC algorithm has received wide usage because of its accuracy and computational efficiency. However, the sharp wavefronts of elastic waves create an inaccuracy due to Gibbs’ phenomenon. Of all the mitigation procedures available we have found that the filter methods, in particular, Lanczos’ sigma factors, provide the best results without contributing to the computational requirements of inversion. The results obtained through the DAC algorithm coupled with Lanczos’ sigma factors are compared with results from DYNA3D, a large-scale, dynamic explicit FE code, and found to be in excellent agreement Our method, thus verified, is applied to investigate optimization problems in composite strips. We look for designs that will minimize peak stress, and mean square stress for composites subject to a step loading. The step load is an approximation to a more realistic impact load. Therefore, we continue by examining the same optimization criteria for composites subject to more realistic impact boundary conditions; impact by a semi-infinite elastic flying plate, a finite elastic plate and a rigid plate. This portion of the study provides quantitative evidence of the validity of the stress step approximation.
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