## 7 Conclusions  
In this study, the dynamic response of optimized multiple intersecting MICEPH under the effect of non-contact UNDEX was explored. The simulation technique was followed to avoid the expenses and complexity of physical tests. First, the multiple intersecting MICEPH subjected to hydrostatic pressure was optimized. Thereafter, using the optimum design results, the numerical simulation was carried out. Then, the response modes, breathing, accordion and whipping for the MICEPH subjected to non-contact UNDEX were discussed. Furthermore, the effects of applying various failure criterions such as maximum stress, Azzi-Tsai-Hill, and Tsai-Hill criteria for the damage initiation on failure strengths of pressure hull were studied. Based on the analysis and the simulation results, the following conclusions were drawn:  
* The explosion weight and standoff distance greatly affects the computed POR field distribution, propagation and its magnitude. * Based on the study of response modes, for nodes \(A\) and \(B\), the greatest acceleration occurs in the athwart direction, which is the main direction of the shock wave, followed by the vertical and longitudinal directions. Meanwhile, for nodes \(C\) and \(D\), which are located at the top and the bottom of the MICEPH, the greatest acceleration occurs in the vertical direction followed by the athwart and longitudinal directions. Likewise, for nodes \(E\) and \(F\), which are located at the center of each end of the MICEPH (fore and aft) directions, the greatest acceleration occurs in the longitudinal direction, followed by the vertical and athwart directions. * The cavitation occurs immediately after the incident shock wave hits the MICEPH. * The local cavitation has a major effect on athwart acceleration. Additionally, the uploading of structure and the first bubble pulse have also, a major effect on athwart acceleration. * This analysis can predict the failure index of the optimized pressure hull, which can be effectively used to determine the safe explosion weights and standoff distance to avoid the failure. * The failure index of the pressure hull, caused by the shock wave due to detonation of 20 kg TNT charge at offset distance 5.5 m away from the side of the amidships of the hull is higher than one. Therefore, in this case, the pressure hull will collapse. * On the other hand, at offset distance 15.5 m and 20.5 m, the failure index of the pressure hull is less than one, and the pressure hull will avoid the failure. Consequently, the standoff distance has a great effect on the failure index. * The test results showed that applying different failure criterion such as maximum stress, Azzi-Tsai-Hill, and Tsai-Hill criteria for the damage initiation have a slight to no difference among them on the failure strengths of pressure hull. * The simulation technique utilized in this study and its results can serve as a valuable reference for designers to enhance the resistance of underwater vehicles against underwater explosion. E.F. and M.H. ; methodology, E.F. and M.H. ; software, E.F. and M.H. ; validation, E.F.; M.E. ; M.A. ; formal analysis, E.F. and M.H. investigation, H.H. and D.W., M.E., M.A. ; resources, E.F. and M.H. ; data curation, E.F.; writing--original draft preparation, all, writing--review and editing, E.F.; M.E. ; M.A. ; E.F., visualization, E.F. and D.W; supervision, E.F., H.H. and D.W., project administration, D.W.; funding acquisition. The authors are grateful for the support of this research by the 13 th Five Years Key Programs for Science and Technology Development of China (Grant No. 2016 YED0701300), the Chinese Natural Science Foundation (Grant No. 51405076), and Heilongjiang Province Applied Technology Research and Development Program Major Project of China (Grant No. GA168301). Also, the authors are grateful to Military Technical College (Cairo, Egypt), Tair University (Tair, KSA) and Mansoura University (Mansoura, Egypt) for providing all the required facilities to carry out the present research.