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This paper investigates different approximation techniques for planar beam column elements in force-based methods. The three fields, introduced in this review, are: curvature-based displacement interpolation (CBDI) used in matrix-based flexibility formulations, linear displacement approximation applied in state space, and higher-order displacement approximation utilized again in state space. Using these three approximation fields, the responses and their accuracies in some systems are compared in examples. Finally, focusing on the accuracy and regarding the performed analyses, it seems that the computational cost is reduced and accuracy of responses is elevated in many engineering problems using the higher-order approximation field in state space.

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Marine structures are one of the most important industrial and military equipment in each country that should be protected against external forces. The main aim of this paper is a detailed investigation of the underwater explosion (UNDEX) and its effects on marine structures. For this purpose, the UNDEX structure was studied qualitatively and quantitatively using numerical methods. Then, the effects of blast waves on a marine structure reinforced by perpendicular blades were investigated. Finite element and finite volume schemes were used for discretization of the governing equations in the solid and fluid media, respectively. Also, for fluid-structure interaction (FSI), results of fluid and solid media were mapped to each other using the two-way FSI coupling methods. A comparison of numerical results with the empirical formula revealed that the trend of pressure-time curves was reasonable, approving the validity of the numerical method. Moreover, the numerical results indicated that detonation of 1 kg trinitrotoluene (TNT) creates a pressure wave with maximum amplitude of 24 MPa at a distance of 2 m. Also, it was found that the reinforcement blades can be used to improve the resistance of structures against explosive charges, which also results in the reduction of structures deformation.