A coupled closed-form/Doubly Asymptotic Approximation approach for the response of orthotropic plates subjected to an underwater explosion

Abstract

In this paper, a closed-form analytical solution procedure is proposed to solve the coupled fluid-structure interaction (FSI) equations that involve the first-order Doubly Asymptotic Approximation (DAA1) formulation. An efficient method comprised of the nonstandard finite difference (NSFD) scheme is applied. First of all, analytical equations are developed to analyze the response of a rigid mass-spring oscillator in an air-backed condition when it is subjected to a plane shock exponential wave coming from a far-field underwater explosion. After validating the results with LS-DYNA/USA (DAA1), these equations are extended to determine the response of a two-dimensional, simply-supported rectangular plate, and then tested on the isotropic and orthotropic plates within a small deflection regime. Parametric studies are also performed by varying the load decay times, peak pressures, as well as the aspect ratios of the plate. Finally, the advantages and limitations of the proposed formulae are exposed along with suggestions for the future work.

Response of composite plates in air-backed and water-backed conditions subjected to a far-field underwater explosion

“…Equations ( 3) and ( 5) together form a system of coupled differential equations for the FSI and can be solved using NSFD method, see the complete derivations in (Sone Oo et al 2020bOo et al , 2021. The time interval [𝑡 0 , 𝑡] is discretized as:…”

“…Coupling with DAA1 for the air-backed condition has been presented in detail by (Sone Oo et al 2020b, 2021. To entail the purpose of this paper, only a brief summary of the derivation is presented here.…”

“…Note that 𝐷 𝑓 𝑚𝑛 = 𝜌 𝑤 𝑐 𝑤 /𝑀 𝑎 𝑚𝑛 needs to be calculated for each mode 𝑚, 𝑛. The modified formulation of(Greenspon 1961)'s water-added mass per unit area is (also see, SoneOo et al 2021):…”