Product: ABAQUS/Explicit
Simulating the response of submerged structures of simple geometric shapes to various underwater explosions constitutes an important part of the validation of any fluid-structure interaction code. In this example the ability of ABAQUS/Explicit to model the interaction between a spherical elastic shell and a spherical exponentially decaying wave is illustrated. The results obtained using ABAQUS/Explicit are compared with those obtained independently using the Doubly Asymptotic Approximation (Geers (1978), ABAQUS/USA Version 6.1). This problem has been solved analytically by Huang et al (1971).
This problem models the interaction between an air-backed spherical elastic shell and a weak spherical exponentially decaying shock wave with a maximum pressure of 1 MPa and a decay time of 0.685 ms. The source is located 4 m away from the center of the sphere. In contrast to the solution from Huang et al., engineering material parameters for the fluid and solid media are used. The sphere has a radius of 1 m and a thickness of 0.02 m. The sphere is made of steel with a density of 7766 kg/m3, a Young's modulus of 210.0 GPa, and a Poisson's ratio of 0.3. The fluid is water with a density of 997 kg/m3, in which the speed of sound is 1461 m/s. An axisymmetric model is used for this analysis. The spherical shell is represented by a semicircular shell, and the surrounding fluid is represented by an acoustic region bounded by two concentric semicircles and the axis of symmetry. The spherical shell is modeled with SAX1 elements, while the surrounding fluid is modeled with ACAX4R elements. The inner semicircle that bounds the fluid region is coincident with the shell, and the outer semicircle has a radius of 3 m. A spherical nonreflective boundary condition is imposed on the outer semicircle using the *SIMPEDANCE option. The fluid response is coupled to that of the structure using the *TIE option. The fluid-solid system is excited by a spherical exponentially decaying wave applied at the point where the semicircular shell intersects the axis of symmetry through the use of the *INCIDENT WAVE option. A linear bulk viscosity parameter of 0.2 and a quadratic bulk viscosity parameter of 1.2 are used.
The results from ABAQUS/Explicit show good qualitative comparison with those in the referenced literature. We also compare the numerical values for radial velocities at the leading and trailing points on the spherical shell obtained using ABAQUS/Explicit with those obtained using ABAQUS/USA (Version 6.1). As shown in Figure 1.13.10–1 and Figure 1.13.10–2, the results agree closely.
Geers, T., “Doubly Asymptotic Approximations for Transient Motions of Submerged Structures,” Journal of the Acoustical Society of America, vol. 64, pp. 1500–1508, 1978.
Huang, H., Y. P. Lu, and Y. F. Wang, “Transient Interaction of Spherical Acoustic Waves and a Spherical Elastic Shell,” Journal of Applied Mechanics, pp. 71–74, March 1971.
