Coupled cylindrical shell response to a planar step wave

This example illustrates the use of Abaqus/Explicit to model the interaction between two fluid-coupled concentric cylinders and a planar step wave. The results obtained using Abaqus/Explicit are compared with those obtained independently using the Doubly Asymptotic Approximation (Geers (1978), Abaqus/USA 6.1). This problem has been solved analytically by Huang (1979).

This page discusses:

ProductsAbaqus/Explicit

Problem description

This problem models the interaction between two fluid-coupled concentric elastic cylinders and a weak planar step shock wave with a maximum pressure of 1.0 MPa. The inner cylinder is air-backed. In contrast to Huang's solution, engineering material parameters for the fluid and solid media are used. The inner cylindrical shell has a radius of 0.8 m and a thickness of 23.24 mm, while the outer cylindrical shell has a radius of 1 m and a thickness of 5.81 mm. The shells are made of steel with a density of 7766 kg/m3, a Young's modulus of 206.4 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 1524 m/s. A half-symmetry model is used. Each cylindrical shell is modeled with 18 S4R elements, with each element spanning 10° in the circumferential direction and 175 mm in the axial direction. Axial symmetry boundary conditions are applied on the edges of the shell elements to represent the infinite axial dimensions of the problem. The fluid in between the cylinders and outside the outer cylinder is meshed with AC3D8R elements, with each acoustic element spanning 10° in the circumferential direction. The exterior fluid region is concentric with the cylinders and has a radius of 2.002 m. A circular nonreflective boundary condition is imposed on the outer surface of the exterior fluid region using surface impedance. The fluid response is coupled to that of the structure using a tie constraint. The fluid-solid system is excited by a planar step wave applied at the outer cylindrical shell using incident wave loading. A linear bulk viscosity parameter of 0.25 and a quadratic bulk viscosity parameter of 10.0 are used.

Results and discussion

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 edges of the inner and outer cylinders obtained using Abaqus/Explicit with those obtained using Abaqus/USA 6.1. As shown in Figure 1 and Figure 2, the results agree closely.

References

  1. Geers,  T., “Doubly Asymptotic Approximations for Transient Motions of Submerged Structures,” Journal of the Acoustical Society of America, vol. 64, pp. 1500–1508, 1978.
  2. Huang,  H., “Transient Response of Two Fluid-Coupled Cylindrical Elastic Shells to an Incident Pressure Pulse,” Journal of Applied Mechanics, vol. 46, pp. 513–518, September 1979.

Figures

Figure 1. Comparison of the radial velocity at the leading edge of the outer cylindrical shell obtained with the Doubly Asymptotic Approximation method and with Abaqus/Explicit.

Figure 2. Comparison of the radial velocity at the leading edge of the inner cylindrical shell obtained with the Doubly Asymptotic Approximation method and with Abaqus/Explicit.