Zhixiong Gong

Application of Smoothed Finite Element Method to Two-Dimensional Exterior Problems of Acoustic Radiation

In this work, the smoothed finite element method using four-node quadrilateral elements (SFEM-Q4) is employed to resolve underwater acoustic radiation problems. The SFEM-Q4 can be regarded as a com...

Coupled Analysis of Structural–Acoustic Problems Using the Cell-Based Smoothed Three-Node Mindlin Plate Element

The cell-based smoothed finite element method (CS-FEM) using the original three-node Mindlin plate element (MIN3) has recently established competitive advantages for analysis of solid mechanics problems. The three-node configuration of the MIN3 is achieved from the initial, complete quadratic deflection via ‘continuous’ shear edge constraints. In this paper, the proposed CS-FEM-MIN3 is firstly combined with the face-based smoothed finite element method (FS-FEM) to extend the range of application to analyze acoustic fluid–structure interaction problems. As both the CS-FEM and FS-FEM are based on the linear equations, the coupled method is only effective for linear problems. The cell-based smoothed operations are implemented over the two-dimensional (2D) structure domain discretized by triangular elements, while the face-based operations are implemented over the three-dimensional (3D) fluid domain discretized by tetrahedral elements. The gradient smoothing technique can properly soften the stiffness which is overly stiff in the standard FEM model. As a result, the solution accuracy of the coupled system can be significantly improved. Several superior properties of the coupled CS-FEM-MIN3/FS-FEM model are illustrated through a number of numerical examples.

Hybrid gradient smoothing technique with discrete shear gap method for shell structures

Abstract In order to enhance the performance of the discrete shear gap technique (DSG) for shell structures, the coupling of hybrid gradient smoothing technique (H-GST) with DSG using triangular elements (HS-DSG3) is presented to solve the governing partial differential equations of shell structures. In the formulation HS-DSG3, we firstly employ the node-based gradient smoothing technique (N-GST) to obtain the node-based smoothed strain field, then a scale factor α ∈ [ 0 , 1 ] is used to reconstruct a new strain field which includes both the strain components from standard DGS3 and the strain components from node-based smoothed DSG3 (NS-DSG3). The HS-DSG3 takes advantage of the “overly-soft” NS-DSG3 model and the “overly-stiff” DSG3 model, and has a relatively appropriate stiffness of the continuous system. Therefore, the degree of the solution accuracy can be improved significantly. Several typical benchmark numerical examples have been investigated and it is demonstrated that the present HS-DSG3 can provide better numerical solutions than the original DSG3 for shell structures.

Multipole expansion of acoustical Bessel beams with arbitrary order and location

An exact solution of expansion coefficients for a T-matrix method interacting with acoustic scattering of arbitrary order Bessel beams from an obstacle of arbitrary location is derived analytically. Because of the failure of the addition theorem for spherical harmonics for expansion coefficients of helicoidal Bessel beams, an addition theorem for cylindrical Bessel functions is introduced. Meanwhile, an analytical expression for the integral of products including Bessel and associated Legendre functions is applied to eliminate the integration over the polar angle. Note that this multipole expansion may also benefit other scattering methods and expansions of incident waves, for instance, partial-wave series solutions.

Underwater acoustic scattering of Bessel beam by spherical shell using T-matrix method

The Bessel beam has been proved to show several advantages over the plane wave for its superior characteristics, including nondiffraction and self-reconstruction properties. The Bessel beam is characterized by an important parameter, called the half-conical angle, which describes the angle of the planar wave components of the beam relative to the beam axis. In this research paper, the T-matrix method (TMM) is combined with a Bessel beam to compute the acoustic scattering field. The backscattering form functions of a tungsten carbide sphere and a steel spherical shell are calculated and curved as a function of dimensionless frequency. Several Rayleigh resonance patterns are depicted to further confirm the orders of resonance. By selecting appropriate half-conical angles, several corresponding resonances can be suppressed and this phenomenon may have some potential value in practical applications.

T-matrix method implementation for acoustic Bessel beam scattering from elastic solids and shells

T-matrix method (TMM) has been demonstrated to be an effective tool for the application of acoustic Bessel beam (ABB) scattering from rigid shapes, owing to the fact that the incident ABBs could be appropriate to expand on the basis of spherical harmonics [Gong et al., J. Sound Vibr. 383, 233-247 (2016)]. In this work, we try to extend the TMM to further calculate ABB scattering from complicated elastic shapes, spheroids/ spheroidal shells for instance. Some numerical techniques are successfully implemented to overcome the instability problem during matrix inversion procedures for nonspherical shapes. Resonance scattering theory and ray theory [Kargl and Marston, J. Acoust. Soc. Am. 88, 1103-1113 (1990)] are employed to explore and interpret several novel properties of scattering from elastic shapes illuminated by ABBs, thus revealing the corresponding mechanism of scattering by ABBs. Furthermore, the present work will perform as a foundation work to extend the applicability of TMM to study acoustic radia...

Application of smoothed finite element method to acoustic scattering from underwater elastic objects

In this work, the smoothed finite element method (S-FEM) is employed to solve the acoustic scattering from underwater elastic objects. The S-FEM, which can be regarded as a combination of the standard finite element method (FEM) and the gradient smoothing technique (GST) from the meshless methods, was initially proposed for solid mechanics problems and has been demonstrated to possess several superior properties. In the S-FEM, the smoothed gradient fields are acquired by performing the GST over the obtained smoothing domains. Due to the proper softening effects provided by the gradient smoothing operations, the original “overly-stiff” FEM model is softened and the present S-FEM possesses a relatively appropriate stiffness of the continuous system. Therefore, the quality of the numerical results can be significantly improved. The numerical results from several typical numerical examples demonstrate that the S-FEM is quite effective to handle acoustic scattering from underwater elastic objects and can provi...