ScholarBank@NUShttps://scholarbank.nus.edu.sgThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Thu, 27 Jun 2019 10:38:55 GMT2019-06-27T10:38:55Z5081- A strip element method for analyzing wave scattering by a crack in an immersed composite laminatehttps://scholarbank.nus.edu.sg/handle/10635/57839Title: A strip element method for analyzing wave scattering by a crack in an immersed composite laminate
Authors: Liu, G.R.; Xi, Z.C.; Lam, K.Y.; Shang, H.M.
Abstract: A strip element method is presented for analyzing wave scattering by a crack in a composite laminate submerged in a fluid. In this method, the fluid and laminated plate are modeled using hvo-nodal-line and three-nodal-line strip elements, respectively. A system of governing equations of the fluid and solid strip elements in frequency domain are derived using a variational method and the Hamilton principle, which are converted as a set of characteristic equations in wave number domain by applying Fourier transform techniques. A particular solution to the equations is obtained using a modal analysis method in conjunction with inverse Fourier transform techniques. A complementary . solution to the equations is found employing horizontal boundary conditions on cross sections at the crack tips. The addition of the particular and complementary solutions yields a general solution. Numerical examples are presented for immersed steel and composite plates with either a horizontal or a vertical crack. Computed results indicate that the fluid has considerable influence on the wave fields scattered by a crack in a composite laminate. Copyright © 1999 by ASME.
Fri, 01 Jan 1999 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/578391999-01-01T00:00:00Z
- A strip element method for analyzing wave scattering by a crack in an axisymmetric cross-ply laminated composite cylinderhttps://scholarbank.nus.edu.sg/handle/10635/57838Title: A strip element method for analyzing wave scattering by a crack in an axisymmetric cross-ply laminated composite cylinder
Authors: Xi, Z.C.; Liu, G.R.; Lam, K.Y.; Shang, H.M.
Abstract: A strip element method is presented for analyzing waves scattered by a crack in an axisymmetric cross-ply laminated composite cylinder. The cylinder is at the outset discretized as axisymmetric strip elements through the radial direction. The application of the Hamilton variational principle develops a set of governing ordinary differential equations. The particular solutions to the resulting equations are found using a modal analysis approach in conjunction with the Fourier transform technique. The complementary solutions are formulated by the superposition of eigenvectors, the unknown coefficients of which are determined from axial stress boundary conditions at the tips of the crack. The summation of the particular and complementary solutions gives the general solutions. Numerical examples are given for cross-ply laminated composite cylinders with radial cracks. The results show that the present method is effective and efficient. Copyright © 2000 by ASME.
Sat, 01 Jan 2000 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/578382000-01-01T00:00:00Z
- Dispersion and characteristic surfaces of waves in laminated composite circular cylindrical shellshttps://scholarbank.nus.edu.sg/handle/10635/58116Title: Dispersion and characteristic surfaces of waves in laminated composite circular cylindrical shells
Authors: Xi, Z.C.; Liu, G.R.; Lam, K.Y.; Shang, H.M.
Abstract: The dispersion behaviors and characteristic surfaces of waves in a laminated composite circular cylindrical shell are investigated using a semianalytical method based on the theory of three-dimensional elasticity. The radial displacement of the shell is modeled by finite elements, while the axial and circumferential displacements are expanded as the complex exponentials. The associated characteristic equation is developed by means of the Hamilton's principle. The eigenvalues are established in terms of the Rayleigh quotient. Six characteristic wave surfaces, viz., the phase velocity, phase slowness, and phase wave surfaces, as well as the group velocity, group slowness, and group wave surfaces, are introduced to visualize the effects of anisotropy on wave propagation. Numerical examples demonstrate that the ratio of the inner radius to the thickness of the shell has a stronger influence on the frequency spectra in the circumferential wave than on that in the axial wave; that negative group velocity appears at a range of smaller wave numbers and the range varies as the wave normal and the ratio of the inner radius to the thickness of the shell; and that the characteristic wave surfaces vary with the propagation modes of waves, the ratio of the inner radius to the thickness of theshell, and the lay-ups of the laminated shells. (C) 2000 Acoustical Society of America.
Sat, 01 Jan 2000 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/581162000-01-01T00:00:00Z
- Elastodynamic responses of an immersed composite laminate to a Gaussian beam pressurehttps://scholarbank.nus.edu.sg/handle/10635/58245Title: Elastodynamic responses of an immersed composite laminate to a Gaussian beam pressure
Authors: Liu, G.R.; Wang, X.J.; Xi, Z.C.
Abstract: An analytical method is presented for analyzing elastodynamic responses of an immersed composite laminate subjected to a Gaussian beam pressure. Firstly, the Fourier transform technique and a modal analysis method are combined to obtain the surface displacements in the frequency domain. Complex path techniques are proposed for dealing with singularities of the responses associated with the inverse Fourier transformation. A quadrature scheme is adopted to reduce the sampling points in the inverse Fourier transformation. Then elastodynamic responses of the laminate in the time domain can be found by application of Fourier superposition. An exponential window method is employed to overcome singularities of integrands at ω = 0 and cut-off frequencies. The effects of the fluid on displacements in wave number, frequency and time domains are discussed. The presence of the fluid is found to have considerable impact on the responses of the composite laminate.
Thu, 22 Jun 2000 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/582452000-06-22T00:00:00Z
- A strip-element method for analyzing wave scattering by a crack in an immersed axisymmetric laminated composite cylinderhttps://scholarbank.nus.edu.sg/handle/10635/68101Title: A strip-element method for analyzing wave scattering by a crack in an immersed axisymmetric laminated composite cylinder
Authors: Xi, Z.C.; Liu, G.R.; Lam, K.Y.; Shang, H.M.
Abstract: A strip-element method is presented for analyzing wave scattering by a crack in a laminated composite cylinder immersed in a fluid. In this approach, two-nodal-line and three-nodal-line axisymmetric strip elements are employed to model the fluid and laminated cylinder, respectively. Governing equations for the fluid and solid elements in the frequency domain are derived with a variational method and the Hamilton principle. The associated characteristic equations in the wave-number domain are obtained through Fourier transform techniques. Responses of the fluid-loaded cylinder to a line load are found by a modal-analysis method and inverse Fourier transform techniques. Numerical results are presented for cracked laminated composite cylinders submerged in water. Water is found to have strong influence on the scattered wave fields in a cracked laminated composite cylinder. (C) 2000 Acoustical Society of America.
Sat, 01 Jan 2000 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/681012000-01-01T00:00:00Z
- Transient waves in a functionally graded cylinderhttps://scholarbank.nus.edu.sg/handle/10635/61612Title: Transient waves in a functionally graded cylinder
Authors: Han, X.; Liu, G.R.; Xi, Z.C.; Lam, K.Y.
Abstract: A hybrid numerical method (HNM) is presented for analyzing transient waves in a cylinder made of functionally graded material (FGM). In the HNM, the FGM cylinder is divided into N cylindrical elements with three-nodal line in the wall thickness. The elemental material properties are assumed to vary linearly in the thickness direction to better model the spatial variation of material properties of FGM. The Hamilton variational principle is used to develop governing equations of the cylinder. The displacement responses are determined by employing the Fourier transformations together with the modal analysis. The HNM is applied to analyze a number of FGM cylinders, and its efficiency is demonstrated. © 2001 Elsevier Science Ltd. All rights reserved.
Wed, 07 Mar 2001 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/616122001-03-07T00:00:00Z
- A strip-element method for analyzing wave scattering by a crack in a fluid-filled composite cylindrical shellhttps://scholarbank.nus.edu.sg/handle/10635/57841Title: A strip-element method for analyzing wave scattering by a crack in a fluid-filled composite cylindrical shell
Authors: Xi, Z.C.; Liu, G.R.; Lam, K.Y.; Shang, H.M.
Abstract: A strip-element method is presented for analyzing wave scattering by a crack in a laminated composite cylindrical shell filled with a fluid. In this approach, two-nodal-line and three-nodal-line axisymmetric strip elements are employed to model the fluid and shell, respectively. Governing equations of the fluid and solid elements in the frequency domain are derived with a variational method and the Hamilton principle. The associated characteristic equations in the wave-number domain are obtained through Fourier transform techniques. Responses of the fluid-loaded shell to a line load are found by a modal analysis method and inverse Fourier transform techniques. Numerical results are given for fluid-filled laminated composite shells containing either a radial or an axial crack. The fluid is found to have strong influence on the scattered wave fields in composite shells. (C) 2000 Elsevier Science Ltd. All rights reserved.
Tue, 01 Aug 2000 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/578412000-08-01T00:00:00Z
- Dispersion of waves in immersed laminated composite hollow cylindershttps://scholarbank.nus.edu.sg/handle/10635/59970Title: Dispersion of waves in immersed laminated composite hollow cylinders
Authors: Xi, Z.C.; Liu, G.R.; Lam, K.Y.; Shang, H.M.
Abstract: A layer element method (LEM) is presented for analyzing frequency and group velocity dispersive behaviours of waves in a laminated composite cylinder surrounded by a fluid. The LEM applies finite elements to model the radial displacement of the cylinder and the radial pressure of the fluid, and complex exponentials to express the axial and circumferential displacements of the cylinder as well as the axial and tangential pressures of the fluid. The dispersive equation for the fluid-loaded cylinder follows from variational techniques. The frequency and group velocity dispersive relationships of the fluid-coupling cylinder are obtained by means of the Rayleigh quotient. Numerical results are given for hybrid laminated composite cylinders and cylindrical shells submerged in water. The addition of the fluid is proven to have considerable impact on the group velocity spectra of waves in laminated composite cylinders.
Thu, 14 Feb 2002 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/599702002-02-14T00:00:00Z