H.M. Shang

Shape measurement by use of liquid-crystal display fringe projection with two-step phase shifting

The use of an optical fringe projection method with two-step phase shifting for three-dimensional (3-D) shape measurement of small objects is described. In this method, sinusoidal linear fringes are projected onto an objects surface by a programmable liquid-crystal display (LCD) projector and a long-working-distance microscope (LWDM). The image of the fringe pattern is captured by another LWDM and a CCD camera and processed by a phase-shifting technique. Usually a minimum of three phase-shifted fringe patterns is necessary for extraction of the object shape. In this method, a new algorithm based on a two-step phase-shifting technique produces the 3-D object shape. Unlike in the conventional method, phase unwrapping is performed directly by use of an arccosine function without the need for a wrapped phase map. Hence, shape measurement can be speeded up greatly with this approach. A small coin is evaluated to demonstrate the validity of the proposed measurement method, and the experimental results are compared with those of the four-step phase-shifting method and the conventional mechanical stylus method.

Surface roughness measurement in the submicrometer range using laser scattering

A technique for measuring surface roughness in the submi- crometer range is developed. The principle of the method is based on laser scattering from a rough surface. A telecentric optical setup that uses a laser diode as a light source is used to record the light field scattered from the surface of a rough object. The light intensity distribu- tion of the scattered band, which is correlated to the surface roughness, is recorded by a linear photodiode array and analyzed using a single- chip microcomputer. Several sets of test surfaces prepared by different machining processes are measured and a method for the evaluation of surface roughness is proposed.

Locating and sizing of delamination in composite laminates using computational and experimental methods

This paper describes an application of Strip Element Method (SEM) and adaptive Multilayer Perceptron Networks (MLP) for inverse identification of interfacial delaminations in carbon/epoxy laminated composite beams. Displacement responses calculated using SEM for laminated beams containing predetermined delamination parameters (i.e. delamination location, depth and length) are used as training data for the MLP. Once the MLP is trained, the MLP networks are then employed for inverse determination of delamination using experimental displacement responses measured with a scanning laser vibrometer. The outputs of the initially trained MLP, which are the reconstructed delamination parameters, are then compared with the experiments data. The MLP will be re-trained and re-used for parameter reconstruction until satisfactory results are obtained. Examples show that the procedure performs well for the determination of a wide range of values for the location, depth and length of delamination.

A Strip Element Method for Analyzing Wave Scattering by a Crack in an Immersed Composite Laminate

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 two-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.

Dispersion and characteristic surfaces of waves in laminated composite circular cylindrical shells

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 Hamiltons 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 the shell, and the lay-ups of the laminated shells.

Scattering of waves by flaws in anisotropic laminated plates

The strip element method (SEM) is used to investigate wave scattering by rectangular flaws in anisotropic laminated plates. The plates containing flaws are divided by junctions into domains in which the SEM is applied. For each domain, SEM equations are obtained which give a relationship between the traction and displacement vector on the vertical boundaries. A set of equations which gives a relationship between the traction and displacement vector on the junctions is then obtained by assembling the SEM equations for all the domains. This set of equations is solved by using the conditions on the junctions. Scattered wave fields in the frequency domain for isotropic and composite plates with rectangular flaws are computed and discussed in comparison with results for corresponding plates without flaws. A technique for determining the length of a rectangular flaw in a plate is also presented. The results presented in this paper are of importance and could be used in the characterization of flaws in anisotropic laminated plates.

Nondestructive assessment of thinning of plates using digital shearography

A novel method of estimating the remaining thickness of a defective plate having the form of localized thinning using digital shearography, based on a simple relationship between the curvature of the deflected defect and the defect geometry is presented.

A strip-element method for analyzing wave scattering by a crack in a fluid-filled composite cylindrical shell

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.

Axisymmetric sheet forming of knitted fabric composite by combined stretch forming and deep drawing

Previous studies have demonstrated that sheet formability is governed by the interlacing effect of pure stretch forming and pure deep drawing. In this paper, knitted fabric reinforced thermoplastic composite sheets, which exhibit excellent stretchability and drapeability, are investigated for their formability. Initially a new parameter, X, which describes the amount of stretching relative to drawing during forming is introduced. It is shown that sheet forming processes, specified by the use of various combinations of forming conditions, can be characterized by the parameter X. Finally, the overall formability of knitted fabric composite sheet is discussed with reference to the X-factor.

Application of the holographic carrier fringe and FFT technique for deformation measurement

This paper describes a holographic system based on the use of fibre optics and automatic spatial carrier fringe pattern analysis. Carrier fringes are generated by simply translating the object beam between two exposures. Single-mode optical fibres are used to transfer both the object and reference beams. The fast Fourier transform method is used to process the interferograms: it extracts phase from fringe patterns resulting from the interference of tilted wavefronts. The method is illustrated by measuring the deformation of an arbitrarily clamped, uniformly loaded circular plate. The results are given for the perspective plot of the out-of-plane deformation field, the maps of wrapped and unwrapped phase, and a contour map of the unwrapped phase.