Dongwei Shu

Vibration of Delaminated Composite Laminates: A Review

Fiber reinforced composite laminates are increasingly replacing traditional metallic materials. The manufacturing process and service of the composite laminates frequently lead to delamination. Vibration analysis is an integral part of most engineering structures. In the present article we provide a relevant survey on the various analytical models and numerical analyses for the free vibration of delaminated composites. A basic understanding of the influence of the delamination on the natural frequencies and the mode shapes of composite laminates is presented. In addition, other factors affecting the vibration of the delaminated composites are discussed. Particular attention is given to composite laminates having piezoelectric sensors and actuators, and ones subjected to axial loadings.

Buckling of multiple delaminated beams

Abstract Delaminations weaken a laminated beam, which then fails prematurely under in-plane compression. An exact buckling analysis is performed for beams with double delaminations. Novel adoption of two coordinates and choice of slope as the unknown function reduce the buckling equations to simple solvable geometric equations. Complex buckling behaviors emerge for different sizes and depths of the delaminations. “Free mode” and “constrained mode” of buckling are identified. Both global and local buckling occurs, depending upon the slenderness ratios of the delaminations. In addition, an upper bound and a lower bound of buckling loads are obtained by assuming totally “constrained” and totally “free” deformation for the delaminated beam. These bounds are easy to compute and provide useful approximations.

Vibration of sandwich beams with double delaminations

The free vibration of sandwich beams with single and double delaminations has been solved analytically without resorting to numerical approximations. Various assumptions for the vibration mode shapes and local deformation at the delamination fronts have been examined. Comparison with experiments then verifies the validity of these assumptions under given geometry and boundary conditions. The solution for double delaminations reveals a multitude of natural frequencies within a narrow range, resulting from both higher modes and mixed modes of vibrations.

Delamination buckling with bridging

Abstract Delamination in composite laminates may arise from either fabrication processes or impact during service. In transversely stitched composites the delamination is not completely separated but is being held together by the stitches in the form of crack/interface bridging. The influence of this bridging on the buckling of laminates is examined, based upon the assumption that the bridges follow a Winkler elastic foundation type stress separation relation. A special ‘thin-film’ case when the delaminated laminate is very thin compared to the thickness of the composite is first examined. Lower and upper bound buckling loads are obtained, together with the buckling load, by means of the energy method of analysis of a unidirectional beam. It is shown that adequate crack bridging by stitching can significantly increase the buckling strength of delaminated laminated composites under edgewise compression.

Free vibration of bimaterial split beam

The coupling between transverse and longitudinal vibration in an inhomogeneous beam has been formulated and discussed. A special case of bimaterial split beam is solved to show the effect of delamination on the natural frequency of the split beam. High sensitivity of the natural frequency towards the size and location of the delamination is displayed. In conjunction with other techniques, this sensitivity can be used to locate and determine the size of delaminations in beam plates during inspection.

Buckling of delaminated composites re-examined

Abstract Composite laminates under in-plane compression can fail prematurely because of the presence of existing delaminations. A concise buckling analysis is performed to determine the commencement of buckling. A commonly adopted plane-section assumption in the classical beam theory is examined and found to overestimate the strength of the composite laminates. Relaxation of the assumption results in a lower bound solution for the buckling load and thus a useful parameter for design purposes. This simple yet accurate analysis can be adapted to multi-delamination problems. The ultimate strength of the composite laminate is obtained through several simple post-buckling analyses.

Operational Shock Simulation of the Head–Disk Assembly of a Small-Form Factor Drive

We created a finite-element model of the head-disk assembly (HDA) of a small-form factor drive. We conducted operational shock simulation and modal analysis with this finite-element model, and investigated the pulsewidth effect of a half-sine acceleration pulse on the shock responses. We found that the umbrella mode of the disk is the dominant mode for operational shock. Numerical results of the pulsewidth effect on the maximum shock responses further confirm the conclusions in a previous work by the authors.

Mechanical Properties of Carbon Nanotubes Reinforced Ultra High Molecular Weight Polyethylene

Carbon nanotubes (CNT) have been shown to enhance the engineering properties of plastic fibers in ballistic-resistant garments enabling the garments to withstand very high impact forces while remaining to be lightweight. Previous study shows that by reinforcing ultra high molecular weight polyethylene (UHMWPE) fibers with a small amount of carbon nanotubes, the fibers are simultaneously toughened and strengthened. In this paper, we study the mechanical properties of carbon nanotube reinforced ultra high molecular weight polyethylene (UHMWPE) by using micromechanics-based Mori-Tanaka model. Results show that the addition of small amount of carbon nanotubes as reinforcement can substantially improve the mechanical properties of the UHMWPE fibers.

Lower and upper bound limit analyses for pipeline with multi-slots of various configurations

Using the finite element method and mathematical programming techniques, a simplified numerical method for both lower and upper bound limit analyses of a 3-D structure has been developed in our previous work. In this paper, the lower and upper bound limit loads of the 3-D pipeline with one or two part-through slots of various geometrical configurations are calculated by the proposed method. The slots considered here are small spherical slots, circumferential slots, axial slots and large area slots. The loading considered includes internal pressure, axial tension and bending moment at both ends, and the radial loading path scheme is adopted. The effects of slot number and type on the load carrying capacity of the pipeline are discussed in detail. The discrepancy between lower and upper bounds is below 20%. All the numerical results confirm the applicability of the procedure.

Buckling Analysis of Tri-layer Beams with Overlapped Delaminations

An exact solution to the buckling behavior of tri-layer beams with two overlapped delaminations is presented for the first time. In addition, new nondimensionalized parameters, axial and bending stiffnesses and effective slenderness ratio, are introduced. The characteristic equation governing buckling is derived by using the Euler-Bernoulli beam theory, performing proper linearization and by imposing appropriate equilibrium, kinematical continuity, and boundary conditions. Results of the present method are compared with those of homogeneous beams having single and double equal delaminations reported previously, and showed an excellent agreement. A parametric study has been carried out. The buckling load varies monotonically with the normalized axial stiffness whereas it does not with the normalized bending stiffness, where a transition region is observed. The effect of spanwise delamination location on critical buckling load is discussed for a tri-layer beam of carbon/epoxy, glass/epoxy, and carbon/epoxy. The accurate solution can serve as a benchmark solution for other numerical schemes.