• Structural Engineering and Mechanics
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• v.20 no.4
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• pp.465-476
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• 2005

Free vibration of orthotropic functionally graded beams, whose material properties can vary arbitrarily along the thickness direction, is investigated based on the two-dimensional theory of elasticity. A hybrid state-space/differential quadrature method is employed along with an approximate laminate model, which allows us to obtain the semi-analytical solution easily. With the introduction of continuity conditions at each fictitious interface and boundary conditions at the top and bottom surfaces, the frequency equation for an inhomogeneous beam is derived. A completely exact solution of an FGM beam with material constants varying in exponential way through the thickness is also presented, which serves a benchmark to verify the present method. Numerical results are performed and discussed.

• Structural Engineering and Mechanics
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• v.14 no.3
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• pp.345-364
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• 2002

The scaling laws for vibration response of anti-symmetrically laminated plates are derived by applying the similitude transformation to the governing differential equations directly. With this approach, a closed-form solution of the governing equations is not required. This is a significant advantage over the method employed by other researchers where similitude transformation is applied to the closed-form solution. The scaling laws are tested by comparing the similitude fundamental frequencies to the theoretical fundamental frequencies determined from the available closed-form solutions. In case of complete similitude, similitude solutions from the scaling laws exactly agree with the theoretical solutions. Sometimes, it may not be feasible to select the model which obeys the similarity requirement completely, therefore partial similitude is theoretically investigated and approximate scaling laws are recommended. The distorted models in stacking sequences and laminated material properties demonstrate reasonable accuracy. On the contrary, a model with distortion in fiber angle is not recommended. The derived scaling laws are very useful to determine the vibration response of complex prototypes by performing the experiment on a model with required similarities.

• Advances in Computational Design
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• v.2 no.2
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• pp.147-168
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• 2017

Over the past couple decades, externally bonded fiber reinforced polymer (FRP) composites have emerged as a repair and strengthening material for many concrete infrastructure applications. This paper presents an analytical investigation of the use of carbon FRP (CFRP) for a specific problem that occurs in concrete bridge girders wherein the girder ends are damaged by excessive exposure to deicing salts and numerous freezing/thawing cycles. A 3D finite element (FE) model of a full scale prestressed concrete (PC) I-girder is used to investigate the effect of damage to the cover concrete and stirrups in the end region of the girder. Parametric studies are performed using externally bonded CFRP shear laminates to determine the most effective repair schemes for the damaged end region under a short shear span-to-depth ratio. Experimental results on shear pull off tests of CFRP laminates that have undergone accelerated aging are used to calibrate a bond stress-slip model for the interface between the FRP and concrete substrate and approximate the reduced bond stress-slip properties associated with exposure to the environment that causes this type of end region damage. The results of these analyses indicate that this particular application of this material can be effective in recovering the original strength of PC bridge girders with damaged end regions, even after environmental aging.