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An exact solution for the free-vibration analysis of functionally graded carbon-nanotube-reinforced composite beams with arbitrary boundary conditions.

ABSTRACT: We present an exact method to model the free vibration of functionally graded carbon-nanotube-reinforced composite (FG-CNTRC) beams with arbitrary boundary conditions based on first-order shear deformation elasticity theory. Five types of carbon nanotube (CNT) distributions are considered. The distributions are either uniform or functionally graded and are assumed to be continuous through the thickness of the beams. The displacements and rotational components of the beams are expressed as a linear combination of the standard Fourier series and several supplementary functions. The formulation is derived using the modified Fourier series and solved using the strong-form solution and the weak-form solution (i.e., the Rayleigh-Ritz method). Both solutions are applicable to various combinations of boundary constraints, including classical boundary conditions and elastic-supported boundary conditions. The accuracy, efficiency and validity of the two solutions presented are demonstrated via comparison with published results. A parametric study is conducted on the influence of several key parameters, namely, the L/h ratio, CNT volume fraction, CNT distribution, boundary spring stiffness and shear correction factor, on the free vibration of FG-CNTRC beams.

SUBMITTER: Shi Z

PROVIDER: S-EPMC5635134 | biostudies-literature | 2017 Oct

REPOSITORIES: biostudies-literature

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An exact solution for the free-vibration analysis of functionally graded carbon-nanotube-reinforced composite beams with arbitrary boundary conditions.

Shi Zeyu Z Yao Xiongliang X Yao Xiongliang X Yao Xiongliang X Pang Fuzhen F Wang Qingshan Q

Scientific reports 20171010 1

We present an exact method to model the free vibration of functionally graded carbon-nanotube-reinforced composite (FG-CNTRC) beams with arbitrary boundary conditions based on first-order shear deformation elasticity theory. Five types of carbon nanotube (CNT) distributions are considered. The distributions are either uniform or functionally graded and are assumed to be continuous through the thickness of the beams. The displacements and rotational components of the beams are expressed as a line ...[more]

PMID: 29018211

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Project description:This paper is the outcome of experiments on the shear performance of reinforced concrete beams with approved composite-recycled aggregates. The strength grade of composite-recycled aggregate concrete (CRAC) was between 30 MPa and 60 MPa. The shear span-to-depth ratio varied from 1 to 3. The adaptability of HRB400 rebar, with critical yield strength of 400 MPa, used as stirrups was also verified. As the composite technology overcame the shortcomings of recycled coarse aggregate, CRAC had similar mechanical properties with those of conventional concrete. Details on the shear behaviors of test beams under a four-point loading test are presented. The results indicated that the changes of CRAC strain, stirrup strain, and shear-crack width depended on the failure patterns, which are controlled by the shear-span to depth ratio. The stirrups yield at the failure of reinforced CRAC beams. The shear cracking resistance and the shear capacity of reinforced CRAC beams can be predicted by the statistical equations. Based on the design codes GB50010, ACI318-19, Model Code 2010 and DIN-1045-1-2008 for conventional reinforced concrete beams, the shear strengths provided by CRAC and stirrups are statistical analyzed. The rationality of the design equations is examined by the utilization level of shear strength provided by CRAC. The maximum shear-crack widths are extracted from the test data of reinforced CRAC beams at normal service state. Comparatively, by specifying the lower limit of shear strength provided by the CRAC with various shear-span to depth ratios, China code GB50010 gives a rational method for utilizing CRAC. Under the premise that the design of shear capacity would give considerations to meet the normal serviceability, the factored strength of HRB400 rebar should be 360 MPa for the calculation of shear strength provided by stirrups. The design methods in codes of GB50010, ACI318-19 and Model Code 2010 are conservative for the shear capacity of reinforced CRAC beams.

Project description:To promote the engineering application of recycled aggregate for concrete production with good adaptability and economic efficiency, this paper performed a campaign to investigate the flexural performance of steel fiber reinforced composite-recycled aggregate concrete (SFR-CRAC) beams matched with 500 MPa longitudinal rebars. The composite-recycled aggregate has features of the full use recycled fine aggregate and small particle recycled coarse aggregate, and the continuous grading of coarse aggregate ensured by admixing the large particle natural aggregate about 35% to 45% in mass of total coarse aggregate. The properties of SFR-CRAC have been comprehensively improved by using steel fibers. With a varying volume fraction of steel fiber from 0% to 2.0%, 10 beam specimens were produced. The flexural behaviors of the beams during the complete loading procedure were experimentally studied under a four-point bending test. Of which the concrete strain at mid-span section, the appearance of cracks, the crack distribution and crack width, the mid-span deflection, the tensile strain of longitudinal rebars, and the failure patterns of the beams were measured in detail. Results indicated that the assumption of plane cross-section held true approximately, the 500 MPa longitudinal rebars worked at a high stress level within the limit width of cracks on reinforced SFR-CRAC beams at the normal serviceability, and the typical failure occurred with the yield of 500 MPa longitudinal rebars followed by the crushed SFR-CRAC in compression. The cracking resistance, the flexural capacity, and the flexural ductility of the beams increased with the volume fraction of steel fiber, while the crack width and mid-span deflection obviously decreased. Finally, by linking to those for conventional reinforced concrete beams, formulas are suggested for predicting the cracking moment, crack width, and flexural stiffness at normal serviceability, and the ultimate moment at bearing capacity of reinforced SFR-CRAC beams.

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An exact solution for the free-vibration analysis of functionally graded carbon-nanotube-reinforced composite beams with arbitrary boundary conditions.

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An exact solution for the free-vibration analysis of functionally graded carbon-nanotube-reinforced composite beams with arbitrary boundary conditions.

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