• Structural Engineering and Mechanics
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• v.39 no.2
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• pp.169-186
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• 2011

This paper is devoted to the development of the equations which describe the elastic response of a curved laminate subjected to in-plane loads and bending moments. Similar to the classic $6{\times}6$ ABD matrix constitutive relation of a flat laminate, a new $6{\times}6$ matrix constitutive relation between force resultants, moment resultants, mid-plane strains and deformed curvatures for a curved laminate is formulated. This curved lamination theory will provide the fundamental basis for the analyses of curved laminated structures. The stress predictions by the present curved lamination theory are compared to those by the curved laminate analysis that neglected the nonlinear terms in the derivation of the constitutive relation. The results show that the curved laminate analysis that neglected the nonlinear terms cannot reflect the effect of curvature and can no longer predict the stresses accurately as the curvature becomes noticeable. In this paper, a curved lamination theory that retains the nonlinear terms and, therefore, accounts for the effect of the non-flat geometry of the structure will be developed.

• Steel and Composite Structures
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• v.41 no.5
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• pp.637-648
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• 2021

Nowadays, one of the practical, fast and easy ways to strengthen steel elements is the use of Carbon Fiber Reinforced Polymer (CFRP). Most previous research in the CFRP strengthening of steel members has carried out on straight steel members. The main difference between horizontal curved beams and straight beams under vertical load is the presence of torsional moment in the horizontal curved beams. In the other words, the horizontal curved beams are analyzed and designed for simultaneous internal forces included bending moment, torsional moment, and shear force. The horizontal curved steel beams are usually used in buildings, bridges, trusses, and others. This study explored the effect of the CFRP strengthening on the behavior of the horizontal curved square hollow section (SHS) steel beams. Four specimens were analyzed, one non-strengthened curved steel beam as a control column and three horizontal curved steel beams strengthened using CFRP sheets (under concentrated load and uniform distributed load). To analyze the horizontal curved steel beams, three dimensional (3D) modeling and nonlinear static analysis methods using ANSYS software were applied. The results indicated that application of CFRP sheets in some specific locations of the horizontal curved steel beams could increase the ultimate capacity of these beams, significantly. Also, the results indicated when the horizontal curved steel beams were under distributed load, the increase rate in the ultimate capacity was more than in the case when these beams were under concentrated load.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.12
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• pp.3020-3027
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• 1993

Curved beam element has received attention because of its own usefulness and its bearing on general curved elements like shells. In conventional curved beam elements stiffness matrix is overestimated and eigensolutions are poor. To avoid this phenomenon it is necessary to use a large number of elements and, as a result, the total number of degrees of freedom is increased. In this paper the two-noded, with three degrees of freedom at each node, in-plane curvature-based curbed beam element is employed in eigen-analysis of curved beam. It is shown that the curvature-based beam element is very efficient in vibration analysis and also that it is applicable to both thin and thick curved beams.

• International Journal of Concrete Structures and Materials
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• v.10 no.sup3
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• pp.1-17
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• 2016

Recently, advanced transit systems are being constructed to reduce traffic congestions in metropolitan areas. For these projects, curved bridges with various curvatures are required. Many curved bridges in the past were constructed using aesthetically unpleasant straight beams with curved slabs or expensive curved steel box girders with curved slabs. Therefore, many recent studies have been performed to develop less expensive and very safe precast prestressed concrete (PSC) curved girder. One method of reducing the construction cost of a PSC curved girder is to use a reusable formwork that can easily be adjusted to change the curvature and length of a girder. A reusable and curvature/dimension adjustable formwork called Multi-tasking formwork is developed for constructing efficient precast PSC curved girders. With the Multi-tasking formwork, two 40 m precast PSC box girders with different curvatures were constructed to build a two-girder curved bridge for a static flexural test to evaluate its safety and serviceability performance. The static flexural test results showed that the initial cracking load was 1400 kN, exceeding the design cracking load of 450 kN. Also, the code allowed deflection of 50 mm occurred at a load of 1800 kN, verifying the safety and serviceability of the precast PSC curved bridge constructed using the multi-tasking formwork.

• Structural Engineering and Mechanics
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• v.64 no.1
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• pp.121-133
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• 2017

This paper proposes an analytical solution method for free vibration of curved functionally graded (FG) nonlocal beam supposed to different thermal loadings, by considering porosity distribution via nonlocal elasticity theory for the first time. Material properties of curved FG beam are assumed to be temperature-dependent. Thermo-mechanical properties of porous FG curved beam are supposed to vary through the thickness direction of beam and are assumed to be temperature-dependent. Since variation of pores along the thickness direction influences the mechanical and physical properties, porosity play a key role in the mechanical response of curved FG structures. The rule of power-law is modified to consider influence of porosity according to even distribution. The governing equations of curved FG porous nanobeam under temperature field are derived via the energy method based on Timoshenko beam theory. An analytical Navier solution procedure is used to achieve the natural frequencies of porous FG curved nanobeam supposed to thermal loadings with simply supported boundary condition. The results for simpler states are confirmed with known data in the literature. The effects of various parameters such as nonlocality, porosity volume fractions, type of temperature rising, gradient index, opening angle and aspect ratio of curved FG porous nanobeam on the natural frequency are successfully discussed. It is concluded that these parameters play key roles on the dynamic behavior of porous FG curved nanobeam. Presented numerical results can serve as benchmarks for future analyses of curve FG nanobeam with porosity phases.

• Journal of Mechanical Science and Technology
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• v.19 no.2
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• pp.589-604
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• 2005

To overcome the drawback of currently available curved beam theories having non-symmetric thin-walled cross sections, a curved beam theory based on centroid-shear center formulation is presented for the spatially coupled free vibration and elastic analysis. For this, the displacement field is expressed by introducing displacement parameters defined at the centroid and shear center axes, respectively. Next the elastic strain and kinetic energies considering the thickness-curvature effect and the rotary inertia of curved beam are rigorously derived by degenerating the energies of the elastic continuum to those of curved beam. And then the equilibrium equations and the boundary conditions are consistently derived for curved beams having non-symmetric thin-walled cross section. It is emphasized that for curved beams with L- or T-shaped sections, this thin-walled curved beam theory can be easily reduced to the solid beam theory by simply putting the sectional properties associated with warping to zero. In order to illustrate the validity and the accuracy of this study, FE solutions using the Hermitian curved beam elements are presented and compared with the results by previous research and ABAQUS's shell elements.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.1033-1039
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• 2006

To overcome the drawback of currently available curved beam theories having non-symmetric thin-walled cross sections, a curved beam theory based on centroid-shear center formulation is presented for the spatially coupled free vibration and elastic analyses. For this, the elastic strain and kinetic energies considering the thickness-curvature effect and the rotary inertia of curved beam are derived by degenerating the energies of the elastic continuum to those of curved beam. And then the equilibrium equations and the boundary conditions are consistently derived for curved beams having non-symmetric thin-walled cross section. It is emphasized that for curved beams with L- or T-shaped sections, this thin-walled curved beam theory can be easily reduced to tl1e solid beam theory by simply putting the sectional properties associated with warping to zero. In order to illustrate the validity and the accuracy of this study, FE solutions using the Hermitian curved beam elements are presented and compared with the results by previous research and ABAQUS's shell elements.

• Steel and Composite Structures
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• v.46 no.4
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• pp.553-563
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• 2023

In the current research, the nonlinear free vibrations of curved pipes made of functionally graded (FG) carbon nanotube reinforced composite (CNTRC) materials are investigated. It is assumed that the FG-CNTRC curved pipe is supported on a three-parameter nonlinear elastic foundation and is subjected to a uniform temperature rise. Properties of the curved nanocomposite pipe are distributed across the radius of the pipe and are given by means of a refined rule of mixtures approach. It is also assumed that all thermomechanical properties of the nanocomposite pipe are temperature-dependent. The governing equations of the curved pipe are obtained using a higher order shear deformation theory, where the traction free boundary conditions are satisfied on the top and bottom surfaces of the pipe. The von Kármán type of geometrical non-linearity is included into the formulation to consider the large deflection in the curved nanocomposite pipe. For the case of nanocomposite curved pipes which are simply supported in flexure and axially immovable, the motion equations are solved using the two-step perturbation technique. The closed-form expressions are provided to obtain the small- and large-amplitude frequencies of FG-CNTRC curved pipes rested on a nonlinear elastic foundation in thermal environment. Numerical results are given to explore the effects of CNT distribution pattern, the CNT volume fraction, thermal environment, nonlinear foundation stiffness, and geometrical parameters on the fundamental linear and nonlinear frequencies of the curved nanocomposite pipe.

• Structural Engineering and Mechanics
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• v.89 no.1
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• pp.13-22
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• 2024

The nonlinear snap-through buckling of functionally graded (FG) carbon nanotube reinforced composite (CNTRC) curved tubes is analytically investigated in this research. It is assumed that the FG-CNTRC curved tube is supported on a three-parameter nonlinear elastic foundation and is subjected to the uniformly distributed pressure and thermal loads. Properties of the curved nanocomposite tube are distributed across the radius of the pipe and are given by means of a refined rule of mixtures approach. It is also assumed that all thermomechanical properties of the nanocomposite tube are temperature-dependent. The governing equations of the curved tube are obtained using a higher-order shear deformation theory, where the traction free boundary conditions are satisfied on the top and bottom surfaces of the tube. The von Kármán type of geometrical non-linearity is included into the formulation to consider the large deflection in the curved tube. Equations of motion are solved using the two-step perturbation technique for nanocomposite curved tubes which are simply-supported and clamped. Closed-form expressions are provided to estimate the snap-buckling resistance of FG-CNTRC curved pipes rested on nonlinear elastic foundation in thermal environment. Numerical results are given to explore the effects of the distribution pattern and volume fraction of CNTs, thermal field, foundation stiffnesses, and geometrical parameters on the instability of the curved nanocomposite tube.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2001.05a
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• pp.69-73
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• 2001

Damage induced by low-velocity impact on the curved composite laminates was experimentally evaluated for CFRP cylindrical shells with the radius of curvatures of 50, 150, 300, and 500 mm. The result was then compared with that of flat laminates. The radius of curvatures and the effective shell stiffness appeared to considerably affect the dynamic impact response of curved shells. Under the same impact energy level, the maximum contact force increased with the decreasing radius of curvatures, with reaching 1.5 times that for plates at the radius of curvature of 50 mm. Since the maximum contact force is directly related to the impact damage, curved laminates can be more susceptible to delamination and less resistant to the low-velocity impact damage. The distribution of delamination along the thickness direction of curved laminates are also different from that of flat plates. Delamination was distributed rather even]y at each interface along the thickness direction of curved laminates. This implies that the effect of curvatures has to be considered for the design of a curved composite laminate.