• Steel and Composite Structures
• /
• v.36 no.6
• /
• pp.643-656
• /
• 2020

This article presents a comprehensive static analysis of simply supported cross-ply carbon nanotubes reinforced composite (CNTRC) laminated nanobeams under various loading profiles. The nonlocal strain gradient constitutive relation is exploited to present the size-dependence of nano-scale. New higher shear deformation beam theory with hyperbolic function is proposed to satisfy the zero-shear effect at boundaries and parabolic variation through the thickness. Carbon nanotubes (CNTs), as the reinforced elements, are distributed through the beam thickness with different distribution functions, which are, uniform distribution (UD-CNTRC), V- distribution (FG-V CNTRC), O- distribution (FG-O CNTRC) and X- distribution (FG-X CNTRC). The equilibrium equations are derived, and Fourier series function are used to solve the obtained differential equation and get the response of nanobeam under uniform, linear or sinusoidal mechanical loadings. Numerical results are obtained to present influences of CNTs reinforcement patterns, composite laminate structure, nonlocal parameter, length scale parameter, geometric parameters on center deflection ad stresses of CNTRC laminated nanobeams. The proposed model is effective in analysis and design of composite structure ranging from macro-scale to nano-scale.

• Computers and Concrete
• /
• v.7 no.5
• /
• pp.455-468
• /
• 2010

This paper presents a prediction and simulation method of tensile stress-strain curves of Engineered Cementitious Composites (ECC). For this purpose, the bridging stress and crack opening relations were obtained by the fiber bridging constitutive law which is quantitatively able to consider the fiber distribution characteristics. And then, a multi-linear model is employed for a simplification of the bridging stress and crack opening relation. In addition, to account the variability of material properties, randomly distributed properties drawn from a normal distribution with 95% confidence are assigned to each element which is determined on the basis of crack spacing. To consider the variation of crack spacing, randomly distributed crack spacing is drawn from the probability density function of fiber inclined angle calculated based on sectional image analysis. An equation for calculation of the crack spacing that takes into quantitative consideration the dimensions and fiber distribution was also derived. Subsequently, a series of simulations of ECC tensile stress-strain curves was performed. The simulation results exhibit obvious strain hardening behavior associated with multiple cracking, which correspond well with test results.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.33 no.11
• /
• pp.1249-1255
• /
• 2009

Cord-rubber composites widely used in tires show very complicated mechanical behavior such as nonlinearity and large deformation. Three-phase(cord, rubber and the interface) modeling has been used to analyze the stress distribution in the cord-rubber composites more accurately. In this study, finite element methods were performed using two-dimensional generalized plane strain element and plane strain element to investigate the stress distribution and effective modulus of cord-rubber composites. Neo Hookean model was used for rubber property and several interface properties were assumed for various loading directions. It was found that the interface properties affect the effective modulus and the distributions of shear stress.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.13 no.4
• /
• pp.660-669
• /
• 1989

The strain distribution in a wide strip drawn through a wedge-shaped die is obtained from the numerical integration of strain increments along the flow path of material points in the slipline field for a non-hardening material under the plane strain condition. It is shown that the strain in the surface layer increases with friction and that the strain at the mid-plane is a function of area reduction only. The redundant deformation factor, obtained from the average strain in a drawn strip, increases with friction. For the workability analysis of a strip drawing process, the strain states along with hydrostatic stresses are needed for the evaluation of a damage function based on the hole-growth mechanism of ductile fracture. The critical maximum of the damage function is assumed to be a material constant. As a result, mid-plane cracking is likely to occur in a process at a small reduction, with a large die angle, and in poor lubrication. Distortions of an initially transverse line are also calculated.

• Composites Research
• /
• v.31 no.6
• /
• pp.429-434
• /
• 2018

We investigate strain transmissions of a surface bonded distributed optical fiber sensor considering strain variation according to positions. We first derive a strain transmission ratio depending on a wavelength of a strain distribution of the host structure from an analysis model. The strain transmission ratio is compared with numerical results obtained from the finite element method using ABAQUS. We find that the analytical results agree well with the numerical results. The strain transmission ratio is a function of a wavelength, i.e. the strain transmission ratio decreases (increases) as the wavelength of the host strain decreases (increases). Therefore, if an arbitrary strain distribution containing various wavelengths is given to a host structure, a distorted strain distribution will be observed in the distributed optical fiber sensor compare to that of the host structure, because each wavelength shows different strain transmission ratio. The strain transmission ratio derived in this study will be useful for accurately identifying the host strain distribution based on the signal of a distributed optical fiber sensor.

• Transactions of Materials Processing
• /
• v.23 no.6
• /
• pp.369-375
• /
• 2014

Flexible roll forming allows profiles to have variable cross-sections. However, the profile may have some shape errors, such as, warping which is a major defect. The shape error is induced by geometrical deviations in both the concave zone and the convex zone. In the current study, flexible roll forming was modeled with FE simulations to analyze the shape error and the longitudinal strain distribution along the flange section over the profile. A distribution of analytically calculated longitudinal strains was used to develop relationships between the shape error and the longitudinal strain distribution as a function of the defined shape parameters for the profile. The FE simulations showed that the shape error is primarily affected by the deviations between the distribution of analytically calculated longitudinal strain and the longitudinal strain distribution of the profile. The results show that the shape error can be controlled by designing the shape parameters to control the geometrical deviations at the flange section in the transition zones.

• Structural Engineering and Mechanics
• /
• v.90 no.1
• /
• pp.1-18
• /
• 2024

The present study conducts a thorough analysis of thermal vibrations in functionally graded porous nanocomposite beams within a thermal setting. Investigating the temperature-dependent material properties of these beams, which continuously vary across their thickness in accordance with a power-law function, a finite element approach is developed. This approach utilizes a nonlocal strain gradient theory and accounts for a linear temperature rise. The analysis employs four different patterns of porosity distribution to characterize the functionally graded porous materials. A novel two-variable shear deformation beam nonlocal strain gradient theory, based on trigonometric functions, is introduced to examine the combined effects of nonlocal stress and strain gradient on these beams. The derived governing equations are solved through a 3-nodes beam element. A comprehensive parametric study delves into the influence of structural parameters, such as thicknessratio, beam length, nonlocal scale parameter, and strain gradient parameter. Furthermore, the study explores the impact of thermal effects, porosity distribution forms, and material distribution profiles on the free vibration of temperature-dependent FG nanobeams. The results reveal the substantial influence of these effects on the vibration behavior of functionally graded nanobeams under thermal conditions. This research presents a finite element approach to examine the thermo-mechanical behavior of nonlocal temperature-dependent FG nanobeams, filling the gap where analytical results are unavailable.

• Journal of Korean Association for Spatial Structures
• /
• v.5 no.4 s.18
• /
• pp.53-59
• /
• 2005

This paper provides the results of the investigation on the optimum thickness distribution of plate structures with different essential boundary conditions. In this study, the strain energy to be minimized is considered as the objective function and the initial volume of structures is used as the constraint function. The computer-aided geometric design (CAGD) such as Coon's patch representation is used to represent the thickness distribution of plates. A reliable degenerated shell finite element is adopted to calculate the accurate strain energy level of the plates. Robust optimization algorithms provided in the optimizer DOT are adopted to search the optimum thickness values during the optimization iteration. Finally, the square plate is used to find out the optimum thickness distribution of plates according to different essential boundary condition.

• Computers and Concrete
• /
• v.3 no.6
• /
• pp.375-388
• /
• 2006

Poor strength test results are sometimes not an indication of low concrete quality, but rather inferior testing quality. In a compression test, the strain distribution over the ends of the specimen is a critical factor for the test results. Non-uniform straining of a concrete specimen leads to locally different compressive stresses on the cross-section, and eventual premature breaking of the specimen. Its effect on a specimen can be quantified by comparing the compressive strength results of two specimens, one subjected to uniform strain and another to a specified strain gradient. This can be done with the help of a function that relates two parameters, the strain ratio and the test efficiency. Such a function depends on the concrete strength and cross-sectional shape of the specimen. In this study, theoretical relationships between the strain ratio and test efficiency are developed using a concrete stress-strain model. The results show that for the same strain ratio, the test efficiency is larger for normal strength concrete than for high strength concrete. Further, the effect of the strain gradient on the test result depends on the cross-sectional shape of the specimen. Implementation of the results is demonstrated with the aid of two examples.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2001.04a
• /
• pp.267-274
• /
• 2001

In this paper, a analytical model which can simulate the post-cracking behavior and tension stiffening effect in a reinforced concrete(RC) tension member is proposed. Unlike the classical approaches using the bond stress-slip relationship or the assumed bond stress distribution, the tension stiffening effect at post-cracking stage is quantified on the basis of polynomial strain distribution functions of steel and concrete, and its contribution is implemented into the reinforcing steel. The introduced model can be effectively used in constructing the stress-strain curve of concrete at post-cracking stage, and the loads carried by concrete and by reinforcing steel along the member axis can be directly evaluated on the basis of the introduced model. In advance, the prediction of cracking loads and elongations of reinforced steel using the introduced model shows good agreements with results from previous analytical studies and experimental data.