• Structural Engineering and Mechanics
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• v.85 no.2
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• pp.147-161
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• 2023

Based on the ideas of variational differential quadrature (VDQ) and finite element method (FEM), a numerical approach named as VDQFEM is applied herein to study the large deformations of plate-type structures under static loading with arbitrary shape hole made of functionally graded graphene platelet-reinforced composite (FG-GPLRC) in the context of higher-order shear deformation theory (HSDT). The material properties of composite are approximated based upon the modified Halpin-Tsai model and rule of mixture. Furthermore, various FG distribution patterns are considered along the thickness direction of plate for GPLs. Using novel vector/matrix relations, the governing equations are derived through a variational approach. The matricized formulation can be efficiently employed in the coding process of numerical methods. In VDQFEM, the space domain of structure is first transformed into a number of finite elements. Then, the VDQ discretization technique is implemented within each element. As the last step, the assemblage procedure is performed to derive the set of governing equations which is solved via the pseudo arc-length continuation algorithm. Also, since HSDT is used herein, the mixed formulation approach is proposed to accommodate the continuity of first-order derivatives on the common boundaries of elements. Rectangular and circular plates under various boundary conditions with circular/rectangular/elliptical cutout are selected to generate the numerical results. In the numerical examples, the effects of geometrical properties and reinforcement with GPL on the nonlinear maximum deflection-transverse load amplitude curve are studied.

• Journal of Korean Association for Spatial Structures
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• v.8 no.1
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• pp.41-48
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• 2008

Spatial structure is an appropriate shape that resists external force only with in-plane forte by reducing the influence of bending moment, and it maximizes the effectiveness of structure system. the spatial structure should be analyzed by nonlinear analysis regardless static and dynamic analysis because it accompanys large deflection for member. To analyze the spatial structure geometrical and material nonlinearity should be considered in the analysis. In this paper, a geometrically nonlinear finite element model for plane truss structures is developed, and material nonlinearity is also included in the analysis. Arc-length method is used to solve the nonlinear finite element model. It is found that the present analysis predicts accurate nonlinear behavior of plane truss.

• Restorative Dentistry and Endodontics
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• v.33 no.4
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• pp.323-331
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• 2008

Flexibility and fracture properties determine the performance of NiTi rotary instruments. The purpose of this study was to evaluate how geometrical differences between three NiTi instruments affect the deformation and stress distributions under bending and torsional conditions using finite element analysis. Three NiTi files (ProFile .06 / #30, F3 of ProTaper and ProTaper Universal) were scanned using a Micro-CT. The obtained structural geometries were meshed with linear, eight-noded hexahedral elements. The mechanical behavior (deformation and von Mises equivalent stress) of the three endodontic instruments were analyzed under four bending and rotational conditions using ABAQUS finite element analysis software. The nonlinear mechanical behavior of the NiTi was taken into account. The U-shaped cross sectional geometry of ProFile showed the highest flexibility of the three file models. The ProTaper, which has a convex triangular cross-section, was the most stiff file model. For the same deflection, the ProTaper required more force to reach the same deflection as the other models, and needed more torque than other models for the same amount of rotation. The highest von Mises stress value was found at the groove area in the cross-section of the ProTaper Universal. Under torsion, all files showed highest stresses at their groove area. The ProFile showed highest von Mises stress value under the same torsional moment while the ProTaper Universal showed the highest value under same rotational angle.

• Journal of the Society of Naval Architects of Korea
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• v.29 no.2
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• pp.115-122
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• 1992

A sandwich element is a special Hybrid structural form of the composite construction, which is consisted of three main parts : thin, stiff and relatively high density faces separated by a thick, light, and weaker core material. In a sandwich construction, the shear deformation of the faces. Therefore, in the calculation of the bending stiffness, the shear effect should be included. In this paper, the minimum weight is selected as an object function, as the weight critical structures are usually composed of these kind of construction. To obtain the minimum weight of sandwich panel, the principle of minimum potential energy is used and as for the design constraints, the allowable bending stress of face material, the allowable shear stress of core material, the allowable value of panel deflection and the wrinkling stress of faces are adopted, as well as the different boundary conditions. For the engineering purpose of sandwich panel design, the results are tabulated, which are calculated by using the nonlinear optimization technique SUMT.

• Structural Engineering and Mechanics
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• v.25 no.2
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• pp.161-180
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• 2007

A first endeavor is made to exploit the differential quadrature method (DQM) as a simple, accurate, and computationally efficient numerical tool for the large deformation analysis of thin laminated composite skew plates, which has very strong singularity at the obtuse vertex. The geometrical nonlinearity is modeled by using Green's strain and von Karman assumption. A recently developed DQ methodology is used to exactly implement the multiple boundary conditions at the edges of skew plates, which is a major draw back of conventional DQM. Using oblique coordinate system and the DQ methodology, a mapping-DQ discretization rule is developed to simultaneously transform and discretize the equilibrium equations and the related boundary conditions. The effects of skew angle, aspect ratio and different types of boundary conditions on the convergence and accuracy of the presented method are studied. Comparing the results with the available results from other numerical or analytical methods, it is shown that accurate results are obtained even when using only small number of grid points. Finally, numerical results for large deflection behavior of antisymmetric cross ply skew plates with different geometrical parameters and boundary conditions are presented.

• Steel and Composite Structures
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• v.9 no.6
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• pp.569-584
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• 2009

Corrosion of steel rebars in bridge decks which are faced to harsh conditions, is a common problem in construction industries due to the porosity of concrete. In this research, the behavior of one-way concrete slabs reinforced with Glass fiber reinforced polymer (GFRP) molded grating is investigated both theoretically and experimentally. In the analytical method, a closed-form solution for load-deflection behavior of a slab under four-point bending condition is developed by considering a concrete slab as an orthotropic plate and defining stiffness coefficients in principal directions. The available formulation for concrete reinforced with steel is expanded for concrete reinforced with GFRP molded grating to predict ultimate failure load. In finite element modeling, an exact nonlinear behavior of concrete along with a 3-D failure criterion for cracking and crushing are considered in order to estimate the ultimate failure load and the initial cracking load. Eight concrete slabs reinforced with steel and GFRP grating in various thicknesses are also tested to verify the results. The obtained results from the models and experiments are relatively satisfactory.

• Tribology and Lubricants
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• v.31 no.4
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• pp.177-182
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• 2015

Tapered roller bearings are widely used in equipment where high combined thrust and radial loads are experienced. A certain amount of tilting between the tapered rollers and the races always occurs because of bending moment load conditions and shaft deflection. It is now well understood that a coherent elastohydrodynamic lubrication (EHL) film separates the rollers and races. In spite of extensive study on EHL problems for over half a century, relatively few studies have focused on the finite line contacts problem. This study presents a complete numerical analysis of the effects of roller tilting on the EHL characteristics in a tapered roller bearing. We systematically analyze this highly nonlinear problem using finite differences with fully non-uniform grids and the Newton-Raphson method. Detailed EHL pressure distributions and film shapes are presented under moderate loads and material parameters. A very small roller tilting significantly affects the pressure distributions and film shapes near both ends of the roller. Moreover, the effect of tilting on the EHL characteristics at the small end is much greater than that at the large end. Therefore, in designing optimum profiles for tapered roller bearings, the profile radius should be larger at the small end.

• Computers and Concrete
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• v.24 no.6
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• pp.561-570
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• 2019

Understanding the realistic behavior of concrete up to failure under different loading conditions within the framework of damage mechanics and plasticity would lead to an enhanced design of concrete structures. In the present investigation, QR (Quick Response) code based random speckle pattern is used as a non-contact sensor, which is an innovative approach in the field of digital image correlation (DIC). A four-point bending test was performed on RC beams of size 1800 mm × 150 mm × 200 mm. Image processing was done using an open source Ncorr algorithm for the results obtained using random speckle pattern and QR code based random speckle pattern. Load-deflection curves of RC beams were plotted for the results obtained using both contact and non-contact (DIC) sensors, and further, Moment (M)-Curvature (κ) relationship of RC beams was developed. The loading curves obtained were used as input data for material model parameters in finite element analysis. In finite element method (FEM) based software, concrete damage plasticity (CDP) constitutive model is used to predict the realistic nonlinear quasi-static flexural behavior of RC beams for monotonic loading condition. The results obtained using QR code based DIC are observed to be on par with conventional results and FEM results.

• Steel and Composite Structures
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• v.37 no.2
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• pp.117-136
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• 2020

Curved steel-concrete composite box girder has been widely adopted in urban overpasses and ramp bridges. In order to investigate its mechanical behavior under complicated and combined bending, shear and torsion load, two large-curvature composite box girders with interior angles of 25° and 45° were tested under static hogging moment. Based on the strain and deflection measurement on critical cross-sections during the static loading test, the failure mode, cracking behavior, load-displacement relationship, and strain distribution in the steel plate and rebar were investigated in detail. The test result showed the large-curvature composite box girders exhibited notable shear lag in the concrete slab and steel girder. Also, the constraint torsion and distortion effect caused the stress measured at the inner side of the composite beam to be notably higher than that of the outer side. The strain distribution in the steel web was approximately linear; therefore, the assumption that the plane section remains plane was approximately validated based on strain measurement at steel web. Furthermore, the full-process non-linear elaborate finite element (FE) models of the two specimens were developed based on commercial FE software MSC.MARC. The modeling scheme and constitutive model were illustrated in detail. Based on the comparison between the FE model and test results, the FE model effectively simulated the failure mode, the load-displacement curve, and the strain development of longitudinal rebar and steel girder with sufficient accuracy. The comparison between the FE model and the test result validated the accuracy of the developed FE model.

• Steel and Composite Structures
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• v.42 no.6
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• pp.779-789
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• 2022

This work presents a non-linear cylindrical bending analysis of functionally graded plate reinforced by single-walled carbon nanotubes (SWCNTs) in thermal environment using a simple integral higher-order shear deformation theory (HSDT). This theory does not require shear correction factors and the transverse shear stresses vary parabolically through the thickness. The material properties of SWCNTs are assumed to be temperature-dependent and are obtained from molecular dynamics simulations. The material properties of functionally graded carbon nanotube-reinforced composites (FG-CNTCRs) are considered to be graded in the thickness direction, and are estimated through a micromechanical model. The non-linear strain-displacement relations in the Von Karman sense are used to study the effect of geometric non-linearity and the solution is obtained by minimization of the total potential energy. The numerical illustrations concern the nonlinear bending response of FG-CNTRC plates under different sets of thermal environmental conditions, from which results for uniformly distributed CNTRC plates are obtained as benchmarks.