• Steel and Composite Structures
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• v.39 no.5
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• pp.599-614
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• 2021

This study deals with the Lateral-Torsional Buckling (LTB) of a mono-symmetric tapered I-beam, in which the cross-section is varying longitudinally. To obtain the buckling moment, two concentrated bending moments should be applied at the two ends of the structure. This structure is made of Functionally Graded Material (FGM). The Young's and shear modules change linearly along the longitudinal direction of the beam. It is considered that this tapered beam is laterally restrained continuously, by using torsional springs. Furthermore, two rotational bending springs are employed at the two structural ends. To achieve the buckling moment, Ritz solution method is utilized. The response of critical buckling moment of the beam is obtained by minimizing the total potential energy relation. The lateral and torsional displacement fields of the beam are interpolated by harmonic functions. These functions satisfy the boundary conditions. Two different support conditions are considered in this study. The obtained formulation is validated by solving benchmark problems. Moreover, some numerical studies are implemented to show the accuracy, efficiency and high performance of the proposed formulation.

• Structural Engineering and Mechanics
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• v.15 no.5
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• pp.495-511
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• 2003

New material applications and transparency are desired by contemporary architects. Its superb transparency and high strength make glass a very suitable building material -in spite of its brittleness- even for primary load bearing structures. Currently we will focus on load bearing glass beams, subjected to different loading types. Since glass beams have a very slender, rectangular cross section, they are sensitive to lateral torsional buckling. Glass beams fail under a critical buckling load at stresses that lie far below the theoretical simple bending strength, due to the complex combination of torsion and out-of-plane bending, which characterises the instability phenomenon. The critical load can be increased considerably by preventing the upper rim from moving out of the beam's plane. Different boundary conditions are examined for different loading types. The load carrying capacity of glass beams can be increased three times and more using relatively simple, cheap lateral restraints.

• Advances in nano research
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• v.15 no.4
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• pp.339-353
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• 2023

This work aims to present a solution for the buckling behavior of perforated nano/microbeams with deformable boundary conditions using nonlocal strain gradient theory (NLSGT). For the first time, a solution that can provide buckling loads based on the non-local and strain gradient effects of perforated nanostructures on an elastic foundation, while taking into account both deformable and rigid boundary conditions. Stokes' transformation and Fourier series are used to realize this aim and determine the buckling loads under various boundary conditions. We employ the NLSGT to account for size-dependent effects and utilize the Winkler model to formulate the elastic foundation. The buckling behavior of the perforated nano/microbeams restrained with lateral springs at both ends is studied for various parameters such as the number of holes, the length and filling ratio of the perforated beam, the internal length, the nonlocal parameter and the dimensionless foundation parameter. Our results indicate that the number of holes and filling ratio significantly affect the buckling response of perforated nano/microbeams. Increasing the filling ratio increases buckling loads, while increasing the number of holes decreases buckling loads. The effects of the non-local and internal length parameters on the buckling behavior of the perforated nano/microbeams are also discussed. These material length parameters have opposite effects on the variation of buckling loads. This study presents an effective eigenvalue solution based on Stokes' transformation and Fourier series of the restrained nano/microbeams under the effects of elastic medium, perforation parameters, deformable boundaries and nonlocal strain gradient elasticity for the first time.

• Journal of the Korean Society for Precision Engineering
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• v.17 no.12
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• pp.209-216
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• 2000

The lateral behavior of the moving web is critical to the quality of the web products. The alignment of the rollers carrying the web is found to be one of important factors to the lateral behavior of the moving web. But, the study on the effect of the tilting roller in the direction of the normal to the moving web on the lateral behavior has not been reported in the literature yet. For example, the contact roller often contacts the winding roll in a tilted fashion and causes the lateral motion of the winding web, which induces the offset on the wound roll. The lateral dynamics of the moving web induced by a tilted roller in normal direction of a web is investigated in this paper. The two-dimensional dynamic model developed by Shelton is extended to investigate the effect of a titled roller in a normal direction of the moving web on the lateral motion of the moving web. New boundary conditions are developed to solve the extended model. Computer simulation study proved that the model developed can be used to predict the lateral motion of the moving web ？ to a tilted roller in normal direction of the moving web. The lateral deflection is increased exponentially a the tilting angle is increased. As the length of web span is increased, the amount of lateral deflection was increased almost linearly for the same tilting angle. The lateral dynamics turned out to be almost independent to the operating tension. The model developed can be used to solve the offset problem of the staggered winding and also to design a new web guiding mechanism.

• Geomechanics and Engineering
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• v.19 no.1
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• pp.79-91
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• 2019

Renewed interest in the long-term pile foundations has been driven by the increase in offshore wind turbine installation to generate renewable energy. A monopile subjected to repetitive loads experiences an evolution of displacements, pile rotation, and stress redistribution along the embedded portion of the pile. However, it is not fully understood how the embedded pile interacts with the surrounding soil elements based on different pile geometries. This study investigates the long-term soil response around offshore monopiles using finite element method. The semi-empirical numerical approach is adopted to account for the fundamental features of volumetric strain (terminal void ratio) and shear strain (shakedown and ratcheting), the strain accumulation rate, and stress obliquity. The model is tested with different strain boundary conditions and stress obliquity by relaxing four model parameters. The parametric study includes pile diameter, embedded length, and moment arm distance from the surface. Numerical results indicate that different pile geometries produce a distinct evolution of lateral displacement and stress. In particular, the repetitive lateral load increases the global lateral load resistance. Further analysis provides insight into the propagation of the shear localization from the pile tip to the ground surface.

• Geomechanics and Engineering
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• v.19 no.3
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• pp.201-215
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• 2019

A new approach of analyzing the displacements and stress of the surrounding rock for shallow tunnels excavated under non-axisymmetric displacement boundary conditions on a vertical surface is investigated in this study. In the proposed approach, by using a virtual image technique, the shear stress of the vertical ground surface is revised to be zero, and elastic solutions of the surrounding rock are obtained before stress revision. To revise the vertical normal stress and shear stress of horizontal ground surface generated by the combined action of the actual and image sinks, the harmonic functions and corresponding stress function solutions were adopted. Based on the Boussinesq's solutions and integral method, the horizontal normal stress of the vertical ground surface is revised to be zero. Based on the linear superposition principle, the final solution of the displacements and stress were proposed by superimposing the solutions obtained by the virtual image technique and the stress revision on the horizontal and vertical ground surfaces. Furthermore, the ground settlements and lateral displacements of the horizontal and vertical ground surfaces are derived by the proposed approach. The proposed approach was well verified by comparing with the numerical method. The discussion based on the proposed approach in the manuscript shows that smaller horizontal ground settlements will be induced by lower tunnel buried depths and smaller limb distances. The proposed approach for the displacement and stress of the surrounding rocks can provide some practical information about the surrounding rock stability analysis of shallow tunnels excavated under non-axisymmetric displacement boundary conditions on a vertical surface.

• Structural Engineering and Mechanics
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• v.68 no.5
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• pp.603-619
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• 2018

In this research, an effective computational technique is carried out for nonlinear and post-buckling analyses of cracked imperfect composite plates. The laminated plates are assumed to be moderately thick so that the analysis can be carried out based on the first-order shear deformation theory. Geometric non-linearity is introduced in the way of von-Karman assumptions for the strain-displacement equations. The Ritz technique is applied using Legendre polynomials for the primary variable approximations. The crack is modeled by partitioning the entire domain of the plates into several sub-plates and therefore the plate decomposition technique is implemented in this research. The penalty technique is used for imposing the interface continuity between the sub-plates. Different out-of-plane essential boundary conditions such as clamp, simply support or free conditions will be assumed in this research by defining the relevant displacement functions. For in-plane boundary conditions, lateral expansions of the unloaded edges are completely free while the loaded edges are assumed to move straight but restricted to move laterally. With the formulation presented here, the plates can be subjected to biaxial compressive loads, therefore a sensitivity analysis is performed with respect to the applied load direction, along the parallel or perpendicular to the crack axis. The integrals of potential energy are numerically computed using Gauss-Lobatto quadrature formulas to get adequate accuracy. Then, the obtained non-linear system of equations is solved by the Newton-Raphson method. Finally, the results are presented to show the influence of crack length, various locations of crack, load direction, boundary conditions and different values of initial imperfection on nonlinear and post-buckling behavior of laminates.

• Advances in nano research
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• v.8 no.3
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• pp.229-244
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• 2020

In this paper, modified Kelvin's model has been used to analyze the orthotropic vibration frequencies of single walled carbon nanotubes with clamped-clamped and clamped-free boundary conditions. For this system the governing equation is developed with wave propagation approach. Armchair, zigzag and chiral structures are considered for the vibrational analysis to investigate the effect of different modes, in-plane rigidity and mass density per unit lateral area. Throughout the computations, on decreasing the length-to-diameter ratios, the frequencies of said structure increases. In addition, by increasing three different value of in-plane rigidity resulting frequencies also increase and frequencies decrease on increasing mass density per unit lateral area. The results generated using computer software MATLAB to furnish the evidence regarding applicability of present model and also verified by available published literature.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2002.10a
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• pp.1059-1061
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• 2002

A FE model is to develop a personalized biomechanical model of the scoliotic spine that will allow the design of clinical test providing optimal estimation of the post-operation results. A flexible multi-body model of the spine including rib cage, clavicle, and scapular was developed to simulate several mobility simulations. Vertebrae, clavicle and scapular were represented using rigid bodies and ribs and sternum were modeled as flexible bodies. Kinematical Joints and spring elements were used to represent the intervertebral disc and ligaments respectively. Postero-anterior and lateral radiographics of a scoliotic spine were used to represent a 3D reconstruction. CT data for same patient were also used to verify vertebrae rotation driven from postero-anterior and lateral radiographic images. Simulated results showed good reducibility almost uniformly distributed along the spinal segments. It was also found that boundary and loading conditions, required to mimic the operation procedures, were proven to be very sensitive parameters to its results rather than its mechanical properties

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.04a
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• pp.449-456
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• 1998

A consistent finite element formation and analytic solutions are presented for spatial stability of thin-walled circular arch. The total potential energy is derived by applying the principle of linearized virtual work and including second order terms of finite semitangential rotations. As a result the energy functional corresponding to the semitangential rotation is obtained, in which the elastic strain energy terms are considered restrained warping effects. We have obtained analytic solution for the lateral buckling of monosymmetric thin-walled curved beam subjected to pure bending or uniform compression and it's boundary conditions are simply supported. For finite element analysis, the two node cubic Hermitian polynomials are utilized as shape Auctions. In order to illustrate the accuracy of this study, parameter studies for lateral buckling problems of circular arch are presented and compared with available solutions and numerical results analyzed by the FEM using straight beam element.