• Interaction and multiscale mechanics
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• v.2 no.3
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• pp.223-233
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• 2009

This paper presents a new nonlocal stress variational principle approach for the transverse free vibration of an Euler-Bernoulli cantilever nanobeam with an initial axial tension at its free end. The effects of a nanoscale at molecular level unavailable in classical mechanics are investigated and discussed. A sixth-order partial differential governing equation for transverse free vibration is derived via variational principle with nonlocal elastic stress field theory. Analytical solutions for natural frequencies and transverse vibration modes are determined by applying a numerical analysis. Examples conclude that nonlocal stress effect tends to significantly increase stiffness and natural frequencies of a nanobeam. The relationship between natural frequency and nanoscale is also presented and its significance on stiffness enhancement with respect to the classical elasticity theory is discussed in detail. The effect of an initial axial tension, which also tends to enhance the nanobeam stiffness, is also concluded. The model and approach show potential extension to studies in carbon nanotube and the new result is useful for future comparison.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1997.10a
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• pp.28-31
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• 1997

Buckling analysis of thin compressed beam has been carried out. Pre-buckling and post-buckling are simulated by finite element method incorporating with the incremental nonlinear theory and the Newton-Raphson solution technique. In order to find the bifurcation point, the determinent of the stiffness matrix is calculated at every iteration procedure. For post-buckling analysis, a small perturbed initial guess is given along the eigenvector direction at the bifurcation point. Nonlinear elastic buckling and elastic-plastic buckling of cantilever beam are analyzed. The buckling load and buckled shape of the two models are compared.

• Structural Engineering and Mechanics
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• v.59 no.2
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• pp.227-241
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• 2016

A circular plate with constant thickness, finite radius and stiff edge lying on an elastic halfspace is considered. The half-space consists of a soft functionally graded (FGM) layer with arbitrary varying elastic properties and a homogeneous elastic substrate. The plate bends under the action of arbitrary axisymmetric distributed load and response from the elastic half-space. A semi-analytical solution for the problem effective in whole range of geometric (relative layer thickness) and mechanical (elastic properties of coating and substrate, stiffness of the plate) properties is constructed using the bilateral asymptotic method (Aizikovich et al. 2009). Approximated analytical expressions for the contact stresses and deflections of the plate are provided. Numerical results showing the qualitative dependence of the solution from the initial parameters of the problem are obtained with high precision.

• Steel and Composite Structures
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• v.3 no.4
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• pp.261-275
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• 2003

Truss members built-up with double angles back-to-back have monosymmetric cross-section and twisting always accompanies flexion upon the onset of buckling about the axis of symmetry. Approximate formulae for calculating the buckling capacity are presented in this paper for routine design purpose. For a member susceptible only to flexural buckling, its optimal cross-section should consist of slender plate elements so as to get larger radius of gyration. But, occurrence of twisting changes the situation owing to the weakness of thin plates in resisting torsion. Criteria for limiting the leg slenderness are discussed herein. Truss web members in compression are usually considered as hinged at both ends for out-of-plane buckling. In case one (or both) end of member is not supported laterally by bracing member, its adjoining members have to provide an elastic support of adequate stiffness in order not to underdesign the member. The stiffness provided by either compression or tension chords in different cases is analyzed, and the effect of initial crookedness of compression chord is taken into account. Formulae are presented to compute the required stiffness of chord member and to determine the effective length factor for inadequately constrained compressive diagonals.

• Steel and Composite Structures
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• v.33 no.3
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• pp.357-373
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• 2019

Steel storage racks are slender structures whose overall behavior and the capacity depend largely on the flexural behavior of the base-plate to upright connections and on the behavior of beam-to-column connections. The base-plate upright connection assembly details, anchor bolt position in particular, associated with the high-rise steel storage racks differ from those of normal height steel storage racks. Since flexural behavior of high-rise rack base connection is hitherto unavailable, this investigation experimentally establishes the flexural behavior of base-plate upright connections of high-rise steel storage racks. This investigation used an enhanced test setup and considered nine groups of three identical tests to investigate the influence of factors such as axial load, base plate thickness, anchor bolt size, bracket length, and upright thickness. The test observations show that the base-plate assembly may significantly influence the overall behavior of such connections. A rigid plate analytical model and an elastic plate analytical model for the overall rotations stiffness of base-plate upright connections with concentric anchor bolts were constructed, and were found to give better predictions of the initial stiffness of such connections. Analytical model based parametric studies highlight and quantify the interplay of components and provide a means for efficient maximization of overall rotational stiffness of concentrically anchor bolted high-rise rack base-plate upright connections.

• Bulletin of the Society of Naval Architects of Korea
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• v.24 no.3
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• pp.43-51
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• 1987

In this paper, dynamic elastic, plastic response of beam-columns is analysed using discrete models. composed of rigid bars and springs. The equation of motion is formulated including the shear deformation effect, and the stress change of yielding points is calculated with various yielding criteria. The effect of initial axial force is considered by two ways: (1) including the effect in interaction curve only. (2) including the effect directly in the equation of motion in terms of initial stiffness method is also used in nonlinear interaction procedure. It is found that this model is very effective in analysing not only the plastic response but the elastic response, and present method is more efficient than Finite Element Method from the viewpoint of calculation time and accuracy.

• Structural Engineering and Mechanics
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• v.65 no.1
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• pp.121-128
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• 2018

Three structure-dependent integration methods with no numerical dissipation have been successfully developed for time integration. Although these three integration methods generally have the same numerical properties, such as unconditional stability, second-order accuracy, explicit formulation, no overshoot and no numerical damping, there still exist some different numerical properties. It is found that TLM can only have unconditional stability for linear elastic and stiffness softening systems for zero viscous damping while for nonzero viscous damping it only has unconditional stability for linear elastic systems. Whereas, both CEM and CRM can have unconditional stability for linear elastic and stiffness softening systems for both zero and nonzero viscous damping. However, the most significantly different property among the three integration methods is a weak instability. In fact, both CRM and TLM have a weak instability, which will lead to an adverse overshoot or even a numerical instability in the high frequency responses to nonzero initial conditions. Whereas, CEM possesses no such an adverse weak instability. As a result, the performance of CEM is much better than for CRM and TLM. Notice that a weak instability property of CRM and TLM might severely limit its practical applications.

• Computational Structural Engineering
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• v.11 no.1
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• pp.179-190
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• 1998

A geometrically nonlinear finite element formulation of spatial cable networks is presented using two cable elements. Firstly, derivation procedures of tangent stiffness and mass matrices for the space truss element and the elastic catenary cable element are summarized. The load incremental method based on Newton-Raphson iteration method and the dynamic relaxation method are presented in order to determine the initial static state of cable nets subjected to self-weights and support motions. Furthermore, static non-linear analysis of cable structures under additional live loads are performed based on the initial configuration. Challenging example problems are presented and discussed in order to demonstrate the feasibility of the present finite element method and investigate static nonlinear behaviors of cable nets.

• Structural Engineering and Mechanics
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• v.45 no.2
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• pp.169-182
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• 2013

The mechanical behavior of rectangular foundation plates with perimetric beams and internal stiffening beams of the plate is herein analyzed, taking the foundation design into account. A series of dimensionless parameters related to the geometry of the studied elements were defined. In order to generalize the problem statement, an initial settlements was considered. A numeric procedure was developed for the resolution by means of the Finite Differences Method that takes into account the stiffness of the plate, the perimetric and internal plate beams and the soil reaction module. Iterative algorithms were employed which, for each of the analyzed cases, made it possible to find displacements and reaction percentages taken by the plate and those that discharge directly into the perimetric beams, practically without affecting the plate. To enhance its mechanical behavior the internal stiffening beams were prestressed and the results obtained with and without prestressing were compared. This analysis was made considering the load conditions and the soil reaction module constant.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2003.10a
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• pp.209-216
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• 2003

The purpose of this study is to investigate the response characteristics of pushover analysis of upper wall-lower frame system with X and Y-directions' lateral load Pushover analysis estimates initial elastic stiffness, post-yielding stiffness, and plastic hinges on each story of structures through three-dimensional nonlinear analysis program. The conclusions of this study are as follows; (1) As a result of pushover analysis, the magnitude of nonlinear response and distribution of yield hinge in lower structure are similar with both X and Y directions, but not in upper structure because of different relative stiffness. (2) The maximum drift ratio of roof is larger for X-direction than for Y-direction with respect to magnitude of shear wall areas in upper structure.