• Structural Engineering and Mechanics
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• v.31 no.6
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• pp.625-638
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• 2009

Applications of membrane mechanisms are widely found in nano-devices and nano-sensor technologies nowadays. An alternative approach for large deflection analysis of the orthotropic, elliptic membranes - subject to gravitational, uniform pressures often found in nano-sensors - is described in this paper. The material properties of membranes are assumed to be orthogonally isotropic and linearly elastic, while the principal directions of elasticity are parallel to the coordinate axes. Formulating the potential energy functional of the orthotropic, elliptic membranes involves the strain energy that is attributed to inplane stress resultant and the potential energy due to applied pressures. In the solution method, Rayleigh-Ritz method can be used successfully to minimize the resulting total potential energy generated. The set of equilibrium equations was solved subsequently by Newton-Raphson. The unparalleled model formulation capable of analyzing the large deflections of both circular and elliptic membranes is verified by making numerical comparisons with existing results of circular membranes as well as finite element solutions. The results are found in excellent agreements at all cases. Then, the parametric investigations are given to delineate the impacts of the aspect ratios and orthotropic elasticity on large static tensions and deformations of the orthotropic, elliptic membranes.

• Structural Engineering and Mechanics
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• v.54 no.3
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• pp.433-451
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• 2015

This paper focuses on large deflection static behavior of edge cracked simple supported beams subjected to a non-follower transversal point load at the midpoint of the beam by using the total Lagrangian Timoshenko beam element approximation. The cross section of the beam is circular. The cracked beam is modeled as an assembly of two sub-beams connected through a massless elastic rotational spring. It is known that large deflection problems are geometrically nonlinear problems. The considered highly nonlinear problem is solved considering full geometric non-linearity by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. There is no restriction on the magnitudes of deflections and rotations in contradistinction to von-Karman strain displacement relations of the beam. The beams considered in numerical examples are made of Aluminum. In the study, the effects of the location of crack and the depth of the crack on the non-linear static response of the beam are investigated in detail. The relationships between deflections, end rotational angles, end constraint forces, deflection configuration, Cauchy stresses of the edge-cracked beams and load rising are illustrated in detail in nonlinear case. Also, the difference between the geometrically linear and nonlinear analysis of edge-cracked beam is investigated in detail.

• Journal of The Korean Astronomical Society
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• v.37 no.5
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• pp.427-431
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• 2004

We use simulations of large-scale structure formation to study the build-up of magnetic fields (MFs) in the intergalactic medium. Our basic assumption is that cosmological MFs grow in a magnetohy-drodynamical (MHD) amplification process driven by structure formation out of a magnetic seed field present at high redshift. This approach is motivated by previous simulations of the MFs in galaxy clusters which, under the same hypothesis that we adopt here, succeeded in reproducing Faraday rotation measurements (RMs) in clusters of galaxies. Our ACDM initial conditions for the dark matter density fluctuations have been statistically constrained by the observed large-scale density field within a sphere of 110 Mpc around the Milky Way, based on the IRAS 1.2-Jy all-sky redshift survey. As a result, the positions and masses of prominent galaxy clusters in our simulation coincide closely with their real counterparts in the Local Universe. We find excellent agreement between RMs of our simulated galaxy clusters and observational data. The improved numerical resolution of our simulations compared to previous work also allows us to study the MF in large-scale filaments, sheets and voids. By tracing the propagation of ultra high energy (UHE) protons in the simulated MF we construct full-sky maps of expected deflection angles of protons with arrival energies $E = 10^{20}\;eV$ and $4 {\times} 10^{19}\;eV$, respectively. Accounting only for the structures within 110 Mpc, we find that strong deflections are only produced if UHE protons cross galaxy clusters. The total area on the sky covered by these structures is however very small. Over still larger distances, multiple crossings of sheets and filaments may give rise to noticeable deflections over a significant fraction of the sky; the exact amount and angular distribution depends on the model adopted for the magnetic seed field. Based on our results we argue that over a large fraction of the sky the deflections are likely to remain smaller than the present experimental angular sensitivity. Therefore, we conclude that forthcoming air shower experiments should be able to locate sources of UHE protons and shed more light on the nature of cosmological MFs.

• Journal of Advanced Marine Engineering and Technology
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• v.29 no.7
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• pp.785-794
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• 2005

Modern ship hulls of large oil carriers and container carrers have become more flexible with scantling optimization and increase in ship length. On the other hand. as the demand for power has increased with the ship size. shaft diameters have become larger and stiffer. Consequently. the alignment of the propulsion system has become more sensitive to hull girder deflections. resulting in difficulties in analyzing the alignment and conducting the alignment procedure. Accordingly. the frequency of shaft alignment related bearing damages has increased significantly in recent years. The alignment related damages are mostly attributed to inadequate analyses. changes in the design of the vessel. shipyards' practices in conducting the alignment. and a lack of well defined analytical criteria. The hull deflections should be considered at the design stage to minimize the bearing damage caused by hull deflection. Hull deflections can be estimated by analytical approach and reverse calculation using the measured data. The hull girder deflection analysis using the reverse calculation will be introduced in this paper.

• Transactions of Materials Processing
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• v.3 no.4
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• pp.401-414
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• 1994

Springback for the three point bending is anlayzed and experimented. Neutral axis is assumed to remain at the midthickness for large ratio of radius of curvature to thickness. Pure bending theory is used to be extended to the analysis of the springback for three point bending. The specimen is thought to be divided into numerous small elements. The theory for pure bending is then adopted for analysis of each element to obtain springback in terms of the relationship between initial and final deflections. the boundary conditions between neighborhood elements are the deflection and slope which should be the same. Deflection is calculated by summing up the deflections of each element. Experiments have been performed for different conditions which are punch radius, span length, and initial deflections. Comparisons between the analytical solution and experimental results show the same trends.

• Nuclear Engineering and Technology
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• v.30 no.5
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• pp.387-395
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• 1998

In general, the laminated rubber bearing (LRB), a composite structure laminated with the elastic rubber and steel plates, has a complex hysteretic nonlinear characteristics in relationships between the restoring force and shear deflection. The representative nonlinear characteristics of LRB include the change of hysteresis loop with cyclic shear deflections and the hardening effects at large shear deflection regions. Changes of the hysteresis loop of LRB with cyclic shear deflections affect the horizontal stiffness and the damping characteristics. The hardening behavior of LRB in large shear deflection region results in an increased horizontal stiffness and therefore, has a great impacton the seismic responses. In this paper, the seismic response analysis is carried out using the modified hysteretic bi-linear model of LRB, which takes into account the hysteresis loop change and the hardening behavior with cyclic shear deflection. The results on seismic responses are compared with those obtained using the widely used hysteretic hi-linear model. The new model is found to reveal the greater amount of peak acceleration response.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.22 no.1
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• pp.25-34
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• 2009

RC flat plate, which has no large flexural stiffness by boundary beams, may be governed by serviceability as well as strength condition. A construction sequence and its impact on distributions of construction loads among slabs tied by shores are decisive factors on immediate and long term performances of flat plate. The over-loading and tensile cracking in early-aged slabs significantly increase the deflection of flat plate system. In this study, for slab deflections, the practical analysis scheme using a linear analysis program is formulated with considering construction sequence and concrete cracking effects. The concept of the effective moment of inertia in calculating deflections of one-way bending member, that is presented in structural design codes, is extended to the finite element analysis of the two-way slab system of flat plates. Effects of over-loads during construction on deflections of flat plate system are analyzed by applying the proposed practical analysis scheme into the critical construction load conditions calculated from the simplified method.

• Steel and Composite Structures
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• v.13 no.1
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• pp.71-89
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• 2012

The paper investigates beam lateral buckling stability according to linear and non-linear models. Closed form solutions for single-symmetric cross sections are first derived according to a non-linear model considering flexural-torsional coupling and pre-buckling deformation effects. The closed form solutions are compared to a beam finite element developed in large torsion. Effects of pre-buckling deflection and gradient moment on beam stability are not well known in the literature. The strength of singly symmetric I-beams under gradient moments is particularly investigated. Beams with T and I cross-sections are considered in the study. It is concluded that pre-buckling deflections effects are important for I-section with large flanges and analytical solutions are possible. For beams with T-sections, lateral buckling resistance depends not only on pre-buckling deflection but also on cross section shape, load distribution and buckling modes. Effects of pre-buckling deflections are important only when the largest flange is under compressive stresses and positive gradient moments. For negative gradient moments, all available solutions fail and overestimate the beam strength. Numerical solutions are more powerful. Other load cases are investigated as the stability of continuous beams. Under arbitrary loads, all available solutions fail, and recourse to finite element simulation is more efficient.

• Steel and Composite Structures
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• v.6 no.5
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• pp.401-415
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• 2006

Based on a non-linear model taking into account flexural-torsional couplings, analytical solutions are derived for lateral buckling of simply supported I beams under some representative load cases. A closed form is established for lateral buckling moments. It accounts for bending distribution, load height application and pre-buckling deflections. Coefficients $C_1$ and $C_2$ affected to these parameters are then derived. Regard to well known linear stability solutions, these coefficients are not constant but depend on another coefficient $k_1$ that represents the pre-buckling deflection effects. In numerical simulations, shell elements are used in mesh process. The buckling loads are achieved from solutions of eigenvalue problem and by bifurcations observed on non linear equilibrium paths. It is proved that both the buckling loads derived from linear stability and eigenvalue problem lead to poor results, especially for I sections with large flanges for which the behaviour is predominated by pre-buckling deflection and the coefficient $k_1$ is large. The proposed solutions are in good agreement with numerical bifurcations observed on non linear equilibrium paths.

• Wind and Structures
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• v.39 no.1
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• pp.47-69
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• 2024

Pounding of structures may result in considerable damages, to the extent of total failure during severe lateral loading events (e.g., earthquakes and wind). With the new generation of tall buildings in densely occupied locations, wind-induced pounding becomes of higher risk due to such structures' large deflections. This paper aims to develop mathematical formulations to determine the maximum pounding force when two adjacent structures come into contact. The study will first investigate wind-induced pounding forces of two equal-height structures with similar dynamic properties. The wind loads will be extracted from the Large Eddy Simulation models and applied to a Finite Element Method model to determine deflections and pounding forces. A Genetic Algorithm is lastly utilized to optimize fitting parameters used to correlate the maximum pounding force to the governing structural parameters. The results of the wind-induced pounding show that structures with a higher natural frequency will produce lower maximum pounding forces than those of the same structure with a lower natural frequency. In addition, taller structures are more susceptible to stronger pounding forces at closer separation distances. It was also found that the complexity of the mathematical formula from optimization depends on achieving a more accurate mapping for the trained database.