• Coupled systems mechanics
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• v.6 no.4
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• pp.399-415
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• 2017

This paper deals with the nonlinear static deflections of functionally graded (FG) porous under thermal effect. Material properties vary in both position-dependent and temperature-dependent. The considered nonlinear problem is solved by using Total Lagrangian finite element method within two-dimensional (2-D) continuum model in the Newton-Raphson iteration method. In numerical examples, the effects of material distribution, porosity parameters, temperature rising on the nonlinear large deflections of FG beams are presented and discussed with porosity effects. Also, the effects of the different porosity models on the FG beams are investigated in temperature rising.

• Structural Engineering and Mechanics
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• v.53 no.1
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• pp.131-146
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• 2015

In the present paper a three-dimensional non-linear truss element and a short computer program for the modeling and predicting approximate lateral deflections in thin glass plates by the method of incremental loading are proposed. Due to the out-of-plane large deflections of thin glass plates compared to the plate thickness within each loading increment, the equilibrium and stiffness conditions are written with respect to the deformed structure. An application is presented on a thin fully tempered monolithic rectangular glass plate, laterally supported around its perimeter subjected to uniform wind pressure. The results of the analysis are compared with published experimental results and found to have satisfactory approximation. It is also observed that the large deflections of a glass plate lead to a part substitution of the bending plate behavior by a tensioned membrane behavior which is favorable.

• Journal of the Korean Society for Precision Engineering
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• v.23 no.9 s.186
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• pp.134-141
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• 2006

Surface deflections have a great effect on the external appearance of automobiles. Usually, they are occurred on large flat panels containing sudden shape changes and of very small size about $\pm$30$\sim$300$\mu$m. Since the current numerical method is not sufficient for predicting these defects, the correction of these defects still depends on trial and error, which requires a great deal of time and expense. Consequently, developing the numerical method to predict and prevent these defects is very important far improving cosmetic surface qualities. In this study, an evaluation system that can analyze surface deflections using numerical simulation and a visualization system are reported. To calculate the surface deflections numerically, robust algorithms and simulation methodologies are suggested and to visualize them quantitatively, the curvature variation algorithm is proposed. To verify the developed systems, the experimental die of the handle portion of exterior door is analyzed. The results showed that the experimental and simulational visualization are in good agreement. Compensation methods to correct the surface deflections are also tested. The evaluation system proposed in this paper could be used to predict and minimize the occurrence of surface deflections in die manufacturing.

• Steel and Composite Structures
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• v.27 no.5
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• pp.567-576
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• 2018

The objective of this work is to analyze large deflections of a fiber reinforced composite cantilever beam under point loads. In the solution of the problem, finite element method is used in conjunction with two dimensional (2-D) continuum model. It is known that large deflection problems are geometrically nonlinear problems. The considered non-linear problem is solved considering the total Lagrangian approach with Newton-Raphson iteration method. In the numerical results, the effects of the volume fraction and orientation angles of the fibre on the large deflections of the composite beam are examined and discussed. Also, the difference between the geometrically linear and nonlinear analysis of fiber reinforced composite beam is investigated in detail.

• Structural Engineering and Mechanics
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• v.19 no.4
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• pp.413-423
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• 2005

This paper presents the solution of large static deflection due to uniformly distributed self weight and the critical or maximum applied uniform loading that a simply supported beam with variable-arc-length can resist. Two analytical approaches are presented and validated experimentally. The first approach is a finite-element discretization of the span length based on the variational formulation, which gives the solution of large static sag deflections for the stable equilibrium case. The second approach is the shooting method based on an elastica theory formulation. This method gives the results of the stable and unstable equilibrium configurations, and the critical uniform loading. Experimental studies were conducted to complement the analytical results for the stable equilibrium case. The measured large static configurations are found to be in good agreement with the two analytical approaches, and the critical uniform self weight obtained experimentally also shows good correlation with the shooting method.

• Structural Engineering and Mechanics
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• v.32 no.4
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• pp.501-516
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• 2009

This paper aims to study the large deflections of variable-arc-length elastica subjected to the terminal forces (e.g., axial force and torque). Based on Kirchhoff's rod theory and with help of Euler parameters, the set of nonlinear governing differential equations which free from the effect of singularity are established together with boundary conditions. The system of nonlinear differential equations is solved by using the shooting method with high accuracy integrator, seventh-eighth order Runge-Kutta with adaptive step-size scheme. The error norm of end conditions is minimized within the prescribed tolerance ($10^{-5}$). The behavior of VAL elastica is studied by two processes. One is obtained by applying slackening first. After that keeping the slackening as a constant and then the twist angle is varied in subsequent order. The other process is performed by reversing the sequence of loading in the first process. The results are interpreted by observing the load-deflection diagram and the stability properties are predicted via fold rule. From the results, there are many interesting aspects such as snap-through phenomenon, secondary bifurcation point, loop formation, equilibrium configurations and effect of variable-arc-length to behavior of elastica.

• Structural Engineering and Mechanics
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• v.51 no.6
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• pp.955-971
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• 2014

Large post-buckling behavior of Timoshenko beams subjected to non-follower axial compression loads are studied in this paper by using the total Lagrangian Timoshenko beam element approximation. Two types of support conditions for the beams are considered. In the case of beams subjected to compression loads, load rise causes compressible forces end therefore buckling and post-buckling phenomena occurs. It is known that post-buckling problems are geometrically nonlinear problems. The considered highly non-linear 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 lower-Carbon Steel. In the study, the relationships between deflections, rotational angles, critical buckling loads, post-buckling configuration, Cauchy stress of the beams and load rising are illustrated in detail in post-buckling case.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.30 no.4
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• pp.343-350
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• 2017

The RC flat plate system has benefits such as a short construction time, an improvement of workability and a floor height reduction. In the case of long span slab, cracking damages and large deflections tend to occur due to the low flexural stiffness of flat plates. Specially, over-loading by self-weight of slab during construction increases short and long-term deflections. These problems may be solved by the use of void slab that has benefits of the reduced self-weight. In this study, to analyze an effect of self-weight reduction of void slab on slab deflections, the parametric study is performed. Including variable conditions such as a concrete strength, a slab construction cycle, the number of shored floors, a compressive reinforcement ratio and a tensile reinforcement ratio, slab construction loads and deflections are calculated by considering the construction stages, concrete cracking, and long-term effects. The short-term deflections during construction and the long-term deflections after construction of both of normal and void slabs are compared and the effects of void slab on the reduction of slab deflections are analyzed.

• Journal of Korean Society of Steel Construction
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• v.22 no.4
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• pp.345-354
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• 2010

This paper presents an experimental investigation of the structural performance of a large-span girder bridge with an under-tension system. Typical long-span structures with beam and girder members have greater structural member depths and sizes to carry the moment and deflection. An under-tension system can be an effective structural system, as it allows the cables to resist some portions of the vertical loadings and deflections. To evaluate the serviceability and ultimate strength of the under-tension system, two $10m{\times}2.4m$ experimental under-tension systems were built and tested. One was developed with an H-beam section, and the other was made with a PF500 section that had the advantages of fast construction and lower construction cost. In the test, the maximum deflections at the mid-point of both beams were effectively reduced using under-tension systems. Also, the increased tension forces in the cable reduced the deflections. The PF500 members, which had a new shape and were developed using the module systems, performed better than the typical H-beam sections in terms of the deflections and ultimate strength.

• Steel and Composite Structures
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• v.18 no.6
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• pp.1569-1582
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• 2015

This study explores the lateral deflections of diagonal braces in concentrically-braced earthquake-resisting frames. The performance of this widely-used system is often compromised by the flexural buckling of slender braces in compression. In addition to reducing the compressive resistance, buckling may also cause these members to undergo sizeable lateral deflections which could damage surrounding structural components. Different approaches have been used in the past to predict the mid-length lateral deflections of cyclically loaded steel braces based on their theoretical deformed geometry or by using experimental data. Expressions have been proposed relating the mid-length lateral deflection to the axial displacement ductility of the member. Recent experiments were conducted on hollow and concrete-filled circular hollow section (CHS) braces of different lengths under cyclic loading. Very slender, concrete-filled tubular braces exhibited a highly ductile response, undergoing large axial displacements prior to failure. The presence of concrete infill did not influence the magnitude of lateral deflection in relation to the axial displacement, but did increase the number of cycles endured and the maximum axial displacement achieved. The corresponding lateral deflections exceeded the deflections observed in the majority of the previous experiments that were considered. Consequently, predictive expressions from previous research did not accurately predict the mid-height lateral deflections of these CHS members. Mid-length lateral deflections were found to be influenced by the member non-dimensional slenderness (${\bar{\lambda}}$) and hence a new expression was proposed for the lateral deflection in terms of member slenderness and axial displacement ductility.