• Steel and Composite Structures
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• v.27 no.1
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• pp.13-25
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• 2018

The main objective of this study is to develop a dual approach for geometrically nonlinear finite element analysis of plane truss structures. The geometric nonlinearity is considered using the Total Lagrangian formulation. The nonlinear solution is obtained by introducing and minimizing an objective function subjected to displacement-type constraints. The proposed method can fully trace the whole equilibrium path of geometrically nonlinear plane truss structures not only before the limit point but also after it. No stiffness matrix is used in the main approach and the solution is acquired only based on the direct classical stress-strain formulations. As a result, produced errors caused by linearization and approximation of the main equilibrium equation will be eliminated. The suggested algorithm can predict both pre- and post-buckling behavior of the steel plane truss structures as well as any arbitrary point of equilibrium path. In addition, an equilibrium path with multiple limit points and snap-back phenomenon can be followed in this approach. To demonstrate the accuracy, efficiency and robustness of the proposed procedure, numerical results of the suggested approach are compared with theoretical solution, modified arc-length method, and those of reported in the literature.

• Composites Research
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• v.12 no.6
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• pp.65-73
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• 1999

Crippling stress and failure behavior of Z-section graphite/epoxy composite laminated stringers are investigated by the nonlinear finite element method. Stringers are idealized using 9-node laminated shell element. The complete unloading model is introduced into the finite element method for the progressive failure analysis. A modified Riks method is used to trace the post-failure equilibrium path after local buckling. Finite element results are validated with previous experimental results. The results show that the most important parameter affecting the crippling stress of Z-section stringers is the flange width. In terms of stacking sequence. the highest cripping stress is found at the stringer with $[{\pm}45/0/90]s$ lamination.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.10 no.2
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• pp.11-22
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• 1990

An automatic incremental algorithm for geometric non-linear finite element analysis of the structures subjected to the conservative and non-conservative forces is presented. By making efficient combination of the load incremental method and the displacement incremental method, this scheme can trace various post-buckling equilibrium path such as snap-through and turning-back. Several numerical examples to demonstrate the feasibility of the present algorithm, over ranges of deformation that are well beyond those likely to occur in practical structures, are given and discussed.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.40 no.5
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• pp.423-430
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• 2012

In this paper, the effect of wrinkling on the cut propagation direction of thin membrane was studied using geometrically nonlinear shell element post-buckling analysis. In the analysis, rectangular tensile membrane configuration with a slanted center cut was considered. The cut propagation direction was predicted by maximum energy release rate method, $K_{II}$-zero method, and maximum tangential stress method. The cut propagation angle and the $J$-integral values were calculated for the wrinkled and unwrinkled cases and the results were compared. Various initial cut orientation angles were considered and the effect on the propagation direction was studied. The cut propagation paths were also predicted by virtual cut extension approach.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.28 no.2A
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• pp.233-242
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• 2008

This study presents a non-prismatic beam element for modeling the elastic and inelastic behavior of steel beams, which have the post-Northridge(cover plate) connections in steel moment frames that are subjected to earthquake ground motions. The elastic stiffness matrix for non-prismatric members with increased beam section (IBS) connection is in the closed-form. The plasticity model is of a discrete type and is composed of a series of nonlinear hinges connected by rigid links. The hardening rules can model the inelastic behavior for monotonic and random cyclic loading, and the effects of local buckling. Moreover the determination of yield surfaces, stiffness parameters, and hardening (or softening) rule parameters for IBS beam element were described. Analytical results of the IBS beam element show good correlation with test data and FEM results.

• Journal of Korean Society of Steel Construction
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• v.23 no.4
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• pp.429-438
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• 2011

In this study, the explicit numerical algorithm was proposed to simulate the stress erection process and ultimate-load analysis of the strarch (stressed arch) system. The strarch system is a unique and innovative structural system and member prestress comprising prefabricated plane truss frames erected through a post-tensioning stress erection procedure. The flexible bottom chord, which has sleeve and gap details, is closed by the reaction force of the prestressing tendon. The prestress imposed on the tendon will enable the strarch system to be erected. This post-tensioning process is called "stress erection process." During this process, plastic rigid-body rotation occurs to the flexible top chord due to the excessive amount of plastic strain, and the structural characteristic is unstable. In this study, the dynamic relaxation method (DRM) was adopted to calculate the nonlinear equilibrium equation of the system, and a displacement-based finite-element-formulated filament beam element was used to simulate the nonlinear behavior of the top chord sections of the strarch system. The section of the filament beam element was composed by the amount of filaments, which can be modeled by various material models. The Ramberg-Osgood and bilinear kinematic elastic plastic material models were formulated for the nonlinear material behaviors of the filaments. The numerical results that were obtained in the present study were compared with the experiment results of the stress erection and with the results of the ultimate-load analysis of the strarch unit frame. The results of the present studies are in good agreement with the previous experiment results, and the explicit DRM enabled the analysis of the post-buckling behaviors of the strarch unit frame.

• Journal of Korean Society of Steel Construction
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• v.21 no.6
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• pp.597-608
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• 2009

In this paper, large-deformation elasto-plastic analysis of space frames that considersjoint connection properties is presented. This method is based on the large-deformation formula with finite rotation, which was developed initially for elastic systems, and is extended herein to include the elasto-plastic effect and the member joint connection properties of semi-rigid what?. The analytical method was derived from the Eulerian concept, which takes into consideration the effects of large joint translations and rotations. The localmember force-deformation relationships were obtained from the beam-column approach, and the change caused by the axial strain in the member chord lengths and flexural bowing were taken into account. The effect of the axial force of the member on bending and torsional stiffness, and on the plastic moment capacity, is included in the analysis. The material is assumed to be ideally elasto-plastic, and yielding is considered concentrated at the member ends in the form of plastic hinges. The semi-rigid properties of the member joint connection are considered based on the power or linear model. The arc length method is usedto trace the post-buckling range of the elastic and elasto-plastic problems with the semi-rigid connection. A sample non-linear buckling analysis was carried out with the proposed space frame formulations to demonstrate the potential of the developed method in terms of its accuracy and efficiency.

• Structural Engineering and Mechanics
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• v.66 no.5
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• pp.557-568
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• 2018

An investigation is made in the present work on the post-buckling and geometrically nonlinear behaviors of moderately thick perfect and imperfect rectangular plates made-up of functionally graded materials. Spectral collocation approach based on Legendre basis functions is developed to analyze the functionally graded plates while they are subjected to end-shortening strain. The material properties in this study are varied through the thickness according to the simple power law distribution. The fundamental equations for moderately thick rectangular plates are derived using first order shear deformation plate theory and taking into account both geometric nonlinearity and initial geometric imperfections. In the current study, the domain of interest is discretized with Legendre-Gauss-Lobatto nodes. The equilibrium equations will be obtained by discretizing the Von-Karman's equilibrium equations and also boundary conditions with finite Legendre basis functions that are substituted into the displacement fields. Due to effect of geometric nonlinearity, the final set of equilibrium equations is nonlinear and therefore the quadratic extrapolation technique is used to solve them. Since the number of equations in this approach will always be more than the number of unknown coefficients, the least squares technique will be used. Finally, the effects of boundary conditions, initial geometric imperfection and material properties are investigated and discussed to demonstrate the validity and capability of proposed method.

• Smart Structures and Systems
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• v.18 no.2
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• pp.293-315
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• 2016

Seismic isolation is often used in protecting mission-critical structures including hospitals, data centers, telecommunication buildings, etc. Such structures typically house vibration-sensitive equipment which has to provide continued service but may fail in case sustained accelerations during earthquakes exceed threshold limit values. Thus, peak floor acceleration is one of the two main parameters that control the design of such structures while the other one is peak base displacement since the overall safety of the structure depends on the safety of the isolation system. And in case peak base displacement exceeds the design base displacement during an earthquake, rupture and/or buckling of isolators as well as bumping against stops around the seismic gap may occur. Therefore, obtaining accurate peak floor accelerations and peak base displacement is vital. However, although nominal design values for isolation system and superstructure parameters are calculated in order to meet target peak design base displacement and peak floor accelerations, their actual values may potentially deviate from these nominal design values. In this study, the sensitivity of the seismic performance of structures equipped with linear and nonlinear seismic isolation systems to the aforementioned potential deviations is assessed in the context of a benchmark shear building under different earthquake records with near-fault and far-fault characteristics. The results put forth the degree of sensitivity of peak top floor acceleration and peak base displacement to superstructure parameters including mass, stiffness, and damping and isolation system parameters including stiffness, damping, yield strength, yield displacement, and post-yield to pre-yield stiffness ratio.

• Journal of Korean Society of Steel Construction
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• v.11 no.1 s.38
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• pp.69-78
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• 1999

When the lateral forces are applied to a frame, columns in the frame are usually accompanied with sidesway. If this sidesway is large, the frame is subjected to buckling and an early yielding of members which reduces the overall frame stiffness. In this study, numerical analysis of frames were conducted to evaluate the ultimate lateral strength of steel moment resisting frames permitted to sidesway under axial and lateral forces, and develope the procedure for determining the limits of column slenderness ratios. In the numerical analysis, the effects of the relative stiffness ratio between beam and column, deterioration of overall frame stiffness, slenderness ratio and loading conditions were considered. The elasto-plastic analysis method in which the $P-{\Delta}$effect is implemented, presented by the author previously, was adopted in the analysis. Incremental lateral forces were applied to the frame under constant axial loads and the generalized inverse is employed for the post-ultimate behavior.