• 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.

• 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.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.42 no.11
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• pp.919-926
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• 2014

In this paper, the effect of material properties on fracture behavior was studied using cohesive zone model and extended finite element method. The rectangular tensile specimen with a central inclined initial crack was modeled by plane stress elements. In the CZM modeling, cohesive elements were inserted between every bulk elements in the predicted crack propagation region before analysis, while in the XFEM the enrichment to the elements was added as needed during analysis. The crack propagation behavior was examined for brittle and ductile materials. For thin specimen configuration, wrinkle deformation was accounted for by geometrically nonlinear post-buckling analysis and the effect of wrinkling on the crack propagation was investigated.

• 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.

• Composites Research
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• v.12 no.6
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• pp.43-52
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• 1999

This paper explains the development of a concurrent engineering system for the rlesign of composite structures. The concurrent engineering system is developed to meet the demand for the better quality products with lower production cost and time. In this study, to compose the architecture of concurrent engineering system, the commercial and noncommercial programs related to design and analysis of composite structures are surveyed and classified. The concurrent engineering system is including various design modules such as design/analysis of composite structures using CLPT and FEM, buckling and post bucking analysis, thermo-elastic analysis of carbon-carbon composite, and optimum design using expert system and genetic algorithm. For the integration and management of softwares, the concurrent engineering system is realized by Microsoft visual $C++{^\circledR}$ that provide multi-tasking and graphic user interface environment.

• 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.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1999.03b
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• pp.14-17
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• 1999

The wrinkling behavior of a thin sheet with perfect geometry is a kind of compressive instability. The compressive instability is influenced by many factors such as stress state mechanical properties of the sheet material geometry of the body contact conditions and plastic anisotropy. The analysis of compressive instability in plastically deforming body is difficult considering all the factors because the effects of the factors are very complex and the instability behavior may show wide variation for small deviation of the factors. In this study the bifurcation theory is introduced for the finite element analysis of puckering initiation and growth of a thin sheet with perfect geometry. All the above mentioned analysis and the post-bifurcation behavior is analyzed by introducing the branching scheme proposed by Riks. The finite element formulation is based on the incremental deformation theory and elastic-plastic material modeling. in order to investigate the effect of plastic anisotropy on the compressive instability a square plate that is subjected to compression in one direction and tension in the other direction is analyzed by the above-mentionedfinite element analysis. The critical stress ratios above which the buckling does not take place are found for various plastic anisotropic modeling method and discussed. Finally the effect of plastic anisotropy on the puckering behavior in the spherical cup deep drawing process is investigated.

• Steel and Composite Structures
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• v.28 no.3
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• pp.267-278
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• 2018

Structures may need retrofitting as a result of design and calculation errors, lack of proper implementation, post-construction change in use, damages due to accidental loads, corrosion and changes introduced in new editions of construction codes. Retrofitting helps to compensate weakness and increase the service life. Fiber Reinforced Polymer (FRP) is a modern material for retrofitting steel elements. This study aims to investigate the effect of deficiency location on the axial behavior of compressive elements of Circular Hollow Section (CHS) steel short columns. The deficiencies located vertically or horizontally at the middle or bottom of the element. A total of 43 control column and those with deficiencies were investigated in the ABAQUS software. Only 9 of them tested in the laboratory. The results indicated that the deficiencies had a significant effect on the increase in axial deformation, rupture in deficiency zone (local buckling), and decrease in ductility and bearing capacity. The damages of steel columns were responsible for resistance and stiffness drop at deficiency zone. Horizontal deficiency at the middle and vertical deficiency at the bottom of the steel columns were found to be the most critical. Using Carbon Fiber Reinforced Polymer (CFRP) as the most effective material in retrofitting the damaged columns, significantly helped the increase in resistance and rupture control around the deficiency zone.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.39 no.11
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• pp.1005-1012
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• 2011

In this paper, the effect of wrinkling on the failure behavior of thin membrane was studied using geometrically nonlinear shell element post-buckling analysis with global-local analysis strategy. In the analysis, double-edge notched and single-edge notched tensile specimen configurations were considered. The analyses were performed for both cases with allowing and suppressing the wrinkling deformation. The results were investigated focusing on the effect of wrinkle development on the variation of J-integral values at the cut tip. The effect of cut lengths and the specimen lengths were also systematically studied.

• 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.