• Structural Engineering and Mechanics
• /
• v.58 no.1
• /
• pp.59-91
• /
• 2016

Laminated composite shells are commonly used in various engineering applications including aerospace and marine structures. In this paper, using semi-analytical finite strip method, the buckling behavior of laminated composite deep as well as thick shells of revolution under follower forces which remain normal to the shell is investigated. The stiffness caused by pressure is calculated for the follower forces subjected to external fibers in thick shells. The shell is divided into several closed strips with alignment of their nodal lines in the circumferential direction. The governing equations are derived based on first-order shear deformation theory which accounts for through thickness-shear flexibility. Displacements and rotations in the middle surface of shell are approximated by combining polynomial functions in the meridional direction as well as truncated Fourier series with an appropriate number of harmonic terms in the circumferential direction. The load stiffness matrix which accounts for variation of loads direction will be derived for each strip of the shell. Assembling of these matrices results in global load stiffness matrix which may be un-symmetric. Upon forming linear elastic stiffness matrix called constitutive stiffness matrix, geometric stiffness matrix and load stiffness matrix, the required elements for the second step analysis which is an eigenvalue problem are provided. In this study, different parameter effects are investigated including shell geometry, material properties, and different boundary conditions. Afterwards, the outcomes are compared with other researches. By considering the results of this article, it can be concluded that the deformation-dependent pressure assumption can entail to decrease the calculated buckling load in shells. This characteristic is studied for different examples.

• Computational Structural Engineering
• /
• v.7 no.1
• /
• pp.69-81
• /
• 1994

This paper summarizes a dynamic analysis of the shallow circular arches under dynamic loading, considering the geometric nonlinearity. The major emphasis is placed on the development of computer program, which is utilized for the analysis of the nonlinear dynamic behavior and for the evaluation of the critical buckling loads of the shallow circular arches. Geometric nonlinearity is modeled using Lagrangian description of the motion and a finite element analysis procedure is used to solve the dynamic equation of motion. A circular arch subject to normal step load is analyzed and the results are compared with those from other researches to verify the developed program. The critical buckling loads of arches are estimated using the non-dimensional time, load and shape parameters and the results are also compared with those from the linear analysis. It is found that geometric nonlinearity plays and important role in the analysis of shallow arches and the probability of buckling failure is getting higher as arches become shallower.

• Computational Structural Engineering
• /
• v.10 no.4
• /
• pp.205-216
• /
• 1997

In order to trace the lateral post-buckling behaviors of thin-wafled space frames, a geometrically nonlinear finite element formulation is presented by applying incremental equilibrium equations based on the updated Lagrangian formulation and introducing Vlasov's assumption. The improved displacement field for symmetric thin-walled cross sections is introduced based on inclusion of second order terms of finite rotations, and the potential energy corresponding to the semitangential rotations and moments is consistently derived. For finite element analysis, tangent stiffness matrices of the thinwalled space frame element with 7 degrees of freedom including the restrained warping for each node are derived by using the Hermition polynomials as shape functions. A co-rotational formulation in order to evaluate the unbalanced loads is presented by separating the rigid body rotations and pure deformations from incremental displacements and evaluating the updated direction cosines of the frame element due to rigid body rotations and incremental member forces from pure deformations. Finite element solutions for the spatial buckling and post-buckling analysis of thin-walled space frames are presented and compared with available solutions and other researcher's results.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.37 no.1
• /
• pp.83-88
• /
• 2013

Progressive collapse is a chain reaction of failures propagating throughout a portion of a structure that is disproportionate to the original local failure. When column members are subjected to unexpected load (compression load), they will buckle if the applied load is greater than the critical load that induces buckling. The post-buckling strength of the columns will decrease rapidly, but if there is enough residual strength, the members will absorb the potential energy generated by the impact load to prevent progressive collapse. Thus, it is necessary to identify the relationship of the load-deformation of a column member in the progressive collapse of a structure up to final collapse. In this study, we carried out nonlinear FEM analysis and based on deflection theory, we investigated the load-deformation relationship of H-section steel columns when both ends were fixed.

• Computers and Concrete
• /
• v.25 no.4
• /
• pp.311-325
• /
• 2020

In this research work, the hygrothermal and mechanical buckling responses of simply supported FG sandwich plate seated on Winkler-Pasternak elastic foundation are investigated using a novel shear deformation theory. The current model take into consideration the shear deformation effects and ensures the zero shear stresses on the free surfaces of the FG-sandwich plate without requiring the correction factors "Ks". The material properties of the faces sheets of the FG-sandwich plate are assumed varies as power law function "P-FGM" and the core is isotropic (purely ceramic). From the virtual work principle, the stability equations are deduced and resolved via Navier model. The hygrothermal effects are considered varies as a nonlinear, linear and uniform distribution across the thickness of the FG-sandwich plate. To check and confirm the accuracy of the current model, a several comparison has been made with other models found in the literature. The effects the temperature, moisture concentration, parameters of elastic foundation, side-to-thickness ratio, aspect ratio and the inhomogeneity parameter on the critical buckling of FG sandwich plates are also investigated.

• Structural Engineering and Mechanics
• /
• v.73 no.5
• /
• pp.487-500
• /
• 2020

Stiffeners can be utilised to enhance the strength of thin-walled wind turbine towers in engineering practise, thus, structural performance of wind turbine towers by means of different stiffening schemes should be compared to explore the optimal structural enhancement method. In this paper two alternative stiffening methods, employing horizontal or vertical stiffeners, for steel tubular wind turbine towers have been studied. In particular, two groups of three wind turbine towers of 50m, 150m and 250m in height, stiffened by horizontal rings and vertical strips respectively, were analysed by using FEM software of ABAQUS. For each height level tower, the mass of the stiffening rings is equal to that of vertical stiffeners each other. The maximum von Mises stresses and horizontal sways of these towers with vertical stiffeners is compared with the corresponding ring-stiffened towers. A linear buckling analysis is conducted to study the buckling modes and critical buckling loads of the three height levels of tower. The buckling modes and eigenvalues of the 50m, 150m and 250m vertically stiffened towers were also compared with those of the horizontally stiffened towers. The numbers and central angles of the vertical stiffeners are considered as design variables to study the effect of vertical stiffeners on the structural performance of wind turbine towers. Following an extensive parametric study, these strengthening techniques were compared with each other and it is obtained that the use of vertical stiffeners is a more efficient approach to enhance the stability and strength of intermediate and high towers than the use of horizontal rings.

• Steel and Composite Structures
• /
• v.18 no.2
• /
• pp.443-465
• /
• 2015

In this paper, an efficient and simple trigonometric shear deformation theory is presented for thermal buckling analysis of functionally graded plates. It is assumed that the plate is in contact with elastic foundation during deformation. The theory accounts for sinusoidal distribution of transverse shear stress, and satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate without using shear correction factor. Unlike the conventional trigonometric shear deformation theory, the proposed sinusoidal shear deformation theory contains only four unknowns. It is assumed that the mechanical and thermal non-homogeneous properties of functionally graded plate vary smoothly by distribution of power law across the plate thickness. Using the non-linear strain-displacement relations, the equilibrium and stability equations of plates made of functionally graded materials are derived. The boundary conditions for the plate are assumed to be simply supported on all edges. The elastic foundation is modelled by two-parameters Pasternak model, which is obtained by adding a shear layer to the Winkler model. The effects of thermal loading types and variations of power of functionally graded material, aspect ratio, and thickness ratio on the critical buckling temperature of functionally graded plates are investigated and discussed.

• Structural Engineering and Mechanics
• /
• v.86 no.4
• /
• pp.443-459
• /
• 2023

This study investigates the theoretical thermal buckling analyses of thick porous rectangular functionally graded (FG) plates with different geometrical boundary conditions resting on a Winkler-Pasternak elastic foundation using a new higher-order shear deformation theory (HSDT). This new theory has only four unknowns and involves indeterminate integral variables in which no shear correction factor is required. The variation of material properties across the plate's thickness is considered continuous and varied following a simple power law as a function of volume fractions of the constituents. The effect of porosity with two different types of distribution is also included. The current formulation considers the Von Karman nonlinearity, and the stability equations are developed using the virtual works principle. The thermal gradients are involved and assumed to change across the FG plate's thickness according to nonlinear, linear, and uniform distributions. The accuracy of the newly proposed theory has been validated by comparing the present results with the results obtained from the previously published theories. The effects of porosity, boundary conditions, foundation parameters, power index, plate aspect ratio, and side-to-thickness ratio on the critical buckling temperature are studied and discussed in detail.

• Proceedings of the Korean Society For Composite Materials Conference
• /
• 2002.10a
• /
• pp.88-91
• /
• 2002

The two dimensional size effect of specimen gauge section (length x width) was investigated on the compressive behavior of a T300/924 [45/-45/0/90]3s, carbon fiber-epoxy laminate. A modified ICSTM compression test fixture was used together with an anti-buckling device to test 3mm thick specimens with a 30$\times$30, 50$\times$50, 70$\times$70, and 90mm$\times$90mm gauge length by width section. In all cases failure was sudden and occurred mainly within the gauge length. Post failure examination suggests that $0^{\circ}$ fiber microbuckling is the critical damage mechanism that causes final failure. This is the matrix dominated failure mode and its triggering depends very much on initial fiber waviness. It is suggested that manufacturing process and quality may play a significant role in determining the compressive strength. When the anti-buckling device was used on specimens, it was showed that the compressive strength with the device was slightly greater than that without the device due to surface friction between the specimen and the device by pretoque in bolts of the device. In the analysis result on influence of the anti-buckling device using the finite element method, it was found that the compressive strength with the anti-buckling device by loaded bolts was about 7% higher than actual compressive strength. Additionally, compressive tests on specimen with an open hole were performed. The local stress concentration arising from the hole dominates the strength of the laminate rather than the stresses in the bulk of the material. It is observed that the remote failure stress decreases with increasing hole size and specimen width but is generally well above the value one might predict from the elastic stress concentration factor. This suggests that the material is not ideally brittle and some stress relief occurs around the hole. X-ray radiography reveals that damage in the form of fiber microbuckling and delamination initiates at the edge of the hole at approximately 80% of the failure load and extends stably under increasing load before becoming unstable at a critical length of 2-3mm (depends on specimen geometry). This damage growth and failure are analysed by a linear cohesive zone model. Using the independently measured laminate parameters of unnotched compressive strength and in-plane fracture toughness the model predicts successfully the notched strength as a function of hole size and width.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.30 no.6A
• /
• pp.503-512
• /
• 2010

In AASHTO LRFD (2007), a compact section is defined as a section in which no premature failure caused by local buckling of web and flange plate or later buckling occurs before the section reaches the plastic moment, Mp. The current AASHTO LRFD (2007) provides the compact section requirement by limiting the web slenderness only for webs without longitudinal stiffeners. The role of longitudinal stiffener is to increase the web buckling strength caused flexure. Although a web does not satisfy the compactness requirement without longitudinal stiffeners, the web buckling can be prevented by use of valid longitudinal stiffeners. Therefore, the web may be able to reach the plastic moment. However, the reason why a longitudinal stiffener may not be used to satisfy compactness requirement is not cleary explained in AASHTO LRFD (2007). In this study, the buckling and ultimate strength behaviors of stiffened webs subjected to bending are investigated through the linear buckling and nonlinear finite element analysis. It is found that steel plate girders having webs that do not satisfy the compactness requirement are able to reach the plastic moment if the longitudinal stiffeners have sufficient rigidities and are properly located. From a nonlinear regression analysis of the results, a new compactness requirement is suggested for webs stiffened with one longitudinal stiffener.