• Steel and Composite Structures
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• v.39 no.5
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• pp.565-581
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• 2021

In this paper the buckling analysis of the nanoplate made of arbitrary bi-directional functionally graded (BDFG) materials with small scale effects are investigated. To study the small-scale effects on buckling load, the Eringen's nonlocal theory is applied. Employing the principle of minimum potential energy, the governing equations are obtained. Generalize differential quadrature method (GDQM) is used to solve the governing equations for various boundary conditions to obtain the buckling load of BDFG nanoplates. These models can degenerate into the classical models if the material length scale parameter is taken to be zero. Comparison between the results of GDQ method and other papers for buckling analysis of a simply supported rectangular nano FGM plate reveals the accuracy of GDQ method. At the end some numerical results are presented to study the effects of material length scale parameter, plate thickness, aspect ratio, Poisson's ratio boundary condition and side to thickness ratio on size dependent Frequency.

• Journal of the Society of Naval Architects of Korea
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• v.36 no.2
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• pp.94-104
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• 1999

Plate buckling is very important design criteria when the ship is composed of high tensile steel plates. In general, the plate element contributes to inplane stiffness against the action of inplane load. If the inplane stiffness of the plating decreases due to buckling including the secondary buckling, the flexural rigidity of the cross section of a ship's hull also decreases. In these cases, the precise estimation of plate's behaviour after buckling is necessary, and geometric nonlinear behaviour of isolated plates is required for structural system analysis. In this connection, the author investigated the geometric nonlinear behaviour of simply supported rectangular plates under uniaxial compression in the longitudinal direction in which the principle of minimum potential energy method is employed. Based on the energy method, elastic large deflection analysis of isolated palate is performed and simple expression are derived to discuss the bifurcation paint type buckling and limit point type buckling.

• Structural Engineering and Mechanics
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• v.82 no.1
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• pp.41-53
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• 2022

We developed an accurate and simple vibration model to calculate the natural frequencies and their corresponding vibration modes for multi-span beam bridges with non-uniform cross-sections. A closed set of characteristic functions of a single-span beam was used to construct the vibration modes of the multi-span bridges, which were considered single-span beams with multiple constraints. To simplify the boundary conditions, the restraints were converted into spring constraints. Then the functional of the total energy has the same form as the penalty method. Compared to the conventional penalty method, the penalty coefficients in the proposed approach can be calculated directly, which can avoid the iteration process and convergence problem. The natural frequencies and corresponding vibration modes were obtained via the minimum total potential energy principle. By using the symmetry of the eigenfunctions or structure, the matrix size can be further reduced, which increases the computational efficiency of the proposed model. The accuracy and efficiency of the proposed approach were validated by the finite element method.

• Structural Engineering and Mechanics
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• v.30 no.3
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• pp.263-278
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• 2008

Structural pipe-in-pipe cross-sections have significant potential for application in offshore oil and gas production systems because of their property that combines insulation performance with structural strength in an integrated way. Such cross-sections comprise inner and outer thin walled pipes with the annulus between them fully filled by a selectable thick filler material to impart an appropriate combination of properties. Structural pipe-in-pipe cross-sections can exhibit several different collapse mechanisms and the basis of the preferential occurrence of one over others is of interest. This paper presents an elastic analyses of a structural pipe-in-pipe cross-section when subjected to external hydrostatic pressure. It formulates and solves the static and elastic buckling problem using the variational principle of minimum potential energy. The paper also investigates a simplified formulation of the problem where the outer pipe and its contact with the filler material is considered as a 'pipe on an elastic foundation'. Results are presented to show the variation of elastic buckling pressure with the relative elastic modulus of the filler and pipe materials, the filler thickness and the thicknesses of the inner and outer pipes. The range of applicability of the simplified 'pipe on an elastic foundation' analysis is also presented. A brief review of the types of materials that could be used as the filler is combined with the results of the analysis to draw conclusions about elastic buckling behaviour of structural pipe-in-pipe cross-sections.

• Journal of Ocean Engineering and Technology
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• v.33 no.6
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• pp.535-546
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• 2019

The paper presents a closed-form analytical solution for the ultimate strength of sandwich panels with metal faces and an elastic isotropic core during combined in-plane compression and lateral pressure under clamped boundary condition. By using the principle of minimum potential energy, the stress distribution in the faces during uni-axial edge compression and constant lateral pressure was obtained. Then, the ultimate edge compression was derived on the basis that collapse occurs when yield has spread from the mid-length of the sides of the face plates to the center of the convex face plates. The results were validated by nonlinear finite element analysis. Because the solution is analytical and closed-form, it is rapid and efficient and is well-suited for use in practical structural design methods, including repetitive use in structural optimization. The solution applies for any elastic isotropic core material, but the application that stimulated this study was an elastomer-cored steel sandwich panel that had excellent energy absorbing and protective properties against fire, collisions, ballistic projectiles, and explosions.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.13 no.3
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• pp.351-360
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• 2000

A simple numerical modelling technique is proposed for estimating the shear lag effects of framed-tube system with multiple internal tubes. The tube(s)-in-tube structure is analysed by using an analogy approach in which each tube is individually modelled by a beam that can accounts for the flexural and shear deformations, as well as the shear lag effects. The numerical analysis is based on the minimum potential energy principle in conjunction with the variational approach. The shear lag phenomenon of such structures is studied with additional bending stresses. Structural parameters governing the shear lag behaviour in tube(s)-in-tube structures are also investigated through thirty-three numerical examples.

• Steel and Composite Structures
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• v.36 no.6
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• pp.671-687
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• 2020

The aim of this research is to analyze buckling and bending behavior of a sandwich Reddy beam with porous core and composite face sheets reinforced by boron nitride nanotubes (BNNTs) and shape memory alloy (SMA) wires resting on Vlasov's foundation. To this end, first, displacement field's equations are written based on the higher-order shear deformation theory (HSDT). And also, to model the SMA wire properties, constitutive equation of Brinson is used. Then, by utilizing the principle of minimum potential energy, the governing equations are derived and also, Navier's analytical solution is applied to solve the governing equations of the sandwich beam. The effect of some important parameters such as SMA temperature, the volume fraction of SMA, the coefficient of porosity, different patterns of BNNTs and porous distributions on the behavior of buckling and bending of the sandwich beam are investigated. The obtained results show that when SMA wires are in martensite phase, the maximum deflection of the sandwich beam decreases and the critical buckling load increases significantly. Furthermore, the porosity coefficient plays an important role in the maximum deflection and the critical buckling load. It is concluded that increasing porosity coefficient, regardless of porous distribution, leads to an increase in the critical buckling load and a decrease in the maximum deflection of the sandwich beam.

• Steel and Composite Structures
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• v.13 no.1
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• pp.91-107
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• 2012

In this research, mechanical buckling of hybrid functionally graded plates is considered using a new four variable refined plate theory. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The theory presented is variationally consistent, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. The plate properties are assumed to be varied through the thickness following a simple power law distribution in terms of volume fraction of material constituents. Governing equations are derived from the principle of minimum total potential energy. The closed-form solution of a simply supported rectangular plate subjected to in-plane loading has been obtained by using the Navier method. The effectiveness of the theories is brought out through illustrative examples.

• Structural Engineering and Mechanics
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• v.57 no.4
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• pp.733-762
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• 2016

Based on a reduced displacement field, a layer-wise (LW) formulation is developed for analysis of thick shell panels which is subjected to axial tension. Employing the principle of minimum total potential energy, the local governing equations of thick panel which is subjected to axial extension are obtained. An analytical method is developed for solution of the governing equations for various edge conditions. The governing equations are solved for free and simply supported edge conditions. The interlaminar stresses in the panel are investigated by means of Hooke's law and also by means of integration of the equilibrium equations of elasticity. Dependency of the result upon the number of numerical layers in the layerwise theory (LWT) is studied. The accuracy of the numerical results is validated by comparison with the results of the finite element method and with other available results in the open literature and good agreement is seen between the results. Numerical results are then presented for the distribution of interlaminar normal and shear stresses within the symmetric and un-symmetric cross-ply thick panels with free and simply supported boundaries. The effects of the geometrical parameters such as radius to thickness and width to thickness ratio are investigated on the distribution of the interlaminar stresses in thick panels.

• Structural Engineering and Mechanics
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• v.44 no.1
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• pp.15-34
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• 2012

In the present paper, an improved high-order theory is used for bending analysis of soft-core sandwich plates. Third-order plate assumptions are used for face sheets and quadratic and cubic functions are assumed for transverse and in-plane displacements of the orthotropic soft core. Continuity conditions for transverse shear stresses at the interfaces as well as the conditions of zero transverse shear stresses on the upper and lower surfaces of the plate are satisfied. Also, transverse flexibility and transverse normal strain and stress of the orthotropic core are considered. The equations of motion and boundary conditions are derived by principle of minimum potential energy. Analytical solution for bending analysis of simply supported sandwich plates under various transverse loads are presented using Navier's solution. Comparison of the present results with those of the three-dimensional theory of elasticity and some plate theories in the literature confirms the accuracy of the proposed theory.