• Structural Engineering and Mechanics
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• v.35 no.6
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• pp.677-697
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• 2010

This paper focuses on geometrically non-linear static analysis of a simply supported beam made of hyperelastic material subjected to a non-follower transversal uniformly distributed load. As it is known, the line of action of follower forces is affected by the deformation of the elastic system on which they act and therefore such forces are non-conservative. The material of the beam is assumed as isotropic and hyperelastic. Two types of simply supported beams are considered which have the following boundary conditions: 1) There is a pin at left end and a roller at right end of the beam (pinned-rolled beam). 2) Both ends of the beam are supported by pins (pinned-pinned beam). In this study, finite element model of the beam is constructed by using total Lagrangian finite element model of two dimensional continuum for a twelve-node quadratic element. The considered highly non-linear problem is solved by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. In order to use the solution procedures of Newton-Raphson type, there is need to linearized equilibrium equations, which can be achieved through the linearization of the principle of virtual work in its continuum form. In the study, the effect of the large deflections and rotations on the displacements and the normal stress and the shear stress distributions through the thickness of the beam is investigated in detail. It is known that in the failure analysis, the most important quantities are the principal normal stresses and the maximum shear stress. Therefore these stresses are investigated in detail. The convergence studies are performed for various numbers of finite elements. The effects of the geometric non-linearity and pinned-pinned and pinned-rolled support conditions on the displacements and on the stresses are investigated. By using a twelve-node quadratic element, the free boundary conditions are satisfied and very good stress diagrams are obtained. Also, some of the results of the total Lagrangian finite element model of two dimensional continuum for a twelve-node quadratic element are compared with the results of SAP2000 packet program. Numerical results show that geometrical nonlinearity plays very important role in the static responses of the beam.

• Computational Structural Engineering
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• v.11 no.1
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• pp.191-204
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• 1998

The general formulation for free vibration and stability analysis of unsymmetric thin-wared space frames is presented in case where the shear deformation effects are neglected. The kinetic and total potential energies are derived by applying the extended virtual work principle, introducing displacement parameters defined at the arbitrarily chosen axis and including warping deformation and second order terms of finite semitangential rotations. In formulating the finite element procedure, cubic Hermitian polynomials are utilized as shape functions of the two node space frame element. Mass, elastic stiffness, and geometric stiffness matrices for the unsymmetric thin-walled section are evaluated, and load-correction stiffness matrices for off-axis distributed loadings are considered. In order to illustrate the accuracy and practical usefulness of this formulation, finite element solutions for the free vibration and stability problems of thin-walled beam-columns and space frames are presented and compared with available solutions.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.17 no.2
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• pp.151-160
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• 2004

In the present study, Loop scheme is applied to generate smooth surfaces. To be consistent with the limit points of target surface, the initial sampling points are properly rearranged. The pointwise errors of curvature and position in the sequence of subdivision process are evaluated in the Loop subdivision scheme. A first-order shear deformable Loop subdivision triangular element which can handle transverse shear deformation of moderately thick shell are developed. The developed element is more general than the previous one based on classical shell theory, since the new one includes the effect of transverse shear deformation and has standard six degrees of freedom per node. The quartic box spline function is used as interpolation basis function. Numerical examples for the benchmark static shell problems are analyzed to assess the performance of the developed subdivision shell element and locking trouble.

• Coupled systems mechanics
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• v.9 no.3
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• pp.237-264
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• 2020

This article investigates the static behaviour of functionally graded (FG) plates sometimes declared as advanced composite plates by using a simple and accurate quasi-3D and 2D hyperbolic higher-order shear deformation theories. The properties of functionally graded materials (FGMs) are assumed to vary continuously through the thickness direction according to exponential law distribution (E-FGM). The kinematics of the present theories is modeled with an undetermined integral component and satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate; therefore, it does not require the shear correction factor. The fundamental governing differential equations and boundary conditions of exponentially graded plates are derived by employing the static version of principle of virtual work. Analytical solutions for bending of EG plates subjected to sinusoidal distributed load are obtained for simply supported boundary conditions using Navier'is solution procedure developed in the double Fourier trigonometric series. The results for the displacements and stresses of geometrically different EG plates are presented and compared with 3D exact solution and with other quasi-3D and 2D higher-order shear deformation theories to verify the accuracy of the present theory.

• Bulletin of the Society of Naval Architects of Korea
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• v.22 no.1
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• pp.21-30
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• 1985

This paper deals whth the buckling as well as postbuckling analysis of axisymmertric shells taking the initial deflection effects into account. Incremental equilibrium equations, based on the principle of virtual work, were derived by the finite element method, the successive step-by-step Newton-Raphson iterative technique was adopted. To define the transition pattern of postbuckling behavior from the prebuckling state more accurately, a simple solution method was developed, i.e. the critical load was calculated by the load extrapolation method with the determinant of tangent stiffness matrix and the equilibrium configuration in the immediate postbuckling stage was obtained by perturbation scheme and eigenvalue analysis. Degenerated isoparametric shell elements were used to analyse the axisymmetric shell of revolution. And by the method developed in this paper, the computer program applicable to the nonlinear analysis of both thin and moderately thick shells was constructed. To verify the capabilities and accuracies of the present solution method, the computed results were compared with the results of analytical solutions. These results coincided fairly well in both the small deflection and large deflection ranges. Various numerical analyses were done to show the effect of initial deflection and shape of shells on buckling load and postbuckling behavior. Futhermore, corrected directions of applied loads at every increment steps were used to determine the actual effects of large deflection in non-conservative load systems such as hydrostatic pressure load. The following conclusions can be obtained. (1) The method described in this paper was found to be both economic and effective in calculating buckling load and postbuckling behavior of shell structure. (2) Buckling and postbuckling behavior of spherical caps is critically dependent upon their geometric configuration, i.e. the shape of spherical cap and quantities of the initial deflection. (3) In the analysis of large deflection problems of shells by the incremental method, corrections of the applied load directions are needed at every incremental step to compensate the follower force effects.

• Journal of the Korean Geotechnical Society
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• v.20 no.1
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• pp.121-129
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• 2004

In this study, a slope stability chart for assessing stability of homogeneous simple soil slopes is proposed. Most existing slope stability charts are based on limit equilibrium method, which is not rigorous in mechanical standpoint. Meanwhile, limit analysis based on the principle of virtual work and the bound theorems of plasticity is suitable for evaluating the stability of geotechnical structures such as slope due to its simplicity in computation and mechanical rigor. Numerical limit analysis taking advantage of finite elements and linear programming can consider various slope conditions and, in addition, find the optimum stability solution with effeciency. In this study, a numerical limit analysis program in terms of effective stress is developed and a mechanically rigorous slope stability chart is proposed by performing stability analyses for various slope conditions. Pore pressure ratio, commonly used in stability charts, is applied to consider the effects of pore pressure for effective stress analysis. As a result of comparison between proposed stability chart and Spencer's stability chart, it was found that Spencer's chart solutions are biased to lower bound which means conservative in design.

• Steel and Composite Structures
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• v.25 no.1
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• pp.105-116
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• 2017

This paper presents the dynamic stability study of laminated composite plates with different force combinations and aspect ratios. Optimum non-diverging stacking is obtained for certain loading combination and aspect ratio. In addition, the stability force is maximized for a definite operating frequency. A dynamic version of the principle of virtual work for laminated composites is used to obtain force-frequency relation. Since dynamic stiffness governs the divergence or flutter, an efficient optimization method is necessary for the response functional and the relevant constraints. In this way, a model based on the ant colony optimization (ACO) algorithm is proposed to search for the proper stacking. The ACO algorithm is used since it treats with large number of dynamic stability parameters. Governing equations are formulated using classic laminate theory (CLT) and von-Karman plate technique. Load-frequency relations are explicitly obtained for fundamental and secondary flutter modes of simply supported composite plate with arbitrary aspect ratio, stacking and boundary load, which are used in optimization process. Obtained results are compared with the finite element method results for validity and accuracy convince. Results revealed that the optimum stacking with stable dynamic response and maximum critical load is in angle-ply mode with almost near-unidirectional fiber orientations for fundamental flutter mode. In addition, short plates behave better than long plates in combined axial-shear load case regarding stable oscillation. The interaction of uniaxial and shear forces intensifies the instability in long plates than short ones which needs low-angle layup orientations to provide required dynamic stiffness. However, a combination of angle-ply and cross-ply stacking with a near-square aspect ratio is appropriate for the composite plate regarding secondary flutter mode.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.13 no.4
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• pp.142-151
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• 1999

Linear Pulse Motors (LPM) are used a field where SImOth linear motion is required, and it's position accuracy higher than that of a lead According to the advanUlge such as simplicity of rrechanical frarre, high reliability, precise open-loop operation, low inertia etc. LPM is awlied largely where it have made motor of this kind more and rmre attractive in many application areas such as factory automation and high speed positioning. This paper is researched to analyze for force characteristics of hybrid LPM with high accuracy and repeatability. Both the thrust and normal force are very sensitive to the airgap and tooth pitches of the forcer and platen. Here, the thrust shows a high content while the normal force is much higher than the thrust. For magnetic circuits of hybrid LPM is the complicated structure, the finite element rrethod (FEM) is employed with suitable rrethod for calculating the force. Therefore, both the virtual work principle and maxwell stress tensor have been used.n used.

• Transactions of the Korean Society of Mechanical Engineers
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• v.13 no.5
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• pp.820-830
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• 1989

The tire inflation and contact problem has been solved by a finite element method. The finite element formulation is derived from the equilibrium equations by the principle of virtual work in the form of an updated Lagrangian formulation for incremental analysis. Then, a contact formulation is added to the finite element formulation to calculate stress state of tire in contact with flat rigid road under the load due to the self-weight of a vehicle. In the finite element analysis, equations of effective material properties are introduced to analyze a plane strain model of the shell-like tire by considering the bending effect of reinforced steel cords. The proposed equations of effective material properties produced stress concentration around the edge of belt layers, which does not appear when other well-known equations of material properties are adopted. The result from the above algorithm demonstrates the validity of the formulation and the proposed equations for the effective elastic constants. The result fully interprets the cause of separation between belt layers by showing the stress concentration.

• Structural Engineering and Mechanics
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• v.74 no.3
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• pp.365-380
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• 2020

The focus of this paper is to develop an analytical approach based on an efficient shear deformation theory with stretching effect for bending stress analysis of cross-ply laminated composite plates subjected to transverse parabolic load and line load by using a new kinematic model, in which the axial displacements involve an undetermined integral component in order to reduce the number of unknowns and a sinusoidal function in terms of the thickness coordinate to include the effect of transverse shear deformation. The present theory contains only five unknowns and satisfies the zero shear stress conditions on the top and bottom surfaces of the plate without using any shear correction factors. The governing differential equations and its boundary conditions are derived by employing the static version of principle of virtual work. Closed-form solutions for simply supported cross-ply laminated plates are obtained applying Navier's solution technique, and the numerical case studies are compared with the theoretical results to verify the utility of the proposed model. Lastly, it can be seen that the present outlined theory is more accurate and useful than some higher-order shear deformation theories developed previously to study the static flexure of laminated composite plates.