• Steel and Composite Structures
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• v.35 no.6
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• pp.717-727
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• 2020

The homotopy perturbation method (HPM) to predict the pre- and post-buckling behaviour of simply supported steel beams with rectangular hollow section (RHS) is presented in this paper. The non-linear differential equations solved by HPM derive from a kinematics where large twist and cross-sections distortions are considered. The results (linear and non-linear paths) given by the present HPM are compared to those provided by the Newton-Raphson algorithm with arc length and by the commercial FEM code Abaqus. To investigate the effect of cross-sectional distortion of beams, some numerical examples are presented.

• Journal of Electrical Engineering and Technology
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• v.9 no.5
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• pp.1577-1581
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• 2014

This paper presents a method to minimize torque ripple of a V-type IPMSM using the PSO (Particle Swarm Optimization) method with FEM. The proposed algorithm includes one objective function and three design variables for a notch on the surface of a rotor. The simulation model of the V-type IPMSM has 3-phases, 8-poles and 48 slots with 2 notches on the one-pole rotor surface. The arc-angle, length and width of the notch are optimized to minimize the torque ripple of the motor. The cogging torque of the model is reduced by 55.6% and the torque ripple is decreased by 15.5 %. Also, the efficiency of the motor is increased by 15.5 %.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.4 no.4
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• pp.127-135
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• 1984

This paper considers the problem of optimum shaping of steel arches subjected to general loading. The weight of arches is considered as the objective function and the appropriate combinations of section forces, material volume, arc length, and closed section area of arches are considered as the stress constraints. The shape optimization problems are formulated in terms of the design variables of sectional areas of each element. First the cost sensitivity of the design is investigated. Then the investigation comprises the search for the optimum arch form as well as the optimum area distribution along the arch. Two spaces of shape optimization algorithm will be treated, the first space corresponding to the section optimization by the Modified Newton Raphson Method, and the second space to the coordinate optimization by the Powell Method. The optimization algorithm is evaluated and the optimum span-rise ratios for the given arches are evaluated.

• Smart Structures and Systems
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• v.15 no.5
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• pp.1233-1252
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• 2015

This study investigates the problem of crack detection in post-buckled beam-type structures. The beam under the axial compressive force has a crack, assumed to be open and through the width. The crack, which is modeled by a massless rotational spring, divides the beam into two segments. The crack detection is considered as an optimization problem, and the weighted sum of the squared errors between the measured and computed natural frequencies is minimized by the bees algorithm. To find the natural frequencies, the governing nonlinear equations of motion for the post-buckled state are first derived. The solution of the nonlinear differential equations of the two segments consists of static and dynamic parts. The differential quadrature method along with an arc length strategy is used to solve the static part, while the same method is utilized for the solution of the linearized dynamic part and the extraction of the natural frequencies of the cracked beam. The investigation includes several numerical as well as experimental case studies on the post-buckled simply supported and clamped-clamped beams having open cracks. The results show that several parameters such as the amount of applied compressive force and boundary conditions influences the outcome of the crack detection scheme. The identification results also show that the crack position and depth can be predicted well by the presented 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.

• Composites Research
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• v.13 no.1
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• pp.69-77
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• 2000

This paper presents a modified arc-length method for the nonlinear finite element analysis of a structure which is loaded in incremental and fixed forces, simultaneously. The main idea of the method is to separate the displacement term by the constant force from that by the incremental force. Presented method is applied to the nonlinear analysis of isotropic shell structures separately loaded by lateral pressure or compression, and shows the excellent agreement with previous results. As an illustrative example of the applicability of the present algorithm, a parametric study is performed on the nonlinear buckling analysis of composite cylindrical panels under the combined load of the incremented compression and the constant lateral pressure.

• Structural Engineering and Mechanics
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• v.85 no.2
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• pp.147-161
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• 2023

Based on the ideas of variational differential quadrature (VDQ) and finite element method (FEM), a numerical approach named as VDQFEM is applied herein to study the large deformations of plate-type structures under static loading with arbitrary shape hole made of functionally graded graphene platelet-reinforced composite (FG-GPLRC) in the context of higher-order shear deformation theory (HSDT). The material properties of composite are approximated based upon the modified Halpin-Tsai model and rule of mixture. Furthermore, various FG distribution patterns are considered along the thickness direction of plate for GPLs. Using novel vector/matrix relations, the governing equations are derived through a variational approach. The matricized formulation can be efficiently employed in the coding process of numerical methods. In VDQFEM, the space domain of structure is first transformed into a number of finite elements. Then, the VDQ discretization technique is implemented within each element. As the last step, the assemblage procedure is performed to derive the set of governing equations which is solved via the pseudo arc-length continuation algorithm. Also, since HSDT is used herein, the mixed formulation approach is proposed to accommodate the continuity of first-order derivatives on the common boundaries of elements. Rectangular and circular plates under various boundary conditions with circular/rectangular/elliptical cutout are selected to generate the numerical results. In the numerical examples, the effects of geometrical properties and reinforcement with GPL on the nonlinear maximum deflection-transverse load amplitude curve are studied.

• Journal of the Korean Institute of Telematics and Electronics
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• v.26 no.7
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• pp.157-165
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• 1989

To recover three dimensional information in Shape from Texture, the distorting effects of projection must be distinguished from properties of the texture on which the distortion acts. In this paper, we show an approximated maximum likelihood estimation method in which we find surface orientation of the visible surface (hemisphere) in gaussian sphere using local analysis of the texture. In addition, assuming that an orthogonal projection and a circle is an image formation system and a texel (texture element) respectively, we drive the surface orientation from the distribution of variation by means of orthogonal projection of a tangent direction which exists regularly in the arc length of a circle. We present the orientation parameters of textured surface with slant and tilt in gradient space, and also the surface normal of the resulted surface orientationas as needle map. This algorithm is applied to geographic contour (artificially generated chejudo) and synthetic texture.