• International Journal of Naval Architecture and Ocean Engineering
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• v.4 no.3
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• pp.313-321
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• 2012

Vibration analysis of a thin-walled structure can be performed with a consistent mass matrix determined by the shape functions of all degrees of freedom (d.o.f.) used for construction of conventional stiffness matrix, or with a lumped mass matrix. In similar way stability of a structure can be analysed with consistent geometric stiffness matrix or geometric stiffness matrix with lumped buckling load, related only to the rotational d.o.f. Recently, the simplified mass matrix is constructed employing shape functions of in-plane displacements for plate deflection. In this paper the same approach is used for construction of simplified geometric stiffness matrix. Beam element, and triangular and rectangular plate element are considered. Application of the new geometric stiffness is illustrated in the case of simply supported beam and square plate. The same problems are solved with consistent and lumped geometric stiffness matrix, and the obtained results are compared with the analytical solution. Also, a combination of simplified and lumped geometric stiffness matrix is analysed in order to increase accuracy of stability analysis.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.565-568
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• 1996

In this paper, a solution method is proposed to calculate the optimum solution to discrete optimal H$_{.inf}$ control problem for feedback of linear time-invariant system states and disturbance variable. From the results of this study, condition of existence and uniqueness of its solution is that transfer matrix of controlled variable to input variable is left invertible and has no invariant zeros on the unit circle of the z-domain as well as extra geometric conditions given in this paper. Through a numerical example, the noniterative solution method proposed in this paper is illustrated.

• Steel and Composite Structures
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• v.52 no.3
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• pp.343-356
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• 2024

This paper presents an analytical solution for correctly predicting the Lateral-Torsional Buckling critical moment of simply supported castellated beams, the solution covers uniformly distributed loads combined with compressive loads. For this purpose, the castellated beam section with hexagonal-type perforation is treated as an arrangement of double "T" sections, composed of an upper T section and a lower T section. The castellated beam with regular openings is considered as a periodic repeating structure of unit cells. According to the kinematic model, the energy principle is applied in the context of geometric nonlinearity and the linear elastic behavior of materials. The differential equilibrium equations are established using Galerkin's method and the tangential stiffness matrix is calculated to determine the critical lateral torsional buckling loads. A Finite Element simulation using ABAQUS software is performed to verify the accuracy of the suggested analytical solution, each castellated beam is modelled with appropriate sizes meshes by thin shell elements S8R, the chosen element has 8 nodes and six degrees of freedom per node, including five integration points through the thickness, the Lanczos eigen-solver of ABAQUS was used to conduct elastic buckling analysis. It has been demonstrated that the proposed analytical solution results are in good agreement with those of the finite element method. A parametric study involving geometric and mechanical parameters is carried out, the intensity of the compressive load is also included. In comparison with the linear solution, it has been found that the linear stability underestimates the lateral buckling resistance. It has been confirmed that when high axial loads are applied, an impressive reduction in critical loads has been observed. It can be concluded that the obtained analytical solution is efficient and simple, and offers a rapid and direct method for estimating the lateral torsional buckling critical moment of simply supported castellated beams.

• Architectural research
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• v.13 no.1
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• pp.17-24
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• 2011

Isogeometric solution of Poisson equation is provided. NURBS (NonUniform B-spline Surface) is introduced to express both geometry of structure and unknown field of governing equation. The terms of stiffness matrix and load vector are consistently derived with very accurate geometric definition. The validity of the isogeometric formulation is demonstrated by using two numerical examples such as square plate and L-shape plate. From numerical results, the present solutions have a good agreement with analytical and finite element (FE) solutions with the use of a few cells in isogeometric analysis.

• Structural Engineering and Mechanics
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• v.24 no.6
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• pp.647-664
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• 2006

In this study, an improved finite element formulation with a scheme of solution for the large deflection analysis of inextensible prismatic and nonprismatic slender beams is developed. For this purpose, a three-noded Lagrangian beam-element with two dependent degrees of freedom per node (i.e., the vertical displacement, y, and the actual slope, $dy/ds=sin{\theta}$, where s is the curved coordinate along the deflected beam) is used to derive the element stiffness matrix. The element stiffness matrix in the global xy-coordinate system is achieved by means of coordinate transformation of a highly nonlinear ($6{\times}6$) element matrix in the local sy-coordinate. Because of bending with large curvature, highly nonlinear expressions are developed within the global stiffness matrix. To achieve the solution after specifying the proper loading and boundary conditions, an iterative quasi-linearization technique with successive corrections are employed considering these nonlinear expressions to remain constant during all iterations of the solution. In order to verify the validity and the accuracy of this study, the vertical and the horizontal displacements of prismatic and nonprismatic beams subjected to various cases of loading and boundary conditions are evaluated and compared with analytic solutions and numerical results by available references and the results by ADINA, and excellent agreements were achieved. The main advantage of the present technique is that the solution is directly obtained, i.e., non-incremental approach, using few iterations (3 to 6 iterations) and without the need to split the stiffness matrix into elastic and geometric matrices.

• 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.

• Communications of the Korean Mathematical Society
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• v.12 no.1
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• pp.177-192
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• 1997

The basic theory of the quasi-birth-and-death process is extended to a process which is inhomogeous in levels. Several key results in the standard homogeneous theory hold in a more general context than that usually stated, in particular not requiring positive recurrence. Theser results are subsumed under our development. The treatment is entirely probabilistic.

• Transactions of the Korean Society of Mechanical Engineers
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• v.12 no.4
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• pp.631-641
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• 1988

Computational procedures associated with finite element nonlinear analysis of plane frame structures were examined and new solution schemes were suggested. Element stiffness matrix was derived from the principle of virtual displacements. Geometric and material nonlinearities were considered in the formulation. Solution method was based upon the constant displacement length method in conjunction with the Newton-Raphson method. New solution schemes were introduced in determining the initial load increment and the sign of load increments and predicting the length of displacement increment to improve user convenience, efficiency and stability. Numerical experiments were performed for several typical problems and suggested schemes were found efficient and convenient for analyzing nonlinear frame structures.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.28 no.1
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• pp.79-92
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• 1992

This is analyzed using the finite element method which is appling excellent isoparametric curve element in the aspect of large usages of dynamic responses in which is regarding geometric and material nonlinear of a large scale shell structure of an airplane, a submarine, a ship, and an ocean structure. The solution of dynamic equations is got by direct integration method using time-stepping procedure and regarding Central Difference Method of the both solutions. But because formal matrix factorization is not necessary in each time step and it does not take less time to compute relatively, this method must be regarded very few time steps on the condition. Axisymmatric shell problems are inspected using 8 node Isoparametric element in this paper. Partial axisymmatric spherical shell is used as a model to analyze axisymmatric nonlinear dynamic behavior regarding. Total Lagrangian formulation in geometric nonlinear behavior and elastio-viscoplastic in material nonlinear behavior.

• Journal of Korean Institute of Industrial Engineers
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• v.21 no.3
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• pp.345-356
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• 1995

The aim of this paper is to analyze the batch service queueing model M/M(a, b ; ${\mu}_k/1$) under general bulk service rule with mean service rate ${\mu}_k$ for a batch of k units, where $a{\leq}k{\leq}b$. This queueing model consists of the two-dimensional state space so that it is characterized by two-dimensional state Markov process. The steady-state solution and performane measure of this process are derived by using Matrix Geometric method. Meanwhile, a new approach is suggested to calculate the two-dimensional traffic density R which is used to obtain the steady-state solution. In addition, to determine the optimal service initiation threshold a, a decision model of this queueing system is developed evaluating cost of service per batch and cost of waiting per customer. In a job order production system, the decision-making procedure presented in this paper can be applicable to determining when production should be started.