• Structural Engineering and Mechanics
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• v.7 no.2
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• pp.203-216
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• 1999

A previously proposed finite element formulation method is refined and modified to generate a new type of elements. The method is based on selecting a set of general solution modes for element formulation. The constant strain modes and higher order modes are selected and the formulation method is designed to ensure that the element will pass the basic single element test, which in turn ensures the passage of the basic patch test. If the element is to pass the higher order patch test also, the element stiffness matrix is in general asymmetric. The element stiffness matrix depends only on a nodal displacement matrix and a nodal force matrix. A symmetric stiffness matrix can be obtained by either modifying the nodal displacement matrix or the nodal force matrix. It is shown that both modifications lead to the same new element, which is demonstrated through numerical examples to be more robust than an assumed stress hybrid element in plane stress application. The method of formulation can also be used to arrive at the conforming displacement and hybrid stress formulations. The convergence of the latter two is explained from the point of view of the proposed method.

• Structural Engineering and Mechanics
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• v.51 no.4
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• pp.601-625
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• 2014

Based on continuum mechanics and the principle of virtual displacements, incremental total Lagrangian formulation (T.L.) and incremental updated Lagrangian formulation (U.L.) were presented. Both T.L. and U.L. considered the large displacement stiffness matrix, which was modified to be symmetrical matrix. According to the incremental updated Lagrangian formulation, small strain, large displacement, finite rotation of three dimensional Timoshenko fiber beam element tangent stiffness matrix was developed. Considering large displacement and finite rotation, a new type of tangent stiffness matrix of the beam element was developed. According to the basic assumption of plane section, the displacement field of an arbitrary fiber was presented in terms of nodal displacement of centroid of cross-area. In addition, shear deformation effect was taken account. Furthermore, a nonlinear finite element method program has been developed and several examples were tested to demonstrate the accuracy and generality of the three dimensional beam element.

• Journal of the Korean Society for Railway
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• v.2 no.1
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• pp.47-55
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• 1999

In this paper, an efficient and accurate formulation for the transient analysis of constrained multibody systems is presented. The formulation employs Kane's method along with the null space method. Kane's method reduces the dimension of equations of motion by using partial velocity matrix: it can improve the efficiency of the formulation. Furthermore, the formulation partitions the coefficient matrix of linear and nonlinear equations into several sub-matrices using kinematic uncoupling. This can solve the equations more efficiently. The proposed formulation can be used to perform dynamic analysis of systems which can be partitioned into several sub-systems such as train systems. One numerical example is given to demonstrate the efficiency and accuracy of the formulation, and another numerical example is given to show its application to the train systems.

• Structural Engineering and Mechanics
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• v.14 no.4
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• pp.473-489
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• 2002

A static linear programming formulation for minimum weight design of frames that is based on a matrix displacement method is presented in this paper. According to elementary theory of plasticity, minimum weight design of frames can be carried out by using only the equilibrium equations, because the system is statically determinate when at an incipient collapse state. In the present formulation, a statically determinate released frame is defined by introducing hinges into the real frame and the bending moments in yield constraints are expressed in terms of unit hinge rotations and the external loads respectively, by utilizing the matrix displacement method. Conventional Simplex algorithm with some modifications is utilized for the solution of linear programming problem. As the formulation is based on matrix displacement method, it may be easily adopted to the weight optimization of frames with displacement and deformation limitations. Four illustrative examples are also given for comparing the results to those obtained in previous studies.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.16 no.27
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• pp.83-89
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• 1993

In order to model the Group Technology Problem three formulations are used, that is, generally the following formulations are used: (1) Matrix formulation, (2) Mathematical programming formulation, (3) Graph formulation. In the case of Matrix formulation, it is difficult to discribe the situation using the multi-job machine. But this paper proposed the model of Group Technology using the multi-job machin, taking the method of making practical application of principle of similarity coefficient.

• 유체기계공업학회:학술대회논문집
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• 2006.08a
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• pp.349-352
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• 2006

The conventional segregated finite element formulation produces a small and simple matrix at each step than in an integrated formulation. And the memory and cost requirements of computations are significantly reduced because the pressure equation for the mass conservation of the Navier-Stokes equations is constructed only once if the mesh is fixed. However, segregated finite element formulation solves Poisson equation of elliptic type so that it always needs a pressure boundary condition along a boundary even when physical information on pressure is not provided. On the other hand, the conventional integrated finite element formulation in which the governing equations are simultaneously treated has an advantage over a segregated formulation in the sense that it can give a more robust convergence behavior because all variables are implicitly combined. Further it needs a very small number of iterations to achieve convergence. However, the saddle-paint-type matrix (SPTM) in the integrated formulation is assembled and preconditioned every time step, so that it needs a large memory and computing time. Therefore, we newly proposed the P2PI semi-segregation formulation. In order to utilize the fact that the pressure equation is assembled and preconditioned only once in the segregated finite element formulation, a fixed symmetric SPTM has been obtained for the continuity constraint of the present semi-segregation finite element formulation. The momentum equation in the semi-segregation finite element formulation will be separated from the continuity equation so that the saddle-point-type matrix is assembled and preconditioned only once during the whole computation as long as the mesh does not change. For a comparison of the CPU time, accuracy and condition number between the two methods, they have been applied to the well-known benchmark problem. It is shown that the newly proposed semi-segregation finite element formulation performs better than the conventional integrated finite element formulation in terms of the computation time.

• Korean Journal of Computational Design and Engineering
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• v.15 no.6
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• pp.411-417
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• 2010

In this paper, the boom of a floating crane is modeled as a 3-dimensional elastic beam in order to analyze the dynamic response of the crane and its cargo. The boom is divided into more than two elements based on finite element formulation, and deformation of each element is expressed in terms of shape matrix and nodal coordinates. The equations of motion for the elastic boom consist of a mass matrix, a stiffness matrix, and a quadratic velocity vector that contains the gyroscopic and Coriolis forces. The size and complicity of the matrices increase in proportion with the number of elements. Therefore, it is not possible to derive the equations of motion explicitly for different number of elements. To overcome this difficulty, matrices for one 3-dimensional element are expressed with elementary sub-matrices. In particular, the quadratic velocity vector is derived as a product of a shape matrix and a 3-dimensional rotation matrix. By using the derived matrices, the equations of motion for the multi-element boom are automatically constructed. To verify the implementation of the elastic boom based on finite element formulation, we simulated a simple vibration of the elastic boom and compared the average deformation with the analytic solution. Finally, heave motion of the floating crane and surge motion of the cargo are presented as application examples of the elastic boom.

• Proceedings of the KSR Conference
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• 1998.11a
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• pp.437-444
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• 1998

In this paper, an efficient and accurate formulation for the transient analysis of constrained multibody systems is presented. The formulation employs Kane's method along with the null space method. Kane's method reduces the dimension of equations of motion by using partial velocity matrix: it can improve the efficiency of the formulation. Furthermore, the formulation partitions the coefficient matrix of linear and nonlinear equations into several sub-matrices using kinematic uncoupling. This can solve the equations more efficiently. The proposed formulation can be used to perform dynamic analysis of systems which can he partitioned into several sub-systems such as train systems. One numerical example is given to demonstrate the efficiency and accuracy of the formulation, and another numerical example is given to show its application to the train systems.

• Journal of Pharmaceutical Investigation
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• v.32 no.2
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• pp.95-101
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• 2002

Matrix tablets of nifedipine (NP) were prepared with Eudragit, diluent (lactose or Ca. phosphate) and Mg. stearate employing two different preparation methods (wet granulation and direct compression) to develop its sustained-release dosage forms. The effects of various formulation factors on the dissolution rate of the drug were investigated. Dissolution test was studied in pH 6.8 phosphate buffer containing 1% sodium lauryl sulfate using the paddle method. Formulation factors were the type and content of Eudragit, the type of diluent and the tablet preparation method. The optimum formula of NP matrix tablet, which resulted in a similar dissolution profile to that from Adalat Oros used as a reference, was 30 mg NP, 10% Eudragit RS, 2% Mg. stearate and an adequate quantity of lactose to yield 500 mg weight using the wet granulation method.

• Journal of Pharmaceutical Investigation
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• v.29 no.1
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• pp.7-12
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• 1999

The captopril matrix tablets composed of polyethylene oxide(PEO) was prepared and administered to beagle dogs. Captopril matrix tablets were prepared using direct compressed method and wet granulation compressed method with various ratios of drug to PEO. The diffusion rate of captopril matrix tablets followed on the Higuchi's diffusion model. With increasing hardness of captopril matrix tablets, release rate was decreased. Each formulation was evaluated by the area under the curve (AUC) and time course of plasma captopril concentration after oral administration to beagle dogs. The $AUC_{0-12}$ were $9.126\;{\mu}g\;h/ml$ and $6.417\;{\mu}g\;h/ml$ for the matrix tablets and conventional tablets, respectively. Therefore, the bioavailability of captopril matrix tablets was greater than that of commercial product. It is suggested that captopril matrix tablets using PEO is a useful sustained release formulation.