• Structural Engineering and Mechanics
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• 제51권4호
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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 Mechanical Science and Technology
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• 제19권spc1호
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• pp.283-291
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• 2005

Accurate seismic analyses of large deformable moving structures are still unsolved problems in the field of earthquake engineering. In order to analyze these problems, the nonlinear finite element method formulated by the absolute nodal coordinate approach is noticed. Because, this formulation has several advantages over the standard procedures on mass matrix, elastic forces and damping forces in the case of large displacement problems. But, it has not been fully studied to build frame structure models by using beam elements in the absolute nodal coordinate formulation. In this paper, we propose the connecting method of the beam elements formulated by the absolute nodal coordinate. The coordinate transformation matrix of this element is introduced into the frame structure. This beam element has the characteristic that the mass matrix and bending stiffiness matrix are constant even if in the case of large displacement problems, and this characteristic is being kept after the transformation. In order to verify the proposed method, we show the numerical simulation results of frame structures for a vibration problem and a large displacement problem.

• Structural Engineering and Mechanics
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• 제2권4호
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• pp.395-402
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• 1994

An improved finite element-transfer matrix method is applied to the transient analysis of plates with large displacement under various excitations. In the present method, the transfer of state vectors from left to right in a combined finite element-transfer matrix method is changed into the transfer of generally incremental stiffness equations of every section from left to right. Furthermore, in this method, the propagation of round-off errors occurring in recursive multiplications of transfer and point matrices is avoided. The Newmark-${\beta}$ method is employed for time integration and the modified Newton-Raphson method for equilibrium iteration in each time step. An ITNONDL-W program based on this method using the IBM-PC/AT microcomputer is developed. Finally numerical examples are presented to demonstrate the accuracy as well as the potential of the proposed method for dynamic large deflection analysis of plates with random boundaries under various excitations.

• Computers and Concrete
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• 제15권3호
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• pp.373-389
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• 2015

The development of a finite element model for the geometric and material nonlinear analysis of bonded prestressed concrete continuous beams is presented. The nonlinear geometric effect is introduced by the coupling of axial and flexural fields. A layered approach is applied so as to consider different material properties across the depth of a cross section. The proposed method of analysis is formulated based on the Euler-Bernoulli beam theory. According to the total Lagrangian description, the constructed stiffness matrix consists of three components, namely, the material stiffness matrix reflecting the nonlinear material effect, the geometric stiffness matrix reflecting the nonlinear geometric effect and the large displacement stiffness matrix reflecting the large displacement effect. The analysis is capable of predicting the nonlinear behaviour of bonded prestressed concrete continuous beams over the entire loading stage up to failure. Some numerical examples are presented to demonstrate the validity and applicability of the proposed model.

• Structural Engineering and Mechanics
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• 제53권2호
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• pp.205-226
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• 2015

Finite element method (FEM) is an effective quantitative method to solve complex engineering problems. The basic idea of FEM for a complex problem is to be able to find a solution by reducing the problem made simple. If mathematical tools are inadequate to obtain precise result, even approximate result, FEM is the only method that can be used for structural analyses. In FEM, the domain is divided into a large number of simple, small and interconnected sub-regions called finite elements. FEM has been used commonly for linear and nonlinear analyses of different types of structures to give us accurate results of plane stress and plane strain problems in civil engineering area. In this paper, FEM is used to investigate stress analysis of a shear wall which is subjected to concentrated loads and fundamental principles of stress analysis of the shear wall are presented by using matrix displacement method in this paper. This study is consisting of two parts. In the first part, the shear wall is discretized with constant strain triangular finite elements and stiffness matrix and load vector which is attained from external effects are calculated for each of finite elements using matrix displacement method. As to second part of the study, finite element analysis of the shear wall is made by ANSYS software program. Results obtained in the second part are presented with tables and graphics, also results of each part is compared with each other, so the performance of the matrix displacement method is demonstrated. The solutions obtained by using the proposed method show excellent agreements with the results of ANSYS. The results show that this method is effective and preferable for the stress analysis of shell structures. Further studies should be carried out to be able to prove the efficiency of the matrix displacement method on the solution of plane stress problems using different types of structures.

• 전기학회논문지
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• 제66권2호
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• pp.402-408
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• 2017

This paper deals with a robust ${\mathfrak{H}}_{\infty}$ controller design problem for waypoints tracking of large displacement unmanned underwater vehicles (LDUUVs) in Takagi-Sugeno fuzzy form. The LDUUV model uses a rudder to control its horizontal motion. We determine the order of waypoints based on their priorities and consider only surge force. A fuzzy controller in state-feedback form is taken and its design condition of is represented in terms of linear matrix inequalities. A numerical simulation is included to show the effectiveness of the theoretical development.

• Structural Engineering and Mechanics
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• 제15권2호
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• pp.199-223
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• 2003

The formulation of a non-linear shear deformable shell element is presented for the solution of stability problems of stiffened plates and shells. The formulation of the geometrical stiffness presented here is exactly defined on the midsurface and is efficient for analyzing stability problems of thick plates and shells by incorporating bending moment and transverse shear resultant force. As a result of the explicit integration of the tangent stiffness matrix, this formulation is computationally very efficient in incremental nonlinear analysis. The element is free of both membrane and shear locking behaviour by using the assumed strain method such that the element performs very well in the thin shells. By using six degrees of freedom per node, the present element can model stiffened plate and shell structures. The formulation includes large displacement effects and elasto-plastic material behaviour. The material is assumed to be isotropic and elasto-plastic obeying Von Mises's yield condition and its associated flow rules. The results showed good agreement with references and computational efficiency.

• 대한기계학회논문집
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• 제17권7호
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• pp.1658-1667
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• 1993

In this research, a numerical algorithm has been developed, which can be applied to the large deformation and large displacement contact problems between two deformable bodies. The contact conditions expressed in terms of the rate of angle change have been proposed considering the change in geometric shape and rate of contact force. A set of linear simultaneous equations is constructed by adding the geometric shape change and contact conditions to the original stiffness matrix. A new method to determine time increment has been proposed based on Euler method, in which the condition to prevent the contact bodies from penetrating and overrunning each other has been taken into consideration. Practical application to contact problem is extrusion in which bodies are sliding along the contact boundary.

• Ocean Systems Engineering
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• 제10권1호
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• pp.67-86
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• 2020

The main goal of this study is to investigate the free vibration analysis of a large sag catenary with application to the jumper in hybrid riser system. The equation of motion is derived by using the variational method based on the virtual work principle. The finite element method is applied to evaluate the numerical solutions. The large sag catenary is utilized as an initial configuration for vibration analysis. The nonlinearity due to the large sag curvature of static configuration is taken into account in the element stiffness matrix. The natural frequencies of large sag catenary and their corresponding mode shapes are determined by solving the eigenvalue problem. The numerical examples of a large sag catenary jumpers are presented. The influences of bending rigidity and large sag shape on the free vibration behaviors of the catenary jumper are provided. The results indicate that the increase in sag reduces the jumper natural frequencies. The corresponding mode shapes of the jumper with large sag catenary shape are comprised of normal and tangential displacements. The large sag curvature including in the element stiffness matrix increases the natural frequency especially for a case of very large sag shape. Mostly, the mode shapes of jumper are dominated by the normal displacement, however, the tangential displacement significantly occurs around the lowest point of sag. The increase in degree of inclination of the catenary tends to increase the natural frequencies.

• Journal of the Korean Association of Oral and Maxillofacial Surgeons
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• 제29권4호
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• pp.212-218
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• 2003

Matrix metalloproteinases (MMPs) play an important role in the normal morphogenesis, maintenance, and repair of matrix and also have important functions in pathologic conditions characterized by excessive degradation of extracellular matrix, such as rheumatoid arthritis, osteoarthritis, periodontitis and in tumor invasion and metastasis. In this study, expression of MMP-1 and -2 mRNA in retrodiscal tissue of the temporomandibular joint (TMJ) was examined and compared with magnetic resonance imaging (MRI) and surgical findings. MMP mRNAs in the retrodiscal tissue samples were detected by reverse transcription - polymerase chain reaction. TMJ internal derangement (ID) was categorized as normal disc position, disc displacement with reduction, early stage of disc displacement without reduction (DDsR) and late stage of DDsR. TMJ osteoarthrosis (OA) was classified with normal, mild and advanced OA. The amount of synovial fluid collection was divided into not detected, small, large and extremely large amount on MR T2-weighted imaging. Perforation and adhesion were examined during open surgery of the TMJ. Six out of 37 samples were excluded because of little amount of extracted total mRNA. MMP-2 mRNA was detected whole joints, and so the MMP-2 mRNA seems to be expressed normally in retrodiscal tissue. However, MMP-1 mRNA was expressed in 8 of 31 joints. Frequencies of MMP-1 mRNA expression according to the TMJ IDs, amount of synovial fluid and surgical findings made no significant difference. MMP-1 mRNA was detected more frequently in OA groups (7/16 joints, 43.8%) than in normal bony structure group (1/15 joints, 6.7%). Expression of MMP-1 mRNA in retrodiscal tissue might be related with OA of the TMJ.