• Structural Engineering and Mechanics
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• v.3 no.5
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• pp.411-427
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• 1995

The most known continuum damage theories for brittle structures are suitable to model the degradation of the material due to the deformation process and the consequent initiation of a macro-crack. Nevertheless, they are not able to describe the propagation of the crack that leads, eventually, to the breakage of the structure into parts that undergo rigid body motion. This paper presents a theory, formulated from formal arguments of Continuum Mechanics, that may describe not only the degradation but also the fracture of elastic structures. The modeling of such a discontinuous phenomenon through a continuous theory is possible by taking a cohesion variable, related with the links between material points, as an additional degree of kinematical freedom. The possibilities of the proposed theory are discussed through examples.

• Structural Engineering and Mechanics
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• v.89 no.4
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• pp.421-436
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• 2024

This research addresses experimentally the relationship between the excitation frequency and both hoop and axial wall stresses in a water storage tank. A low-density polyethylene tank with six different aspect ratios (water level to tank radius) was tested using a shake table. A laminar box with sand represents a soil site to simulate Soil-Structure Interaction (SSI). Sine excitations with eight frequencies that cover the first free vibration frequency of the tank-water system were applied. Additionally, Ricker wavelet excitations of two different dominant frequencies were considered. The maximum stresses are compared with those using a nonlinear elastic spring-mass model. The results reveal that the coincidence between the excitation frequency and the free-vibration frequency of the soil-tank-water system increases the sloshing intensity and the rigid-like body motion of the system, amplifying the stress development considerably. The relationship between the excitation frequency and wall stresses is nonlinear and depends simultaneously on both sloshing and uplift. In most cases, the maximum stresses using the nonlinear elastic spring-mass model agree with those from the experiments.

• Wind and Structures
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• v.20 no.3
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• pp.423-448
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• 2015

In this paper the unsteady fluid-structure interaction (FSI) problems with large structural displacement are solved by partitioned solution approaches in the arbitrary Lagrangian-Eulerian finite element framework. The incompressible Navier-Stokes equations are solved by the characteristic-based split (CBS) scheme. Both a rigid body and a geometrically nonlinear solid are considered as the structural models. The latter is solved by Newton-Raphson procedure. The equation governing the structural motion is advanced by Newmark-${\beta}$ method in time. The dynamic mesh is updated by using moving submesh approach that cooperates with the ortho-semi-torsional spring analogy method. A mass source term (MST) is introduced into the CBS scheme to satisfy geometric conservation law. Three partitioned coupling strategies are developed to take FSI into account, involving the explicit, implicit and semi-implicit schemes. The semi-implicit scheme is a mixture of the explicit and implicit coupling schemes due to the fluid projection splitting. In this scheme MST is renewed for interfacial elements. Fixed-point algorithm with Aitken's ${\Delta}^2$ method is carried out to couple different solvers within the implicit and semi-implicit schemes. Flow-induced vibrations of a bridge deck and a flexible cantilever behind an obstacle are analyzed to test the performance of the proposed methods. The overall numerical results agree well with the existing data, demonstrating the validity and applicability of the present approaches.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.05a
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• pp.859-865
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• 2007

This paper presents a method to analyze the unbalance response of a high speed polygon mirror scanner motor supported by sintered bearing and flexible supporting structures by using the finite element method and the mode superposition method. The appropriate finite element equations for polygon mirror are described by rotating annular sector element using Kirchhoff plate theory and von Karman non-linear strain, and its rigid body motion is also considered. The rotating components except for the polygon mirror are modeled by Timoshenko beam element including the gyroscopic effect. The flexible supporting structures are modeled by using a 4-node tetrahedron element and 4-node shell element with rotational degrees of freedom. Finite element equations of each component of the polygon mirror scanner motor and the flexible supporting structures are consistently derived by satisfying the geometric compatibility in the internal boundary between each component. The rigid link constraints are also imposed at the interface area between sleeve and sintered bearing to describe the physical motion at this interface. A global matrix equation obtained by assembling the finite element equations of each substructure is transformed to a state-space matrix-vector equation, and both damped natural frequencies and modal damping ratios are calculated by solving the associated eigenvalue problem by using the restarted Arnoldi iteration method. Unbalance responses in time and frequency domain are performed by superposing the eigenvalues and eigenvectors from the free vibration analysis. The validity of the proposed method is verified by comparing the simulated unbalance response with the experimental results. This research also shows that the flexibility of supporting structures plays an important role in determining the unbalance response of the polygon mirror scanner motor.

• Proceedings of the KSME Conference
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• 2002.08a
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• pp.705-706
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• 2002

Hemodynamics of the TPLS(Twin Pulse Life Support System) is numerically investigated to delineate the possibility of hemolysis in blood. Computational method employing finite element algorithm is utilized to solve the blood flow of the sac squeezed by moving actuator. We assume that the blood flow interacts with the sac material which is activated by the rigid body motion of the actuator. Valve dynamics at the ends of the sac is simplified as on/off type motion. We compute the transient viscous flow in the two-dimensional geometry of the blood sac. Incompressible laminar flow is simulated on the assumption of Newtonian fluid. Blood velocity has a step gradient near the throat of the sac formed by the moving actuator. According to the decrease of the gap size of blood passage, the magnitude of shear stress in the blood is dramatically increased. Numerical solutions show that the maximum value of shear stress in the blood flow in TPLS is relatively smaller than that of the roller type ECLS.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.3 s.96
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• pp.251-258
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• 2005

The free vibration of a spinning flexible disk-spindle system supported by hydro dynamic bearings (HDB) in an HDD is analyzed by FEM. The spinning flexible disk is described using Kirchhoff plate theory and von Karman non-linear strain, and its rigid body motion is also considered. It is discretized by annular sector element. The rotating spindle which includes the clamp, hub, permanent magnet and yoke, is modeled by Timoshenko beam including the gyroscopic effect. The flexible supporting structure with a complex shape which includes stator core, housing, base plate, sleeve and thrust pad is modeled by using a 4-node tetrahedron element with rotational degrees of freedom to satisfy the geometric compatibility. The dynamic coefficients of HDB are calculated from the HDB analysis program, which solves the perturbed Reynolds equation using FEM. Introducing the virtual nodes and the rigid link constraints defined in the center of HDB, beam elements of the shaft are connected to the solid elements of the sleeve and thrust pad through the spring and damper element. The global matrix equation obtained by assembling the finite element equations of each substructure is transformed to the state-space matrix-vector equation, and the associated eigen value problem is solved by using the restarted Arnoldi iteration method. The validity of this research is verified by comparing the numerical results of the natural frequencies with the experimental ones. Also the effect of supporting structures to the natural modes of the total HDD system is rigorously analyzed.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.11a
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• pp.572-578
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• 2003

The free vibration of a spinning flexible disk-spindle system supported by hydro dynamic bearings in a HDD is analyzed by FEM. The spinning flexible disk is described using Kirchhoff plate theory and von Karman non-linear strain, and its rigid body motion is also considered. It is discretized by annular sector element. The rotating spindle which includes the clamp, hub, permanent magnet and yoke, is modeled by Timoshenko beam including the gyroscopic effect. The flexible supporting structure with a complex shape which includes stator core, housing, base plate, sleeve and thrust pad is modeled by using a 4-node tetrahedron element with rotational degrees of freedom to satisfy the geometric compatibility. The dynamic coefficients of HDB are calculated from the HDB analysis program, which solves the perturbed Raynolds equation using FEM. Introducing the virtual nodes and the rigid link constraints defined in the center of HDB, beam elements of the shaft are connected to the solid elements of the sleeve and thrust pad through the spring and damper element. The global matrix equation obtained by assembling the finite element equations of each substructure is transformed to the state-space matrix-vector equation, and the associated eigenvalue problem is solved by using the restarted Arnoldi iteration method. The validity of this research is verified by comparing the numerical results of the natural frequencies with the experimental ones. Also the effect of supporting structures to the natural modes of the total HDD system is rigorously analyzed.

• Wind and Structures
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• v.13 no.2
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• pp.169-189
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• 2010

This paper describes the use of coupled Computational Fluid Dynamics (CFD) and Rigid Body Dynamics (RBD) in modelling the aerodynamic behaviour of wind-borne plate type objects. Unsteady 2D and 3D Reynolds Averaged Navier-Stokes (RANS) CFD models are used to simulate the unsteady and non-uniform flow field surrounding static, forced rotating, auto-rotating and free-flying plates. The auto-rotation phenomenon itself is strongly influenced by vortex shedding, and the realisable k-epsilon turbulence modelling approach is used, with a second order implicit time advancement scheme and equal or higher order advection schemes for the flow variables. Sequentially coupling the CFD code with a RBD solver allows a more detailed modelling of the Fluid-Structure Interaction (FSI) behaviour of the plate and how this influences plate motion. The results are compared against wind tunnel experiments on auto-rotating plates and an existing 3D analytical model.

• Interaction and multiscale mechanics
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• v.3 no.4
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• pp.365-372
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• 2010

Station is an important building in high-speed railway, and its vibration and noise may significantly affect the comfort of waiting passengers. A coupling vibration model for train-structure system is established to analyze and evaluate the vibration level of a typical waiting hall under dynamic train load. The motion of a four-axle vehicle with two suspension system is modeled in multi-body dynamics with linear springs and dampers employed. The station is modeled as a whole finite element structure which is 113 m in longitudinal and 163.5 m in lateral, and the stiffness of the station foundation is considered. According to the assumptions that both wheel and rail are rigid bodies and keep contact to each other in vertical direction, and the wheel/rail interaction and displacement coordination in horizontal direction is defined by the simplified Kalker creep theory, the vehicle spatial vibration model has 27 degrees-of-freedom. An overall analysis procedure is made of the train moving through the station, by which the dynamic responses of the train and the station are calculated. According to the comparison between analysis and test results, the actual connection status between different parts of the station is estimated and the vibration level of the waiting hall is evaluated.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.19 no.3
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• pp.36-41
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• 2020

Mechanical systems installed in transport devices, such as vehicles, airplanes, and ships, are mostly subject to translational accelerations at the joints during operations. This base acceleration excitation has a large influence on the performance of the system, therefore, its response must be well analyzed. However, the existing methods for dynamic analysis of structures have some limitations in use. This study presents a new numerical method using relative acceleration to solve these limitations. If the governing equation of motion is linear and the mass matrix, the damping matrix, and the stiffness matrix are constant over time in the finite element analysis, the proposed method can be applied to the transient behavior analysis and the harmonic response analysis of the structure. Because it is not necessary to introduce a virtual mass and the rigid body motions are removed from the analysis, it is possible to use not only the direct integration method in the time domain but also the mode superposition method to obtain the dynamic responses. This paper demonstrates with three examples how the present method is suitable for the dynamic analysis of a structure with multi-degree of freedom.