• Journal of Advanced Marine Engineering and Technology
• /
• 제26권3호
• /
• pp.344-352
• /
• 2002

In the analysis of the 3 dimensional plate structures by the finite element method, the triangular elements are generally used for the global stiffness matrix of the analyzed system. But the triangular elements of the plates have some problems in the process of formulation and in the precision of analysis. The formulation of the finite element method to analyze 3 dimensional plate structures using quadrilateral elements is presented in this paper. The degree of freedom off nodal point is 6, that is, the displacements in the direction off-y-z is and the rotations about x-y-z axis and then the degree of freedom off element is 24. For the comparison of the analysis using triangular elements and quadrilateral elements, the rectangular plates subjected to the uniform load and a concentrated load on the centroid of the plate, for which the theoretical solutions have been obtained, are analyzed. The calculated deflections of the rectangular plates using the finite element method by the triangular elements and the quadrilateral elements are also compared with the deflections of the plates calculated by theoretical solutions. The defections of the rectangular plates calculated by the finite element method using the quadrilateral elements are closer to the theoretical solutions than the defections calculated by the finite element method using the triangular elements. The deflection of the centroid of plate, calculated by the finite element method, converges to that of theoretical solution as the number of elements is increased. This convergence is much more rapid for the case of using the quakrilateral elements than fir the case of using triangular elements.

• Structural Engineering and Mechanics
• /
• 제40권5호
• /
• pp.637-654
• /
• 2011

The present paper studies the variation of the natural frequencies and mode shapes of rectangular plates carrying a three degree-of-freedom spring-mass system (subsystem), when the subsystem changes (stiffness, mass, moment of inertia, location). An analytical approach based on Lagrange multipliers as well as a finite element formulation are employed and compared. Numerically reliable results are presented for the first time, illustrating the convenience of using the present analytical method which requires only the solution of a linear eigenvalue problem. Results obtained through the variation of the mass, stiffness and moment of inertia of the 3-DOF system can be understood under the effective mass concept or Rayleigh's statement. The analysis of frequency values of the whole system, when the 3-DOF system approaches or moves away from the center, shows that the variations depend on each particular mode of vibration. When the 3-DOF system is placed in the center of the plate, "new" modes are found to be a combination of the subsystem's modes (two rotations, traslation) and the bare plate's modes that possess the same symmetry. This situation no longer exists as the 3-DOF system moves away from the center of the plate, since different bare plate's modes enable distinct motions of the 3-DOF system contributing differently to the "new' modes as its location is modified. Also the natural frequencies of the compound system are nearly uncoupled have been calculated by means of a first order eigenvalue perturbation analysis.

• 한국소음진동공학회논문집
• /
• 제18권10호
• /
• pp.1033-1041
• /
• 2008

The purpose of this paper is to investigate natural frequencies of tapered thick plate with concentrated masses subjected to in-plane force on pasternak foundation by means of finite element method and providing kinetic design data for mat of building structures. Finite element analysis of rectangular plate is done by using rectangular finite element with 8-nodes. For analysis, plates is supported on pasternak foundation. The Winkler parameter is varied with 10, 102, the shear foundation parameter is 5. The taper ratio is applied as 0.0, 0.25, 0.5 and the ratio of the concentrated mass to plate mass as 0.25, 0.5 respectively. As results, we can see that when stiffener's sizes or foundation parameter are larger, the natural frequency increases, and when the concentrated mass or taper ratio or in-plane stress is larger, the natural frequency decreases.

• 설비공학논문집
• /
• 제30권1호
• /
• pp.33-43
• /
• 2018

This study numerically investigated statistic and dynamic behaviors of the water droplet on plate with or without various structured-pillars at nano-scale by molecular dynamics simulation. This study considered smooth plate, plate with the rectangular-structured pillar, and the plate with dual-structured pillar under various characteristic energy conditions. The static behavior of water droplet depending on the plate shape, plate surface energy, and the pillar characteristics were examined. After the water droplet reaches its steady state, this study investigated the dynamic behavior of the water droplet by applying a constant force. Finally, this study investigated the static and dynamic behaviors of the water droplet by measuring its contact angle and contact angle hysteresis. As a result, we found that the structure was more hydrophobic.

• Advances in Computational Design
• /
• 제3권3호
• /
• pp.213-232
• /
• 2018

First time, an exact solution for free vibration of the Levy-type rectangular laminated plate is developed considering the most efficient Zig-Zag theory (ZIGT) and third order theory (TOT). The plate is subjected to hard simply supported boundary condition (Levy-type) along x axis. Using the equilibrium equations and the plate constitutive relations, a set of 12 m first order differential homogenous equations are obtained, containing displacements and stress resultant as primary variables. The natural frequencies of a single-layer isotropic, multi-layer composites and sandwich plates are tabulated for three values of length-to-thickness ratio (S) and five set of boundary conditions and further assessed by comparing with existing literature and recently developed 3D EKM (extended Kantorovich method) solution. It is found that for the symmetric composite plate, TOT produces better results than ZIGT. For antisymmetric and sandwich plates, ZIGT predicts the frequency for different boundary conditions within 3% error with respect to 3D elasticity solution while TOT gives 10% error. But, ZIGT gives better predictions than the TOT concerning the displacement and stress variables.

• 대한조선학회논문집
• /
• 제46권2호
• /
• pp.155-164
• /
• 2009

In this paper, a spectral finite element method for a rectangular sandwich plate with viscoelastic core having the Levy-type boundary conditions has been plated. The sandwich plate consists of two isotropic and elastic face plates with a surfaced-bonded viscoelastic core. For the analysis, the in-plane and transverse energy in the face plates and only shear energy in the core are considered, respectively. To account for the frequency dependent complex shear modulus of the viscoelastic core, the Golla-Hughes-McTavish model is adopted. To evaluate the validity and accuracy of the proposed method, the frequency response function and dynamic responses of the sandwich plate with all edges simply supported subject to an impact load are calculated and compared with those calculated by a finite element method. Though these calculations, it is confirmed that the proposed method is very reliable and efficient one for vibration analysis of a rectangular sandwich plate with viscoelastic core having the Levy-type boundary conditions.

• Computers and Concrete
• /
• 제24권5호
• /
• pp.423-436
• /
• 2019

Design equations to evaluate the bursting force in a post-tensioned anchorage zone have been introduced in many design codes, and one equation in AASHTO LRFD is widely used. However, this equation may not determine the bursting force exactly because it was designed on the basis of two-dimensional numerical analyses without considering various design parameters such as the duct hole and shape of the bearing plate. To improve the design equation, modification of the AASHTO LRFD design equation was considered. The behavior of the anchorage zone was investigated using three-dimensional linear elastic finite element analysis with design parameters such as bearing plate size and diameter of sheath hole. Upon the suggestion of a modified design equation for evaluating the bursting force in an anchorage block with a rectangular anchorage plate (Kim and Kwak 2018), additional influences of design parameters that could affect the evaluation of bursting force were investigated. An improved equation was introduced for determining the bursting force in an anchorage block with a circular anchorage plate, using the same procedure introduced in the design equation for an anchorage block with a rectangular anchorage plate. The validity of the introduced design equation was confirmed by comparison with AASHTO LRFD.

• 한국산업융합학회 논문집
• /
• 제24권6_1호
• /
• pp.683-691
• /
• 2021

Bipolar plates with channel width of 0.5 mm, 0.4 mm, and 0.3 mm respectively were printed using a 3D printer. The shape of three b ipolar plates was rectangular, the channel depth was 0.5 mm, and the thickness of base was 0.5 mm. The bipolar plate with channel width of 0.5 mm had 45 channels, and their active area was 44.5 mm × 50 mm. The bipolar plate with channel width of 0.4 mm had 57 channels and its active area was 45.2 mm × 50 mm, and the bipolar plate with channel width of 0.3 mm had 75 channels and its active area was 44.7 mm × 50 mm. The bipolar plates were printed using PLA filament. The cross-sectional lengths of the bipolar plates with channel widths of 0.5 mm and 0.4 mm were identical by 96% of the designed cross-sectional length. Whereas the bipolar plate with a channel length of 0.3 mm had a large difference of 25% from the designed cross-sectional length.

• Structural Engineering and Mechanics
• /
• 제7권5호
• /
• pp.503-512
• /
• 1999

Practicing a hole or an orifice through a plate or a slab constitutes a very frequent engineering situation due to operational reasons imposed on the structural system. From a designer's viewpoint it is important to know the effect of this modification of the mechanical system upon its elastodynamic characteristics. The present study deals with the determination of the lower natural frequencies of the structural element described in the title of the paper using a variational approach and expressing the displacement amplitude of the plate in terms of the double Fourier series which constitutes the classical, exact solution when the structure is simply supported at its four edges.

• 대한기계학회논문집
• /
• 제6권4호
• /
• pp.361-366
• /
• 1982

This paper attempts to predict the stress concentration around the corner of rectangular inserts of different material of mechanical properties from the base material of the finite rectangular plate. The problem is analyzed through the FEM and photo-elastic experiment with the inclination angle of the insert as variable parameters. According to the experiments and the numerical analysis, the maximum stress concentration occurs at the point of tangential discontinuity of a insert. When the lain insert or opening was so inclined that the distance from the free end of the plate to a corner became minimum, the maximum stress concentration factor was found.