• The Journal of the Institute of Internet, Broadcasting and Communication
• /
• v.16 no.6
• /
• pp.319-327
• /
• 2016

In this paper we investigate that most of plants and animals have the symmetric property, such as a tree or a sheep's horn. In addition, the human body is also symmetric and contains the DNA. We can see the logarithm helices in Fibonacci series and animals, and helices of plants. The sunflower has a shape of circle. A circle is circular symmetric because the shapes are same when it is shifted on the center. Einstein's spatial relativity is the relation of time and space conversion by the symmetrically generalization of time and space conversion over the spacial. The left and right helices of plants and animals are the symmetric and have element-wise inverse relationships each other. The weight of center weight Hadamard matrix is 2 and is same as the base 2 of natural logarithm. The helix matrices are symmetric and have element-wise inverses.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2000.10a
• /
• pp.369-376
• /
• 2000

For the general loading condition and boundary condition, it is very difficult to obtain closed-form solutions for buckling loads and natural frequencies of thin-walled structures because its behaviour is very complex due to the coupling effect of bending and torsional behaviour. Consequently most of previous finite element formulations introduced approximate displacement fields using shape functions as Hermitian polynomials, isoparametric interpoation function, and so on. The purpose of this study is to calculate the exact displacement field of a thin-walled straight beam element with the non-symmetric cross section and present a consistent derivation of the exact dynamic stiffness matrix. An exact dynamic element stiffness matrix is established from Vlasov's coupled differential equations for a uniform beam element of non-symmetric thin-walled cross section. This numerical technique is accomplished via a generalized linear eigenvalue problem by introducing 14 displacement parameters and a system of linear algebraic equations with complex matrices. The natural frequencies are evaluated for the non-symmetric thin-walled straight beam structure, and the results are compared with available solutions in order to verify validity and accuracy of the proposed procedures.

• Journal of the Korean Society of Safety
• /
• v.19 no.1
• /
• pp.38-43
• /
• 2004

Many analysis methods, including finite element method, have been suggested and used for assessing the integrity of cracked structures. In the paper, in order to analyze arbitrary three dimensional cracks, the finite element alternating method is extended. The crack is modeled by the symmetric Galerkin boundary element method as a distribution of displacement discontinuities, which is formulated as singularity-reduced integral equations. And the finite element method is used to calculate the stress values for the uncracked body only. Applied the proposed method to several example problems for planner cracks in finite bodies, the accuracy and efficiency of the method were demonstrated.

• Structural Monitoring and Maintenance
• /
• v.6 no.2
• /
• pp.147-159
• /
• 2019

In present article, a size-dependent refined thick beam element has been established based upon nonlocal elasticity theory. Next, it is used to explore vibration response of porous metal foam nanobeams on elastic medium. The established beam element introduces ten degrees of freedom. Different porosity distributions called uniform, symmetric and asymmetric will be employed. Herein, introduced thick beam element contains shear deformations without using correction factors. Convergence and verification studies of obtained results from finite element method are also provided. The impacts of nonlocality factor, foundation factors, shear deformation, slenderness ratio, porosity kinds and porosity factor on vibration frequencies of metal foam nano-sized beams have been explored.

• Communications of the Korean Mathematical Society
• /
• v.39 no.1
• /
• pp.1-10
• /
• 2024

In this paper we will demonstrate some results on a prime ring with involution by introducing two generalized derivations acting on symmetric and skew symmetric elements. This approach allows us to generalize some well known results. Furthermore, we provide examples to show that various restrictions imposed in the hypotheses of our theorems are not superfluous.

• The Transactions of The Korean Institute of Electrical Engineers
• /
• v.56 no.11
• /
• pp.1962-1966
• /
• 2007

Transducer for ultrasonic linear motor with the symmetric and anti-symmetric modes was studied. The ultrasonic linear motor consists of two Langevin type piezoelectric vibrators that cross at right angles with each other in tip. In order to excite symmetric and anti-symmetric resonance modes, the transducer must have a phase shift of 90 degree in space and time. Therefore, the tip of transducer moves on an elliptical motion. In this paper, the finite element analysis was used to optimize dimension and displacement of the transducer. The ultrasonic motor was fabricated using the simulated result and the driving characteristics were measured. No-load velocity was 0.28[m/s] and the maximum efficiency was 30[%] in resonance frequency.

• Structural Engineering and Mechanics
• /
• v.14 no.3
• /
• pp.245-262
• /
• 2002

The free vibration analysis of stiffened laminated composite plates has been performed using the layered (zigzag) finite element method based on the first order shear deformation theory. The layers of the laminated plate is modeled using nine-node isoparametric degenerated flat shell element. The stiffeners are modeled as three-node isoparametric beam elements based on Timoshenko beam theory. Bilinear in-plane displacement constraints are used to maintain the inter-layer continuity. A special lumping technique is used in deriving the lumped mass matrices. The natural frequencies are extracted using the subspace iteration method. Numerical results are presented for unstiffened laminated plates, stiffened isotropic plates, stiffened symmetric angle-ply laminates, stiffened skew-symmetric angle-ply laminates and stiffened skew-symmetric cross-ply laminates. The effects of fiber orientations (ply angles), number of layers, stiffener depths and degrees of orthotropy are examined.

• Structural Engineering and Mechanics
• /
• v.19 no.1
• /
• pp.73-96
• /
• 2005

For the spatially coupled free vibration analysis of shear deformable thin-walled non-symmetric curved beam subjected to initial axial force, an exact dynamic element stiffness matrix of curved beam is evaluated. Firstly equations of motion and force-deformation relations are rigorously derived from the total potential energy for a curved beam element. Next a system of linear algebraic equations are constructed by introducing 14 displacement parameters and transforming the second order simultaneous differential equations into the first order simultaneous differential equations. And then explicit expressions for displacement parameters are numerically evaluated via eigensolutions and the exact $14{\times}14$ dynamic element stiffness matrix is determined using force-deformation relations. To demonstrate the accuracy and the reliability of this study, the spatially coupled natural frequencies of shear deformable thin-walled non-symmetric curved beams subjected to initial axial forces are evaluated and compared with analytical and FE solutions using isoparametric and Hermitian curved beam elements and results by ABAQUS's shell elements.

• Journal of Advanced Marine Engineering and Technology
• /
• v.18 no.4
• /
• pp.69-76
• /
• 1994

Thermal elasto-plastic analysis of axi-symmetric body by the finite element method is presented in this paper for analyzing the process of upset forming of circular section extruded bar. The example of calculation for upset forming of Nimonic extruded bar is also presented. It is shown that remeshing of quadrilateral finite element is necessary because the very highly distorted element by plastic deformation disturbs the calculation. Calculated values for nodal points in new mesh are obtained from nodal points of old mesh by linear interpolation method. The experimental results are compared with calculated values. The appearance of upsetupset forming obtained by experimental method is very similar to that obtained by calculations. So, it is proved that the thermal elasto-plastic analysis of axi-symmetric body by the finite element method is very useful for finding the optimum upsetting condition.

• Journal of Ocean Engineering and Technology
• /
• v.23 no.6
• /
• pp.124-130
• /
• 2009

This study presents a finite element simulation of elastic waves for detecting anti-symmetric damages in an adhesively-bonded single lap joint. Plane strain elements were used for modeling adherents (aluminum) and adhesives (epoxy). Three types of damage were introduced: thickness reduction, elasticity deterioration, and voids in the adhesive layers, and two excitation and reception arrangements (ER1 and ER2) were used to investigate the detectability of the damage. The simulation showed that symmetrically located damage, such as a thickness reduction, can be detected by one excitation and one reception arrangement (ER1) and anti-symmetric damages, such as elasticity deterioration and voids, can be detected by modified two-point elastic wave excitation (ER2). Compared with the ER1 arrangement, the ER2 arrangement does not require a baseline signal for damage detection; hence, an efficient method of anti-symmetric damage detection in an adhesively-bonded single lap joint is proposed.