• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 1997.10a
• /
• pp.190-195
• /
• 1997

Recently it is increased by degrees to construct complex or large lattice type structures such as bridges, towers, cranes, and structures that can be used for space technology. In general, in order to analyze, these structures we have used the finite element method(FEM). In this method, however, it is necessary to use a large amount of computer memory and computation time because the FEM requires many degrees of freedom for solving dynamic problems for these structures. For overcoming this problem, the authors have developed the transfer dynamic stiffness coefficient method(TDSCM). This method is based on the concepts of the transfer and the synthesis of the dynamic stiffness coefficient which is related to force and displacement vector at each node. In this paper, the authors formulate vibration analysis algorithm for a complex and large lattice type structure using the transfer of the dynamic stiffness coefficient. And the validity of TDSCM demonstrated through numerical computational and experimental results.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.20 no.2
• /
• pp.107-121
• /
• 2016

We analyze the complexity of the LLL algorithm, invented by Lenstra, Lenstra, and $Lov{\acute{a}}sz$ as a a well-known lattice reduction (LR) algorithm which is previously known as having the complexity of $O(N^4{\log}B)$ multiplications (or, $O(N^5({\log}B)^2)$ bit operations) for a lattice basis matrix $H({\in}{\mathbb{R}}^{M{\times}N})$ where B is the maximum value among the squared norm of columns of H. This implies that the complexity of the lattice reduction algorithm depends only on the matrix size and the lattice basis norm. However, the matrix structures (i.e., the correlation among the columns) of a given lattice matrix, which is usually measured by its condition number or determinant, can affect the computational complexity of the LR algorithm. In this paper, to see how the matrix structures can affect the LLL algorithm's complexity, we derive a more tight upper bound on the complexity of LLL algorithm in terms of the condition number and determinant of a given lattice matrix. We also analyze the complexities of the LLL updating/downdating schemes using the proposed upper bound.

• Journal of Korean Association for Spatial Structures
• /
• v.3 no.2 s.8
• /
• pp.69-75
• /
• 2003

In case of rectangular lattice dome which shearing rigidity is very small, it has a concern to drop Buckling strength considerably by external force. So, by means of system to increase buckling-strength, there is a method of construction that lattice of dome is one with roof material. In a case like this, shearing rigidity of roof material increases buckling-strength of the whole of structure and can be designed economically from the viewpoint of practice. In case of analysis is achieved considering roof material that adheres to lattice of dame, there is method that considers the rigidity that use effective width frame as method to evaluate rigidity of roof material. therefore, this study is aimed at deciding effective width of roof material united with rectangular lattice dome to evaluate rigidity of roof material by effective width of frame and investigating how much does rigidity of roof material united with lattice of dome increase buckling-strength of the whole of structure according to rise-ratio. Conditions of loading are vertical-type-uniform loading. Analysis method is based on FEM dealing with the geometrically nonlinear deflection problems.

• Steel and Composite Structures
• /
• v.46 no.4
• /
• pp.525-538
• /
• 2023

This paper focuses on the energy absorption of lattice core sandwich structures of different configurations. The diamond lattice unit cell, which has been extensively investigated for energy absorption applications, is the starting point for this research. The energy absorption behaviour of sandwich structures with an expanded metal sheet as the core is investigated at low-velocity impact loading. Numerical simulations were carried out using ABAQUS/EXPLICIT and the results were thoroughly compared with the experimental results, which indicated desirable accuracy. A parametric analysis, using a Box-Behnken design (BBD), as a method for the design of experiments (DOE), was performed. The samples fabricated in three levels of parameters include 0.081, 0.145, and 0.562 mm² Cell sizes, and 0, 45, and 90-degree cell orientation, which were investigated. It was observed from experimental data that the angle of cells orientation had the highest degree of influence on the specific energy absorption. The results showed that the angle of cells orientation has been the most influential parameter to increase the peak forces. The results from using the design expert software showed the optimal specific energy absorption and peak force to be 1786 J/kg and 26314.4 N, respectively. The obtained R2 values and normal probability plots indicated a good agreement between the experimental results and those predicted by the model.

• Journal of the Chungcheong Mathematical Society
• /
• v.20 no.3
• /
• pp.211-221
• /
• 2007

In this paper, we define ${\bigwedge}$-structure, ${\bigvee}$-structure to generalize some lattices, and study the conditions that a lattice which has ${\bigwedge}$-structure or ${\bigvee}$-structure to be continuous or algebraic.

• Korean Journal of Mathematics
• /
• v.32 no.2
• /
• pp.195-211
• /
• 2024

In this paper, we introduce the concept of a fuzzy lattice ordered group, which is based on a fuzzy lattice that Chon developed in his paper "Fuzzy Partial Order Relations and Fuzzy Lattice". We will also discuss fuzzy lattice-ordered groups in detail, provide several results that are analogous to the classical theory of lattice-ordered groups, and characterize the relationship between a fuzzy lattice-ordered group using its level set and support. Moreover, we define the concepts of fl-subgroups, quotients, and cosets of fl-groups and obtain some fundamental results for these fuzzy algebraic structures.

• Journal of the Korean Society of Visualization
• /
• v.17 no.3
• /
• pp.32-38
• /
• 2019

The dynamic stability of swarms is crucial in preventing collisions in clustered flights and safely moving along a defined path. Although there have been many simulation studies on dynamic stability, there have not been many experimental studies using real clusters due to the difficulty in implementation. In this study, we constructed a particle-lattice structure simulating bird flocks or drone swarms, and conducted experiments within turbulent flow. We identified a criterion that describes dynamically stable particle-lattice structures. The stability increased as this newly defined spatial index increased.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2000.11a
• /
• pp.575-580
• /
• 2000

Recently it is increased by degrees to construct complex and large lattice structure such as bridge, tower and crane structures. It is very important problem to know dynamic properties of such structures. Authors presented new dynamic response analysis algorithm for rectilinear structure already. This analysis algorithm is combined transfer stiffness coefficient method with Newmark method. Presented method improves the computational accuracy remarkably owing to advantage of the transfer stiffness coefficient method. This paper formulates dynamic response analysis algorithm for plane lattice structure expanding rectilinear structures.

• Computers and Concrete
• /
• v.2 no.2
• /
• pp.165-176
• /
• 2005

This paper discusses 2D lattice models of beams for simulating the fracture of brittle materials. A simulation of an experiment on a concrete beam subjected to bending, in which two overlapping cracks occur, is used to study the effect of individual beam characteristics and different arrangements of the beams in the overall lattice. It was found that any regular orientation of the beams influences the resulting crack patterns. Methods to implement a wide range of Poisson's ratios are also developed, and the use of the lattice to study arbitrary micro-structures is outlined. The crack patterns that are obtained with lattice are in good agreement with the experimental results. Also, numerical simulations of the tests were performed by means of a lattice model, and non-integer dimensions were measured on the predicted lattice damage patterns.

• Composites Research
• /
• v.34 no.2
• /
• pp.129-135
• /
• 2021

In this paper, in order to examine the effect of fiber volume fraction non-uniformity in thickness direction on the buckling load of cylindrical composite lattice structures, we modified the equation of buckling load of the cylindrical composite lattice structures proposed by Vasiliev. The thickness of each layer of the rib was varied by fiber volume fraction, and material properties were applied differently by using the rule of mixture. Also, we performed linear buckling analysis by varying the structure size, thickness, and average value of the fiber volume fraction of finite element model. Finally, by comparing the calculation results of the buckling load of the equivalent model using the modified buckling load equation and the results of the finite element analysis, we found that the fiber volume fraction non-uniformity in thickness direction can reduce the buckling load of the cylindrical composite lattice structure.