• Structural Engineering and Mechanics
• /
• v.18 no.2
• /
• pp.137-150
• /
• 2004

The optimization of active bars' placement and feedback gains of closed loop control system for random intelligent truss structures under non-stationary random excitation is presented. Firstly, the optimal mathematical model with the reliability constraints on the mean square value of structural dynamic displacement and stress response are built based on the maximization of dissipation energy due to control action. In which not only the randomness of the physics parameters of structural materials, geometric dimensions and structural damping are considered simultaneously, but also the applied force are considered as non-stationary random excitation. Then, the numerical characteristics of the stationary random responses of random intelligent structure are developed. Finally, the rationality and validity of the presented model are demonstrated by an engineering example and some useful conclusions are obtained.

• Journal of Korean Association for Spatial Structures
• /
• v.20 no.4
• /
• pp.35-44
• /
• 2020

In the study, a shape finding procedure for the tensegrity system model inspired by the movement pattern of animal backbone was presented. The proposed system is allowing a dynamic movement by introducing the concept of "saddle" for the variable tensegrity structure. Mathematical process and an algorithm for movable tensegrity to specified points were established. Several examples have applied with in established shape finding analysis procedure. The final tensegrity structures were determined well to a object shape.

• Earthquakes and Structures
• /
• v.24 no.6
• /
• pp.405-413
• /
• 2023

Various methods have been used to strengthen structures against earthquakes. Isolator systems are among the methods to control the structure's response. Instead of increasing the strength and capacity of the structure, these systems react to earthquakes. In this paper, an isolator system was investigated with the flexible piers of ∨ and ∧ elements, which were perpendicular to each other and connected by a rod hinged at both ends. The behavior of the isolator system was studied. Many structures have non-rigid connections; the effect of this issue was considered in the pendulum column's performance in this paper. Its mathematical equations were derived, solved with MATLAB software, and compared with ABAQUS results. Later on, the isolator system was investigated during different earthquakes. The results show that this mechanism is suitable as an isolator. The period was found to be longer in the flexible pier form. The flexible piers have an influential role in the system's response by reducing the system's stiffness considerably. Among the different damping ratios, those with more than 15% had better results. Finally, the tested model verified the theory.

• Steel and Composite Structures
• /
• v.51 no.3
• /
• pp.261-270
• /
• 2024

This paper proposes an effective method for optimizing the structure of functionally graded isotropic and incompressible linear elastic materials. The main emphasis is on utilizing a specialized polytopal composite finite element (PCE) technique capable of handling a broad range of materials, addressing common volumetric locking issues found in nearly incompressible substances. Additionally, it employs a continuum model for bi-directional functionally graded (BFG) material properties, amalgamating these aspects into a unified property function. This study thus provides an innovative approach that tackles diverse material challenges, accommodating various elemental shapes like triangles, quadrilaterals, and polygons across compressible and nearly incompressible material properties. The paper thoroughly details the mathematical formulations for optimizing the topology of BFG structures with various materials. Finally, it showcases the effectiveness and efficiency of the proposed method through numerous numerical examples.

• Communications of Mathematical Education
• /
• v.31 no.3
• /
• pp.279-290
• /
• 2017

This study proposes a self learning material for understanding the key contents of Galois theory. This material is for teachers who have learned algebraic structures like group, field, and vector space which are related with Galois theory but do not clearly understand how algebraic structures are related with the solvability of polynomials and school mathematics. This material is likely to help them to overcome such difficulties. Even though proposed material is used mainly for self learning, the teachers may be helped once or twice by some professionals. In this article, two expressions 'solvability of polynomial' and 'solvability of equation' have the same meaning and 'teacher' means in-service mathematics teacher.

• Smart Structures and Systems
• /
• v.11 no.1
• /
• pp.35-51
• /
• 2013

Over the last two decades Wavelet Transformation (WT) method has been widely utilized for the damage identification of structures. The main objective of this paper is to discuss and present some of common shortcomings and limitations of mathematical software, as well as other precautionary measures that need to be considered when using them for wavelet analysis applications. Due to popular usage of MATLABMATLAB(R) comparing to other mathematical tools among researchers for data processing of structural responses through WT analysis, this software was chosen for specific study. To the best of the authors' knowledge, these limitations and observations have not been previously identified or discussed in the literature. In this work, a square plate with a severe damage, in form of a crack, parallel to the left edge of the plate is selected for a pilot study. The steady state harmonic response is used for measuring the deflection shape across the line parallel to one edge and perpendicular to the damage. Several criteria and cases such as the smallest size damage that can be detected, correlation between the crack width and the number of sampling points, and the influence of the damage thickness on the accuracy of the result are investigated.

• Structural Engineering and Mechanics
• /
• v.19 no.5
• /
• pp.551-566
• /
• 2005

Using two different, but related approaches, an exact dynamic stiffness matrix for a two-part beam-mass system is developed from the free vibration theory of a Bernoulli-Euler beam. The first approach is based on matrix transformation while the second one is a direct approach in which the kinematical conditions at the interfaces of the two-part beam-mass system are satisfied. Both procedures allow an exact free vibration analysis of structures such as a plane or a space frame, consisting of one or more two-part beam-mass systems. The two-part beam-mass system described in this paper is essentially a structural member consisting of two different beam segments between which there is a rigid mass element that may have rotatory inertia. Numerical checks to show that the two methods generate identical dynamic stiffness matrices were performed for a wide range of frequency values. Once the dynamic stiffness matrix is obtained using any of the two methods, the Wittrick-Williams algorithm is applied to compute the natural frequencies of some frameworks consisting of two-part beam-mass systems. Numerical results are discussed and the paper concludes with some remarks.

• Journal of Educational Research in Mathematics
• /
• v.19 no.1
• /
• pp.63-80
• /
• 2009

This paper has a purpose to find out the important points about linguistic factors suited to the assessment purpose and mathematics teaching/learning that a word-problem sentence has to possess. We also examine the degree of understanding of sentence and the perceptive/emotional reactions of students toward two different kinds of word-problem sentences that have same mathematical contents, but different linguistic structures. The objects of this thesis are 124 students from the third to sixth grade in an elementary school. We execute assessment of simple-sentence-word-problem and complex-sentence-word-problem that have same mathematical contexts, but different linguistic structures. Then we have compared and examined their own process of solving the two types word-problems and we make up questionnaire and have an interview with them. The conclusions are as followings: First, simple-sentence-word-problem is more successful to suggest an information for solving a problem than complex one. Second, it is hard to find the strategy for solving a problem in complex-sentence-word-problem than simple one. Third, students think that suggested information and mathematical knowledge are different according to the linguistic structure in the process of perceiving the information after reading a word-problem. Fourth, in spite of same sentence type, the negative mental reaction is showed greatly to complex-sentence-word-problem even before solving a problem.

• Honam Mathematical Journal
• /
• v.36 no.3
• /
• pp.569-596
• /
• 2014

In several applied disciplines like control engineering, computer sciences, error-correcting codes and fuzzy automata theory, the use of fuzzied algebraic structures especially ordered semi-groups and their fuzzy subsystems play a remarkable role. In this paper, we introduce the notion of (${\in},{\in}{\vee}\bar{q}_k$)-fuzzy subsystems of ordered semigroups namely (${\in},{\in}{\vee}\bar{q}_k$)-fuzzy generalized bi-ideals of ordered semigroups. The important milestone of the present paper is to link ordinary generalized bi-ideals and (${\in},{\in}{\vee}\bar{q}_k$)-fuzzy generalized bi-ideals. Moreover, different classes of ordered semi-groups such as regular and left weakly regular ordered semigroups are characterized by the properties of this new notion. Finally, the upper part of a (${\in},{\in}{\vee}\bar{q}_k$)-fuzzy generalized bi-ideal is defined and some characterizations are discussed.

• Wind and Structures
• /
• v.18 no.3
• /
• pp.295-320
• /
• 2014

The characteristics of amplitudes and power spectra of X axial, Y axial, and RZ axial (i.e., body axis) wind forces on a 492 m high-rise building with a section varying along height in typical wind directions are studied via a rigid model wind tunnel test of pressure measurement. Then the corresponding mathematical expressions of power spectra of X axial (across-wind), Y axial (along-wind) and torsional wind forces in $315^{\circ}$ wind directions are proposed. The investigation shows that the mathematical expressions of wind force spectra of the main structure in across-wind and torsional directions can be constructed by the superimposition of an modified wind spectrum function and a peak function caused by turbulent flow and vortex shedding, respectively. While that in along-wind direction can only be constructed by the former and is similar to wind spectrum. Moreover, the fitted parameters of the wind load spectra of each measurement level of altitude are summarized, and the unified parametric results are obtained. The comparisons of the first three order generalized force spectra show that the proposed mathematical expressions accord with the experimental results well.