• Computers and Concrete
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• v.7 no.6
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• pp.483-496
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• 2010

This work deals with the determination of crack openings in 2D reinforced concrete structures using the Finite Element Method with a smeared rotating crack model or an embedded crack model. In the smeared crack model, the strong discontinuity associated with the crack is spread throughout the finite element. As is well known, the continuity of the displacement field assumed for these models is incompatible with the actual discontinuity. However, this type of model has been used extensively due to the relative computational simplicity it provides by treating cracks in a continuum framework, as well as the reportedly good predictions of reinforced concrete members' structural behavior. On the other hand, by enriching the displacement field within each finite element crossed by the crack path, the embedded crack model is able to describe the effects of actual discontinuities (cracks). This paper presents a comparative study of the abilities of these 2D models in predicting the mechanical behavior of reinforced concrete structures. Structural responses are compared with experimental results from the literature, including crack patterns, crack openings and rebar stresses predicted by both models.

• Coupled systems mechanics
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• v.9 no.4
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• pp.311-323
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• 2020

This paper deals with the effect of the mode shapes on the dynamic response of a multi-storey frame subjected to moving train loads which are modelled as loads of constant intervals with constant velocity using the finite element method. The multi-storey frame is modelled as a number of Bernoulli-Euler beam elements. First, the first few modes of the multi-storey frame are determined. Then, the effects of force span length to beam length ratio and velocity on dynamic magnification factor (DMF) are evaluated via 3D velocity-force span length to beam length ratio-DMF graphics and its 2D projections. By using 3D and 2D graphics, the directions of critical speeds that force the structure under resonance conditions are determined. Last, the mode shapes related to these directions are determined by the time history and frequency response graphs. This study has been limited by the vibration of the frame in the vertical direction.

• Journal of the Korean Mathematical Society
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• v.56 no.2
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• pp.539-558
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• 2019

An ideal of a commutative ring is called a d-ideal if it contains the annihilator of the annihilator of each of its elements. Denote by DId(A) the lattice of d-ideals of a ring A. We prove that, as in the case of f-rings, DId(A) is an algebraic frame. Call a ring homomorphism "compatible" if it maps equally annihilated elements in its domain to equally annihilated elements in the codomain. Denote by $SdRng_c$ the category whose objects are rings in which the sum of two d-ideals is a d-ideal, and whose morphisms are compatible ring homomorphisms. We show that $DId:\;SdRng_c{\rightarrow}CohFrm$ is a functor (CohFrm is the category of coherent frames with coherent maps), and we construct a natural transformation $RId{\rightarrow}DId$, in a most natural way, where RId is the functor that sends a ring to its frame of radical ideals. We prove that a ring A is a Baer ring if and only if it belongs to the category $SdRng_c$ and DId(A) is isomorphic to the frame of ideals of the Boolean algebra of idempotents of A. We end by showing that the category $SdRng_c$ has finite products.

• Structural Engineering and Mechanics
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• v.19 no.6
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• pp.619-637
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• 2005

The objective of this research was to determine the Vlasov soil parameters for quadratically varying elasticity modulus $E_s$(z) of the compressible soil continuum and discuss the interaction affect between two close plates. Interaction problem carried on for uniformly distributed load carrying plates. Plate region was simulated by Kirchhoff plate theory based (mixed or displacement type) 2D elements and the foundation continuum was simulated by displacement type 2D elements. At the contact region, plate and foundation elements were geometrically coupled with each other. In this study the necessary formulas for the Vlasov parameters were derived when Young's modulus of the soil continuum was varying as a quadratic function of z-coordinate through the depth of the foundation. In the examples, first the elements and the iterative FE algorithm was verified and later the results of quadratic variation of $E_s$(z) were compared with the previous examples in order to discuss the general behavior. As a final example two plates close to each other resting on elastic foundation were handled to see their interaction influences on the Vlasov foundation parameters. Original examples were solved using both mixed and displacement type plate elements in order to confirm the results.

• Computers and Concrete
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• v.2 no.5
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• pp.345-366
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• 2005

This work presents an assessment of the computational performance of a vector-parallel implementation of probabilistic model for concrete cracking in 3D. This paper shows the continuing efforts towards code optimization as reported in earlier works Paz, et al. (2002a,b and 2003). The probabilistic crack approach is based on the direct Monte Carlo method. Cracking is accounted by means of 3D interface elements. This approach considers that all nonlinearities are restricted to interface elements modeling cracks. The heterogeneity governs the overall cracking behavior and related size effects on concrete fracture. Computational kernels in the implementation are the inexact Newton iterative driver to solve the non-linear problem and a preconditioned conjugate gradient (PCG) driver to solve linearized equations, using an element by element (EBE) strategy to compute matrix-vector products. In particular the paper analyzes code behavior using OpenMP directives in parallel vector processors (PVP), such as the CRAY SV1 and CRAY T94. The impact of the memory architecture on code performance, and also some strategies devised to circumvent this issue are addressed by numerical experiment.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.13 no.5
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• pp.29-37
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• 1993

The extension of the weighted integral method in the area of stochastic finite element analysis is presented. The use of weighted integral method in numerical analysis was extended to CST(constant strain triangle) element by Deodatis to calculate the response variability of 2D stochastic systems. In this paper, the extension of the weighted integral method for general plane-elements is represented. It has been shown that the same mesh used in the deterministic FE analysis can be used in the stochastic FE analysis. Furthermore, because the CST element is a special case which has constant strain-displacement matrix the mingling of CST elements with the other quadrilateral elements in the analysis may also be possible.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.8 s.239
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• pp.1078-1084
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• 2005

The relationship between fatigue crack opening behavior and the reversed plastic zone sizes is studied. An elastic-plastic finite element analysis (FEA) is performed to examine the opening behavior of fatigue crack, where the contact elements are used in the mesh of the track tip area. The smaller element size than reversed plastic zone size is used fer evaluating the distribution of reversed plastic zone. In the author's previous results the FEA could predict the crack opening level, which crack tip elements were in proportion to the theoretical reversed plastic zone size. It is found that the calculated reversed plastic zone size is related to the theoretical reversed plastic zone size and crack opening level. The calculated reversed plastic zone sizes are almost equal to the reversed plastic zone considering crack opening level obtained by experimental results. It can be possible to predict the crack opening level from the reversed plastic zone size calculated by finite element method. We find that the experimental crack opening levels correspond with the opening values of contact nodes on the calculated reversed plastic zone of finite element simulation.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.403-410
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• 2006

For a finite group G, #Cent(G) denotes the number of centralizers of its elements. A group G is called n-centralizer if #Cent(G) = n, and primitive n-centralizer if #Cent(G) = #Cent($\frac{G}{Z(G)}$) = n. The first author in [1], characterized the primitive 6-centralizer finite groups. In this paper we continue this problem and characterize the primitive 7-centralizer finite groups. We prove that a finite group G is primitive 7-centralizer if and only if $\frac{G}{Z(G)}{\simeq}D_{10}$ or R, where R is the semidirect product of a cyclic group of order 5 by a cyclic group of order 4 acting faithfully. Also, we compute #Cent(G) for some finite groups, using the structure of G modulu its center.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.6 no.2
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• pp.144-149
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• 2006

This paper describes a novel automated analysis system for bellows of piping system. An automatic finite element (FE) mesh generation technique, which is based on the fuzzy theory and computational geometry technique, is incorporated into the system, together with one of commercial FE analysis codes and one of commercial solid modelers. In this system, a geometric model, i.e. an analysis model, is first defined using a commercial solid modelers for 3-D shell structures. Node is generated if its distance from existing node points is similar to the node spacing function at the point. The node spacing function is well controlled by the fuzzy knowledge processing. The Delaunay triangulation technique is introduced as a basic tool for element generation. The triangular elements are converted to quadrilateral elements. Practical performances of the present system are demonstrated through several analysis for bellows of piping system.

• Proceedings of the KIEE Conference
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• 2005.10c
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• pp.107-109
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• 2005

This paper presents the development of the magnetic position sensor for servo motor. The magnetization system is designed for the sinusoidal magnetic flux density distribution from permanent magnet using 2D finite element method and Preisach model. The magnetic position sensor is composed of the permanent magnet and two Hall elements. And the algorithm calculating the rotating position is suggested by the phase difference of outputs of Hall elements.