• Title/Summary/Keyword: Closed form solution

Search Result 447, Processing Time 0.025 seconds

Study on stability and free vibration behavior of porous FGM beams

  • Bennai, Riadh;Atmane, Redhwane Ait;Bernard, Fabrice;Nebab, Mokhtar;Mahmoudi, Noureddine;Atmane, Hassen Ait;Aldosari, Salem Mohammed;Tounsi, Abdelouahed
    • Steel and Composite Structures
    • /
    • v.45 no.1
    • /
    • pp.67-82
    • /
    • 2022
  • In this paper, buckling and free vibration of imperfect, functionally graded beams, including porosities, are investigated, using a higher order shear strain theory. Due to defects during the manufacturing process, micro porosities may appear in the material, hence the appearance of this imperfection in the structure. The material properties of the beams are assumed to vary regularly, with power and sigmoid law, in the direction of thickness. A novel porosity distribution affecting the functionally graded volume fraction is presented. For the compact formulation used for cementite-based materials and already used in P-FGM, we have adapted it for the distribution of S-FGM. The equations of motion in the FG beam are derived using Hamilton's principle. The boundary conditions for beam FG are assumed to be simply supported. Navier's solution is used to obtain the closed form solutions of the FG beam. The numerical results of this work are compared with those of other published research to verify accuracy and reliability. The comparisons of different shear shape functions, the influence of porosity, thickness and inhomogeneity parameters on buckling and free vibration of the FG beam are all discussed. It is established that the present work is more precise than certain theories developed previously.

On the free vibration behavior of carbon nanotube reinforced nanocomposite shells: A novel integral higher order shear theory approach

  • Mohammed Houssem Eddine Guerine;Zakaria Belabed;Abdelouahed Tounsi;Sherain M.Y. Mohamed;Saad Althobaiti;Mahmoud M. Selim
    • Structural Engineering and Mechanics
    • /
    • v.91 no.1
    • /
    • pp.1-23
    • /
    • 2024
  • This paper formulates a new integral shear deformation shell theory to investigate the free vibration response of carbon nanotube (CNT) reinforced structures with only four independent variables, unlike existing shell theories, which invariably and implicitly induce a host of unknowns. This approach guarantees traction-free boundary conditions without shear correction factors, using a non-polynomial hyperbolic warping function for transverse shear deformation and stress. By introducing undetermined integral terms, it will be possible to derive the motion equations with a low order of differentiation, which can facilitate a closed-form solution in conjunction with Navier's procedure. The mechanical properties of the CNT reinforcements are modeled to vary smoothly and gradually through the thickness coordinate, exhibiting different distribution patterns. A comparison study is performed to prove the efficacy of the formulated shell theory via obtained results from existing literature. Further numerical investigations are current and comprehensive in detailing the effects of CNT distribution patterns, volume fractions, and geometrical configurations on the fundamental frequencies of CNT-reinforced nanocomposite shells present here. The current shell theory is assumed to serve as a potent conceptual framework for designing reinforced structures and assessing their mechanical behavior.

A Study on the Penetration Characteristics of a Steel Fragment Impacting on the Target Plate of Aluminum 2024 (알루미늄 2024 표적에 대한 HE 탄두 파편의 관통 특성 연구)

  • Kim, Deuksu;Kang, Sunbu;Jung, Daehan;Chung, Youngjin;Park, Yongheon;Park, Seikwon;Hwang, Changsu
    • Journal of the Korean Society for Aeronautical & Space Sciences
    • /
    • v.46 no.3
    • /
    • pp.257-268
    • /
    • 2018
  • We have studied the damage mechanism of a metallic thin plate by the highly energetic fragments generated from high explosive(HE) warhead. The penetration process has presumed that the velocity of a fragment is in the range of 350 m/s to 3353 m/s, the thickness of Aluminum 2024 target plate is in the range of 1 mm~6.3 mm thick. The mass of fragment with hemisphere nose shape is in the range of 0.32 g to 16 g. The analytical solution for penetration process has been derived by using the report of the project THOR. The results of analysis implied that the closed forms by an exponentially decay function well fit the change of the ballistic limit velocity, loss velocity and loss mass of fragment as the mass of fragment and the thickness of target plate increase.

IBN-based: AI-driven Multi-Domain e2e Network Orchestration Approach (IBN 기반: AI 기반 멀티 도메인 네트워크 슬라이싱 접근법)

  • Khan, Talha Ahmed;Muhammad, Afaq;Abbas, Khizar;Song, Wang-Cheol
    • KNOM Review
    • /
    • v.23 no.2
    • /
    • pp.29-41
    • /
    • 2020
  • Networks are growing faster than ever before causing a multi-domain complexity. The diversity, variety and dynamic nature of network traffic and services require enhanced orchestration and management approaches. While many standard orchestrators and network operators are resulting in an increase of complexity for handling E2E slice orchestration. Besides, there are multiple domains involved in E2E slice orchestration including access, edge, transport and core network each having their specific challenges. Hence, handling of multi-domain, multi-platform and multi-operator based networking environments manually requires specified experts and using this approach it is impossible to handle the dynamic changes in the network at runtime. Also, the manual approaches towards handling such complexity is always error-prone and tedious. Hence, this work proposes an automated and abstracted solution for handling E2E slice orchestration using an intent-based approach. It abstracts the domains from the operators and enable them to provide their orchestration intention in the form of high-level intents. Besides, it actively monitors the orchestrated resources and based on current monitoring stats using the machine learning it predicts future utilization of resources for updating the system states. Resulting in a closed-loop automated E2E network orchestration and management system.

Closed Integral Form Expansion for the Highly Efficient Analysis of Fiber Raman Amplifier (라만증폭기의 효율적인 성능분석을 위한 라만방정식의 적분형 전개와 수치해석 알고리즘)

  • Choi, Lark-Kwon;Park, Jae-Hyoung;Kim, Pil-Han;Park, Jong-Han;Park, Nam-Kyoo
    • Korean Journal of Optics and Photonics
    • /
    • v.16 no.3
    • /
    • pp.182-190
    • /
    • 2005
  • The fiber Raman amplifier(FRA) is a distinctly advantageous technology. Due to its wider, flexible gain bandwidth, and intrinsically lower noise characteristics, FRA has become an indispensable technology of today. Various FRA modeling methods, with different levels of convergence speed and accuracy, have been proposed in order to gain valuable insights for the FRA dynamics and optimum design before real implementation. Still, all these approaches share the common platform of coupled ordinary differential equations(ODE) for the Raman equation set that must be solved along the long length of fiber propagation axis. The ODE platform has classically set the bar for achievable convergence speed, resulting exhaustive calculation efforts. In this work, we propose an alternative, highly efficient framework for FRA analysis. In treating the Raman gain as the perturbation factor in an adiabatic process, we achieved implementation of the algorithm by deriving a recursive relation for the integrals of power inside fiber with the effective length and by constructing a matrix formalism for the solution of the given FRA problem. Finally, by adiabatically turning on the Raman process in the fiber as increasing the order of iterations, the FRA solution can be obtained along the iteration axis for the whole length of fiber rather than along the fiber propagation axis, enabling faster convergence speed, at the equivalent accuracy achievable with the methods based on coupled ODEs. Performance comparison in all co-, counter-, bi-directionally pumped multi-channel FRA shows more than 102 times faster with the convergence speed of the Average power method at the same level of accuracy(relative deviation < 0.03dB).

Comparative Study on the Applicability of Point Estimate Methods in Combination with Numerical Analysis for the Probabilistic Reliability Assessment of Underground Structures (수치해석과 연계한 지하구조물의 확률론적 신뢰성 평가를 위한 점추정법의 적용성에 관한 비교 연구)

  • Park, Do-Hyun;Kim, Hyung-Mok;Ryu, Dong-Woo;Choi, Byung-Hee;Han, Kong-Chang
    • Tunnel and Underground Space
    • /
    • v.22 no.2
    • /
    • pp.86-92
    • /
    • 2012
  • Point estimate method has a less accuracy than Monte Carlo simulation that is usually considered as an exact probabilistic method, but this method still remains popular in probability-based reliability assessment in geotechnical and rock engineering, because it significantly reduce the number of sampling points and produces the statistical moments of a performance function in a reasonable accuracy. In the present study, we investigated the accuracy and applicability of point estimate methods proposed by Rosenblueth and Zhou & Nowak by comparing the results of these two methods with those of Monte Carlo simulations. The comparison was carried out for the problem of a lined circular tunnel in an elastic medium where an closed-form analytical solution is given. The comparison results showed that despite the non-linearity of the analytical solution, the statistical moments calculated by the point estimate methods and the Monte Carlo simulations agreed well with an average error of roughly 1-2%. This average error demonstrates the applicability of the two point estimate methods for the probabilistic reliability assessment of underground structures in combination with numerical analysis.

An Analytical Study on the Buckling of Orthotropic Plates and Local Buckling of Compression Members (직교이방성 판의 좌굴 및 압축재의 국부좌굴에 대한 해석적 연구)

  • Choi, Jin-Woo;Lee, Kang-Yeon;Park, Jung-Hwan;Yoon, Soon-Jong
    • Journal of the Korean Society for Advanced Composite Structures
    • /
    • v.3 no.1
    • /
    • pp.21-28
    • /
    • 2012
  • In this paper, we present the analytical study results pertaining to the buckling of the orthotropic plates and local buckling of structural compression members composed of orthotropic plate components. Fiber reinforced polymeric plastic (FRP) materials, have many advantages over conventional structural materials such as steel and concrete. The advantages of the FRP materials are high specific strength and stiffness, high corrosion resistance, right weight, etc. Among the various manufacturing methods, pultrusion process is one of the best choices for the mass production of structural plastic members. Since the major reinforcing fibers are placed along the axial direction of the member, this material is usually considered as an orthotropic (tranversely isotropic, more specifically) material. However, pultruded fiber reinforced plastic structural members have low modulus of elasticity and are composed of orthotropic thin plate components the members are prone to buckle. Therefore, stability is an important issue in the design of the pultruded FRP structural members. In this paper, the buckling of orthotropic plates and the local buckling of pultruded FRP structural members are investigated by following the previous research results and the local buckling strength of the member produced in the domestic manufacturer is found.

Initial Risk Assessment of Acetanilide in OECD High Production Volume Chemical Program

  • Park, Hye-Youn;Park, Yoonho;Sanghwan Song;Kwon, Min-Jeoung;Koo, Hyun-Ju;Jeon, Seong-Hwan;Na, Jin-Gyun;Park, Kwangsik
    • Toxicological Research
    • /
    • v.18 no.1
    • /
    • pp.13-22
    • /
    • 2002
  • In Korea, 2,320 tonnes of acetanilide were mostly wed as intermediates for synthesis in phar-maceuticals or additives in synthesizing hydrogen peroxide, varnishes, polymers and rubber. Only small amount of 120 kg were wed as a stabilizer for hydrogen peroxide solution for hair colouring agents in 1998. Readily available environmental or human exposure data do not exist in Korea at the present time. However, potential human exposures from drinking water, food, ambient water and in work places are expected to be negligible because this chemical is produced in the closed system in only one company in Korea and the processing factory is equipped with local ventilation and air filtering system. Acetanilide could be distributed mainly to water based on EQC model. This substance is readily biodegradable and its bioaccumulation is low. Acute toxicity of acetanilide is low since the L $D_{50}$ of oral exposure in rats is 1,959 mg/kg bw. The chemical is not irritating to skin, but slightly irritating to the eyes of rabbits. horn repeated dose toxicity, the adverse effects in rats were red pulp hyperplasia of spleen, bone marrow hyperplasia of femur and decreased hemoglobin, hematocrit and mean corpuscular hemoglobin concentration. The LOAEL for repeated dose toxicity in rats was 22 mg/kg/day for both sexes. Acetanilide is not considered to be genotoxic. In a reproductive/developmental toxicity study, no treatment-related changes in precoital time and rate of copulation, impregnation, pregnancy were shown in all treated groups. The NOAELs for reproduction and developmental toxicity (off-spring toxicity) are considered to be 200 mg/kg bw/day and 67 mg/kg bw/day, respectively. Ecotoxicity data has been generated in a limited number of aquatic species of algae (72 hr- $E_{b}$ $C_{50}$; 13.5 mg/l), daphnid (48hr-E $C_{50}$ > 100 mg/l) and fish (Oryzias latipes, 96hr-L $C_{50}$; 100 mg/l). Form the acute toxicity values, the predicted no effect concentration (PNEC) of 0.135 mg/1 was derived win an assessment factor of 100. On the basis of these data, acetanilide was suggested as currently of low priority for further post-SIDS work in OECD.in OECD.D.

Prediction of ground-condition ahead of tunnel face using electromagnetic wave - analytical study (전자기파를 이용한 터널전방 예측 -해석기법 중심으로)

  • Choi, Jun-Su;Cho, Gye-Chun;Lee, Geun-Ha;Yoon, Ji-Nam
    • Journal of Korean Tunnelling and Underground Space Association
    • /
    • v.6 no.4
    • /
    • pp.327-343
    • /
    • 2004
  • During tunnel construction, ground failures often occur due to existence of weak zones, such as faults, joints, and cavities, ahead of tunnel face. It is hard to detect effectively weak zones, which can lead underground structure to fail after excavation and before supporting, by using conventional characterization methods. In this study, an enhanced analytical method of predicting weak zones ahead of tunnel face is developed to overcome some problems in the conventional geophysical exploration methods. The analytical method is based on Coulomb's and Gauss' laws with considering the characteristics of electric fields subjected to rock mass. Using the developed method, closed form solutions are obtained to detect a spherical shaped zone and an oriented fault ahead of tunnel face respectively. The analytical results suggest that the presence of weak zones and their sizes, location, and states can be accurately predicted by combining a proper inversion process with resistance measured from several electrodes on the tunnel face. It appears that the skin depth or resistivity in rock mass is affected by the diameter of tunnel face, natural electric potential and noises induced by experimental measurement and spatial distribution of uncertain properties. The developed analytical solution is verified through experimental tests. About 1800 concrete blocks of 5cm by 5cm by 5cm in size are prepared and used to model a joint rock mass around tunnel face. Weak zones are simulated ahead of tunnel face with a material which has relatively higher conductivity than concrete blocks. Experimental results on the model test show a good agreement with analytical results.

  • PDF

Two-step Scheduling With Reduced Feedback Overhead in Multiuser Relay Systems (다중 사용자 릴레이 시스템에서 감소된 피드백 정보를 이용한 두 단계 스케줄링 기법)

  • Jang, Yong-Up;Shin, Won-Yong;Kim, A-Jung
    • The Journal of Korean Institute of Communications and Information Sciences
    • /
    • v.36 no.5A
    • /
    • pp.511-520
    • /
    • 2011
  • In this paper, we introduce a multiuser (MU) scheduling method for multiuser amplify-and-forward relay systems, which selects both the transmission mode, i.e., either one- or two-hop transmission, and the desired user via two steps. A closed-form expression for the average achievable rate of the proposed scheduling is derived under two transmission modes with MU scheduling, and its asymptotic solution is also analyzed in the limit of large number of mobile stations. Based on the analysis, we perform our two-step scheduling algorithm: the transmission mode selection followed by the user selection that needs partial feedback for instantaneous signal-to-noise ratios (SNRs) to the base station. We also analyze the average SNR condition such that the MU diversity gain is fully exploited. In addition, it is examined how to further reduce a quantity of feedback under certain conditions. The proposed algorithm shows the comparable achievable rate to that of the optimal one using full feedback information, while its required feedback overhead is reduced below half of the optimal one.