• 제목/요약/키워드: Mathematical Models

검색결과 1,812건 처리시간 0.022초

A semi-analytical procedure for cross section effect on the buckling and dynamic stability of composite imperfect truncated conical microbeam

  • Zhang, Peng;Gao, Yanan;Moradi, Zohre;Ali, Yasar Ameer;Khadimallah, Mohamed Amine
    • Steel and Composite Structures
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    • 제44권3호
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    • pp.371-388
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    • 2022
  • The present study tackles the problem of forced vibration of imperfect axially functionally graded shell structure with truncated conical geometry. The linear and nonlinear large-deflection of the structure are considered in the mathematical formulation using von-Kármán models. Modified coupled stress method and principle of minimum virtual work are employed in the modeling to obtain the final governing equations. In addition, formulations of classical elasticity theory are also presented. Different functions, including the linear, convex, and exponential cross-section shapes, are considered in the grading material modeling along the thickness direction. The grading properties of the material are a direct result of the porosity change in the thickness direction. Vibration responses of the structure are calculated using the semi-analytical method of a couple of homotopy perturbation methods (HPM) and the generalized differential quadrature method (GDQM). Contradicting effects of small-scale, porosity, and volume fraction parameters on the nonlinear amplitude, frequency ratio, dynamic deflection, resonance frequency, and natural frequency are observed for shell structure under various boundary conditions.

Hysteretic model of isolator gap damper system and its equivalent linearization for random earthquake response analysis

  • Zhang, Hongmei;Gu, Chen
    • Smart Structures and Systems
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    • 제29권3호
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    • pp.485-498
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    • 2022
  • In near-fault earthquake prone areas, the velocity pulse-like seismic waves often results in excessive horizontal displacement for structures, which may result in severe structural failure during large or near-fault earthquakes. The recently developed isolator-gap damper (IGD) systems provide a solution for the large horizontal displacement of long period base-isolated structures. However, the hysteresis characteristics of the IGD system are significantly different from the traditional hysteretic behavior. At present, the hysteretic behavior is difficult to be reflected in the structural analysis and performance evaluation especially under random earthquake excitations for lacking of effective analysis models which prevent the application of this kind of IGD system. In this paper, we propose a mathematical hysteretic model for the IGD system that presents its nonlinear hysteretic characteristics. The equivalent linearization is conducted on this nonlinear model, which requires the variances of the IGD responses. The covariance matrix for the responses of the structure and the IGD system is obtained for random earthquake excitations represented by the Kanai-Tajimi spectrum by solving the Lyapunov equation. The responses obtained by the equivalent linearization are verified in comparison with the nonlinear responses by the Monte Carlo simulation (MCS) analysis for random earthquake excitations.

Monitoring and vibration control of a fluid catalytic cracking unit

  • Battista, Ronaldo C.;Varela, Wendell D.;Gonzaga, Igor Braz N.
    • Smart Structures and Systems
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    • 제29권4호
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    • pp.577-588
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    • 2022
  • Oil refineries' Fluid Catalytic Cracking Units (FCCU) when in full operation may exhibit strong fluid dynamics caused by turbulent flow in the piping system that may induce vibrations in other mechanical and structural components of the Unity. This paper reports on the experimental-theoretical-computational program performed to get the vibration properties and the dynamic response amplitudes to find out alternative solutions to attenuate the excessive vibrations that were causing fatigue fractures in components of the bottle like reactor-regenerator of an FCC unit in operation in an existing oil refinery in Brazil. Solutions to the vibration problem were sought with the aid of a 3D finite element model calibrated with the results obtained from experimental measurements. A short description of the found solutions is given and their effectiveness are shown by means of numerical results. The solutions were guided by the concepts of structural stiffening and dynamic control performed by a nonlinear pendulum controller whose mechanical design was based on parameters determined by means of a parametric study carried out with 2D and 3D mathematical models of the coupled pendulum-structure system. The effectiveness of the proposed solutions is evaluated in terms of the fatigue life of critical welded connections.

Evolution of post-peak localized strain field of steel under quasi-static uniaxial tension: Analytical study

  • Altai, Saif L.;Orton, Sarah L.;Chen, Zhen
    • Structural Engineering and Mechanics
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    • 제83권4호
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    • pp.435-449
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    • 2022
  • Constitutive modeling that could reasonably predict and effectively evaluate the post-peak structural behavior while eliminating the mesh-dependency in numerical simulation remains to be developed for general engineering applications. Based on the previous work, a simple one-dimensional modeling procedure is proposed to predict and evaluate the post-peak response, as characterized by the evolution of localized strain field, of a steel member to monotonically uniaxial tension. The proposed model extends the classic one-dimensional softening with localization model as introduced by (Schreyer and Chen 1986) to account for the localization length, and bifurcation and rupture points. The new findings of this research are as follows. Two types of strain-softening functions (bilinear and nonlinear) are proposed for comparison. The new failure criterion corresponding to the constitutive modeling is formulated based on the engineering strain inside the localization zone at rupture. Furthermore, a new mathematical expression is developed, based on the strain rate inside and outside the localization zone, to describe the displacement field at which bifurcation occurs. The model solutions are compared with the experimental data on four low-carbon cylindrical steel bars of different lengths. For engineering applications, the model solutions are also compared to the experimental data of a cylindrical steel bar system (three steel bars arranged in series). It is shown that the bilinear and nonlinear softening models can predict the energy dissipation in the post-peak regime with an average difference of only 4%.

Deep learning in nickel-based superalloys solvus temperature simulation

  • Dmitry A., Tarasov;Andrey G., Tyagunov;Oleg B., Milder
    • Advances in aircraft and spacecraft science
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    • 제9권5호
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    • pp.367-375
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    • 2022
  • Modeling the properties of complex alloys such as nickel superalloys is an extremely challenging scientific and engineering task. The model should take into account a large number of uncorrelated factors, for many of which information may be missing or vague. The individual contribution of one or another chemical element out of a dozen possible ligants cannot be determined by traditional methods. Moreover, there are no general analytical models describing the influence of elements on the characteristics of alloys. Artificial neural networks are one of the few statistical modeling tools that can account for many implicit correlations and establish correspondences that cannot be identified by other more familiar mathematical methods. However, such networks require careful tuning to achieve high performance, which is time-consuming. Data preprocessing can make model training much easier and faster. This article focuses on combining physics-based deep network configuration and input data engineering to simulate the solvus temperature of nickel superalloys. The used deep artificial neural network shows good simulation results. Thus, this method of numerical simulation can be easily applied to such problems.

전기차량경로문제의 충전소 위치선정문제의 해법 (Solving the Location Problem of Charging Station with Electric Vehicle Routing Problem)

  • 김기태
    • 산업경영시스템학회지
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    • 제45권4호
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    • pp.217-224
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    • 2022
  • Due to the issue of the sustainability in transportation area, the number of electric vehicles has significantly increased. Most automakers have decided or planned to manufacture the electric vehicles rather than carbon fueled vehicles. However, there are still some problems to figure out for the electric vehicles such as long charging time, driving ranges, supply of charging stations. Since the speed of growing the number of electric vehicles is faster than that of the number of charging stations, there are lack of supplies of charging stations for electric vehicles and imbalances of the location of the charging stations. Thus, the location problem of charging stations is one of important issues for the electric vehicles. Studies have conducted to find the optimal locations for the charging stations. Most studies have formulated the problem with deterministic or hierarchical models. In this paper, we have investigated the fluctuations of locations and the capacity of charging stations. We proposed a mathematical model for the location problem of charging stations with the vehicle routing problem. Numerical examples provide the strategy for the location routing problems of the electric vehicles.

How Consignment Should be Implemented to be an Effective Supply Chain Collaboration Program?

  • Chungsuk RYU
    • 산경연구논집
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    • 제14권6호
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    • pp.17-25
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    • 2023
  • Purpose: This study observes how the consignment performs over time and proposes the proper way to operate the consignment to bring its best benefit to the supply chain system. Research design, data, and methodology: The supply chain system is represented as the mathematical model where a manufacturer and a retailer trade one type of products to maximize their own profits. In the numerical examples of the proposed models, the consignment is compared with the fully coordinated system as well as the traditional system, and both advantages and limitations of the consignment are detected. Results: The consignment makes greater profit than the traditional system after a certain time period. The consignment is still outperformed by the fully coordinated system. The numerical examples also show that the performance of the consignment is sensitive to the consignment ratio. Conclusions: This study finds out that a certain time period must be spent until the consignment brings the benefit to the supply chain system. The numerical outcomes also imply that the consignment requires additional features to be a completely effective supply chain collaboration program. To obtain the best result from the consignment, the supply chain members are recommended to decide the appropriate consignment ratio by consent.

The smooth topology optimization for bi-dimensional functionally graded structures using level set-based radial basis functions

  • Wonsik Jung;Thanh T. Banh;Nam G. Luu;Dongkyu Lee
    • Steel and Composite Structures
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    • 제47권5호
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    • pp.569-585
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    • 2023
  • This paper proposes an efficient approach for the structural topology optimization of bi-directional functionally graded structures by incorporating popular radial basis functions (RBFs) into an implicit level set (ILS) method. Compared to traditional element density-based methods, a level set (LS) description of material boundaries produces a smoother boundary description of the design. The paper develops RBF implicit modeling with multiquadric (MQ) splines, thin-plate spline (TPS), exponential spline (ES), and Gaussians (GS) to define the ILS function with high accuracy and smoothness. The optimization problem is formulated by considering RBF-based nodal densities as design variables and minimizing the compliance objective function. A LS-RBF optimization method is proposed to transform a Hamilton-Jacobi partial differential equation (PDE) into a system of coupled non-linear ordinary differential equations (ODEs) over the entire design domain using a collocation formulation of the method of lines design variables. The paper presents detailed mathematical expressions for BiDFG beams topology optimization with two different material models: continuum functionally graded (CFG) and mechanical functionally graded (MFG). Several numerical examples are presented to verify the method's efficiency, reliability, and success in accuracy, convergence speed, and insensitivity to initial designs in the topology optimization of two-dimensional (2D) structures. Overall, the paper presents a novel and efficient approach to topology optimization that can handle bi-directional functionally graded structures with complex geometries.

Dynamic vibration response of functionally graded porous nanoplates in thermal and magnetic fields under moving load

  • Ismail Esen;Mashhour A. Alazwari;Khalid H. Almitani;Mohamed A Eltaher;A. Abdelrahman
    • Advances in nano research
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    • 제14권5호
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    • pp.475-493
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    • 2023
  • In the context of nonclassical nonlocal strain gradient elasticity, this article studies the free and forced responses of functionally graded material (FGM) porous nanoplates exposed to thermal and magnetic fields under a moving load. The developed mathematical model includes shear deformation, size-scale, miscorstructure influences in the framework of higher order shear deformation theory (HSDT) and nonlocal strain gradient theory (NSGT), respectively. To explore the porosity effect, the study considers four different porosity models across the thickness: uniform, symmetrical, asymmetric bottom, and asymmetric top distributions. The system of quations of motion of the FGM porous nanoplate, including the effects of thermal load, Lorentz force, due to the magnetic field and moving load, are derived using the Hamilton's principle, and then solved analytically by employing the Navier method. For the free and forced responses of the nanoplate, the effects of nonlocal elasticity, strain gradient elasticity, temperature rise, magnetic field intensity, porosity volume fraction, and porosity distribution are analyzed. It is found that the forced vibrations of FGM porous nanoplates under thermal and live loads can be damped by applying a directed magnetic field.

쌀가루를 첨가한 양배추 크림수프의 제조조건 최적화 (Optimization of Mixing Condition of Cabbage Cream Soup)

  • 박소연;표서진;주나미
    • 한국식생활문화학회지
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    • 제25권1호
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    • pp.54-60
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    • 2010
  • The principal objective of this study was to determine the optimal mixing condition of two different amounts of cabbage and rice flour for the preparation of a cabbage cream soup. The experimental design was based on the central composite design methodology of response surface, which included 10 experimental points, including two replicates for the cabbage and rice flour. Physiochemical and sensory properties were measured, and these values were applied to the mathematical models. A canonical form and perturbation plot showed the influence of each ingredient on the mixed final product. Water content and pH values increased with increasing quantities of rice flour. Neither cabbage or rice flour affected the L and a values, but the b value increased with greater quantity of both ingredients. Viscosity increased with increasing added cabbage. Sensory evaluation results were significant in the predicted model for flavor (p<0.05), concentration (p<0.01) and overall quality (p<0.01). As a result, the optimum formulations by numerical and graphical methods were calculated as 111.79 g cabbage and 8.99 g rice flour.