JACOBI DISCRETE APPROXIMATION FOR SOLVING OPTIMAL CONTROL PROBLEMS

El-Kady, Mamdouh Korean Mathematical Society 2012 대한수학회지 Vol.49 No.1

This paper attempts to present a numerical method for solving optimal control problems. The method is based upon constructing the n-th degree Jacobi polynomials to approximate the control vector and use differentiation matrix to approximate derivative term in the state system. The system dynamics are then converted into system of algebraic equations and hence the optimal control problem is reduced to constrained optimization problem. Numerical examples illustrate the robustness, accuracy and efficiency of the proposed method.

Assessing sustainability of groundwater resources on Jeju Island, South Korea, under climate change, drought, and increased usage

El-Kadi, A. I.,Tillery, S.,Whittier, R. B.,Hagedorn, B.,Mair, A.,Ha, K.,Koh, G. W. Springer Science + Business Media 2014 Hydrogeology journal Vol.22 No.3

Numerical groundwater models were used to assess groundwater sustainability on Jeju Island, South Korea, for various climate and groundwater withdrawal scenarios. Sustainability criteria included groundwater-level elevation, spring flows, and salinity. The latter was studied for the eastern sector of the island where saltwater intrusion is significant. Model results suggest that there is a need to revise the current estimate of sustainable yield of 1.77 x 10(6) m(3)/day. At the maximum extraction of 84 % of the sustainable yield, a 10-year drought scenario would decrease spring flows by 28 %, dry up 27 % of springs, and decrease hydraulic head by an island-wide average of 7 m. Head values are particularly sensitive to changes in recharge in the western parts of the island, due to the relatively low hydraulic conductivity of fractured volcanic aquifers and increased groundwater extraction for irrigation. Increases in salinity are highest under drought conditions around the current 2-m head contour line, with an estimated increase of up to 9 g/L under 100 % sustainable-yield use. The study lists recommendations towards improving the island's management of potable groundwater resources. However, results should be treated with caution given the available data limitations and the simplifying assumptions of the numerical modeling approaches.

Behavior and design of perforated steel storage rack columns under axial compression

Bassel El Kadi,G. Kiymaz 국제구조공학회 2015 Steel and Composite Structures, An International J Vol.18 No.5

The present study is focused on the behavior and design of perforated steel storage rack columns under axial compression. These columns may exhibit different types of behavior and levels of strength owing to their peculiar features including their complex cross-section forms and perforations along the member. In the present codes of practice, the design of these columns is carried out using analytical formulas which are supported by experimental tests described in the relevant code document. Recently proposed analytical approaches are used to estimate the load carrying capacity of axially compressed steel storage rack columns. Experimental and numerical studies were carried out to verify the proposed approaches. The experimental study includes compression tests done on members of different lengths, but of the same cross-section. A comparison between the analytical and the experimental results is presented to identify the accuracy of the recently proposed analytical approaches. The proposed approach includes modifications in the Direct Strength Method to include the effects of perforations (the so-called reduced thickness approach). CUFSM and CUTWP software programs are used to calculate the elastic buckling parameters of the studied members. Results from experimental and analytical studies compared very well. This indicates the validity of the recently proposed approaches for predicting the ultimate strength of steel storage rack columns.

Strength upgrading of steel storage rack frames in the down-aisle direction

Bassel El Kadi,Cumhur Coşgun,Atakan Mangır,Güven Kıymaz 국제구조공학회 2017 Steel and Composite Structures, An International J Vol.23 No.2

This paper focuses on the seismic performance of pallet-type steel storage rack structures in their down aisle direction. As evidenced by experimental research, the seismic response of storage racks in the down-aisle direction is strongly affected by the nonlinear moment-rotation response of the beam-to-column connections. In their down-aisle direction, rack structures are designed to resist lateral seismic loads with typical moment frames utilizing proprietary beam-to-column moment- resisting connections. These connections are mostly boltless hooked type connections and they exhibit significantly large rotations resulting in large lateral frame displacements when subjected to strong ground motions. In this paper, typical hooked boltless beam-to-column connections are studied experimentally to obtain their non-linear reversed cyclic moment-rotation response. Additionally, a compound type connection involving the standard hooks and additional bolts were also tested under similar conditions. The simple introduction of the additional bolts within the hooked connection is considered to be a practical way of structural upgrade in the connection. The experimentally evaluated characteristics of the connections are compared in terms of some important performance indicators such as maximum moment and rotation capacity, change in stiffness and accumulated energy levels within the cyclic loading protocol. Finally, the obtained characteristics were used to carry out seismic performance assessment of rack frames incorporating the tested beam-to-column connections. The assessment involves a displacement based approach that utilizes a simple analytical model that captures the seismic behavior of racks in their down-aisle direction. The results of the study indicate that the proposed method of upgrading appears to be a very practical and effective way of increasing the seismic performance of hooked connections and hence the rack frames in their down-aisle direction.

Jacobi discrete approximation for solving optimal control problems

Mamdouh El-Kady 대한수학회 2012 대한수학회지 Vol.49 No.1

This paper attempts to present a numerical method for solving optimal control problems. The method is based upon constructing the $n$-th degree Jacobi polynomials to approximate the control vector and use differentiation matrix to approximate derivative term in the state system. The system dynamics are then converted into system of algebraic equations and hence the optimal control problem is reduced to constrained optimization problem. Numerical examples illustrate the robustness, accuracy and efficiency of the proposed method.

Performance ofisolatedandfoldedfootings

Mahmoud Samir El-kady,Essam Farouk Badrawi 한국CDE학회 2017 Journal of computational design and engineering Vol.4 No.2

Folded foundationshavebeenusedasanalternativetotheconventional flat shallowfoundations,insituationsinvolvingheavyloadsorweaksoils. Theycanbegeometricallyshapedinmanyformsespeciallyforisolatedfootings.Thepurposeofthispaperisintroducinganalternativefoundation shapethatreducesthecostoffoundationsbyreducingtheamountofreinforcingsteelbyminimizingoreveneliminatingthetensionzones inthefoldedisolatedfootings.Also,achievinglowersoilstressesthroughchangingtheisolatedfootingshapewillconsequentlyreducetheexpected settlementsandthefootingstresses.Experimentalandnumericalstudiesareperformedon five (5)quarterscalefootingsofwhichone(1) footingof flat shapeistestedasareferencesampleandfour(4)footingsareoffoldedshapebyfoldinganglesof101, 201, 301, and401 withthe horizontal.Resultsshowedthatthefoldedisolatedfootingsachieveeconomicdesignbydecreasingthequantitiesofreinforcement.Italsoinduced lesssoilsettlements,andstresses.Inaddition,thetensilestressesinthereinforcedconcretefootingbodyarealsolessinfoldedisolatedfootings thanthe flat one.Resultsshowthatthefoldedisolatedfootinghaveabetterloadcarryingcapacitywhencomparedwiththeconventionalslab/flat footingofsimilarcrosssectionalareaforbothcasesofexperimentalandnumericalanalysis.

Evaluation of thermal stability of quasi-isotropic composite/polymeric cylindrical structures under extreme climatic conditions

Gadalla, Mohamed,El Kadi, Hany Techno-Press 2009 Structural Engineering and Mechanics, An Int'l Jou Vol.32 No.3

Thermal stability of quasi-isotropic composite and polymeric structures is considered one of the most important criteria in predicting life span of building structures. The outdoor applications of these structures have raised some legitimate concerns about their durability including moisture resistance and thermal stability. Exposure of such quasi-isotropic composite/polymeric structures to various and severe climatic conditions such as heat flux and frigid climate would change the material behavior and thermal viability and may lead to the degradation of material properties and building durability. This paper presents an analytical model for the generalized problem. This model accommodates the non-linearity and the non-homogeneity of the internal heat generated within the structure and the changes, modification to the material constants, and the structural size. The paper also investigates the effect of the incorporation of the temperature and/or material constant sensitive internal heat generation with four encountered climatic conditions on thermal stability of infinite cylindrical quasi-isotropic composite/polymeric structures. This can eventually result in the failure of such structures. Detailed critical analyses for four case studies which consider the population of the internal heat generation, cylindrical size, material constants, and four different climatic conditions are carried out. For each case of the proposed boundary conditions, the critical thermal stability parameter is determined. The results of this paper indicate that the thermal stability parameter is critically dependent on the cylinder size, material constants/selection, the convective heat transfer coefficient, subjected heat flux and other constants accrued from the structure environment.

Photonic sensors for micro-damage detection: A proof of concept using numerical simulation

Sheyka, M.,El-Kady, I.,Su, M.F.,Taha, M.M. Reda Techno-Press 2009 Smart Structures and Systems, An International Jou Vol.5 No.4

Damage detection has been proven to be a challenging task in structural health monitoring (SHM) due to the fact that damage cannot be measured. The difficulty associated with damage detection is related to electing a feature that is sensitive to damage occurrence and evolution. This difficulty increases as the damage size decreases limiting the ability to detect damage occurrence at the micron and submicron length scale. Damage detection at this length scale is of interest for sensitive structures such as aircrafts and nuclear facilities. In this paper a new photonic sensor based on photonic crystal (PhC) technology that can be synthesized at the nanoscale is introduced. PhCs are synthetic materials that are capable of controlling light propagation by creating a photonic bandgap where light is forbidden to propagate. The interesting feature of PhC is that its photonic signature is strongly tied to its microstructure periodicity. This study demonstrates that when a PhC sensor adhered to polymer substrate experiences micron or submicron damage, it will experience changes in its microstructural periodicity thereby creating a photonic signature that can be related to damage severity. This concept is validated here using a three-dimensional integrated numerical simulation.

Effect of Bimodal-Sized Hybrid TiC–CNT Reinforcement on the Mechanical Properties and Coefficient of Thermal Expansion of Aluminium Matrix Composites

Peter Nyanor,Omayma El‑Kady,Hossam M. Yehia,Atef S. Hamada,Mohsen A. Hassan 대한금속·재료학회 2021 METALS AND MATERIALS International Vol.27 No.4

Aluminium (Al) matrix reinforced with carbon nanotubes (CNT), micron-sized titanium carbide (TiC) particles, and bimodal(nano + micron) hybrid TiC–CNT is fabricated by solution ball milling, followed by cold compaction and vacuum sinteringto improve the mechanical properties and reduce thermal expansion. The hardness, wear resistance, compressive strength andCTE of pure Al, 0.6 wt% CNT/Al, 10 wt% TiC/Al, and hybrid 10–0.6 wt% TiC–CNT/Al composites have been investigated inthis work. Analysis of strengthening mechanisms based on theoretical models, microstructure, and properties of constituentmaterials is performed. Microstructure analysis reveals an excellent distribution of the reinforcement phase and no new phaseformation in sintered composites. The hardness value of bimodal TiC–CNT reinforced Al composite is significantly higherthan monomodal TiC reinforced composite, reaching 2.3 times the hardness value of pure Al. Similarly, the wear resistanceimproved, and CTE reduced with CNT and TiC addition but is even significantly better in the hybrid reinforced composite. Experimental values of CTE show good agreement with the theoretical model. The strength and ductility of materials aremutually exclusive, but the compressive strength of pure Al has been doubled without significant loss in ductility throughthe use of bimodal-sized hybrid TiC–CNT reinforcement in this work.

Temporal and spatial variability of rainfall and climate trend on Jeju Island

Alan Mair,Aly I. El-Kadi,하규철,Gi-Won Koh 한국지질과학협의회 2013 Geosciences Journal Vol.17 No.1

The temporal and spatial analyses of rainfall and temperature were conducted for understanding spatial variability and climate trend on Jeju Island. Rainfall data from 1992 to 2009 were used for the spatial analyses, and missing data were adjusted on Mt. Halla and along the northeast coast to reduce uncertainty of spatial variability. In addition, rainfall time series data of both Jeju City and Seogwipo City from 1961 to 2009 were analyzed for a long-term trend and identification of droughts. Mean annual rainfall for the period 1992–2009 shows an area of maximum rainfall centered around Mt. Halla where maximum annual rainfall reaches more than 4,300 mm and mean island rainfall is 2,082 mm. Upward trends in rainfall intensity, magnitude, and dryness conditions at the Jeju City and Seogwipo City from 1961 to 2009 suggest that rainfall has intensified with greater quantities of rainfall occurring over shorter durations, with longer dry periods between storm events. The annual cycle shows a distinct monsoon signature with peak rainfall typically occurring in August. Rainfall seasonality shows a shift in peak rainfall from June, July, and August, to July, August, and September. The most severe droughts in the period 1961–2009 were identified using a 12-month composite SPI. Three severe droughts each lasting around two years were identified over a relatively short nine-year period from 1964–1972.