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https://hdl.handle.net/20.500.12511/4489

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Earthquake performance analysis of a masonry school building's retrofitted state by the equivalent frame method
(2025) Okumuş, Vefa; Mangır, Atakan
Nonlinear analyses of masonry structures are frequently used in both engineering practice and academic studies. Due to the dominant nonlinear behaviour of masonry structures, complex and extensive finite element models are required to obtain accurate analysis results. While masonry walls are usually modelled using fine-meshed shells or solid elements in such structures, high computing power in modelling, analyzing, and post-processing results is necessary for the analyses of large structures. In recent years, the equivalent frame method, as a solution to this problem has been developed and presented in the literature. In this study, the equivalent frame method is used in a masonry structure modelling, and the axial force-bending relationship is represented by force-based fiber elements. The multi-linear load-deformation relationship reflects the shear behaviour of the walls. Within the scope of the study, an existing masonry school building is modelled using the equivalent frame elements with OpenSees software. Seismic performance analyses are done considering the existing and retrofitted states of the structure, and the results are discussed in a comparative manner.
Actual and potential trend analysis under climate change using risk sen's slope (rss) in western black sea basin in Türkiye
(2025) Keskin, Muhammed Zakir; Abu Arra, Ahmad; Akça, Şeyma; Şişman, Eyüp
Several classical and innovative trend methods exist in the literature to identify and evaluate the effects of climate change on hydro-meteorological variables. Among the classical methods, the most commonly used ones are modified Mann–Kendall (MMK) and Sen's slope (SS). As for the innovative methods to identify potential trends (probable risk levels) in hydro-meteorological variables depending on changing the initial conditions and temporal dynamic development behaviour of the trends, the risk Sen's slope (RSS) method was proposed based on different risk values. The actual trends are proposed in this research to comprehensively understand and analyse the climate change trend over the entire period. It uses RSS and the classical trends MMK and SS. Also, the spatiotemporal classical, actual and potential trends in meteorological variables are evaluated. Additionally, the advantages of the RSS method compared with classical SS are discussed in detail. The Western Black Sea basin in Türkiye, with monthly total precipitation and monthly average temperature data from 1961 to 2023, is selected as a representative application. The temperature trend results show that the 0.99 risk level gave approximately 25% higher slope than SS. The maximum temperature-increasing trend within the study area and the time period at 0.99 risk level is 2.10°C. However, the differences between precipitation trend slopes obtained by SS and RSS for different risk levels are relatively low. Furthermore, using different slopes corresponding to several risk levels allows for more proactive and effective measures for sustainable agricultural activities and water management. The actual temperature trend within the basin ranges between 1.33°C and 2.09°C, and the actual precipitation trend ranges between 2.78 and 12.74 mm over the study period.
Mapping coastal resilience: a gis-based Bayesian network approach to coastal hazard identification for queensland's dynamic shorelines
(2024) Durap, Ahmet
Coastal regions worldwide face increasing threats from climate change-induced hazards, necessitating more accurate and comprehensive vulnerability assessment tools. This study introduces an innovative approach to coastal vulnerability assessment by integrating Bayesian Networks (BN) with the modern coastal vulnerability (CV) framework. The resulting BN-CV model was applied to Queensland's coastal regions, with a particular focus on tide-modified and tide-dominated beaches, which constitute over 85% of the studied area. The research methodology involved beach classification based on morphodynamic characteristics, spatial subdivision of Queensland's coast into 78 sections, and the application of the BN-CV model to analyze interactions between geomorphological features and oceanic dynamics. This approach achieved over 90% accuracy in correlating beach types with vulnerability factors, significantly outperforming traditional CVI applications. Key findings include the identification of vulnerability hotspots and the creation of detailed exposure and sensitivity maps for Gold Coast City, Redland City, Brisbane City, and the Sunshine Coast Regional area. The study revealed spatial variability in coastal vulnerability, providing crucial insights for targeted management strategies. The BN-CV model demonstrates superior precision and customization capabilities, offering a more nuanced understanding of coastal vulnerability in regions with diverse beach typologies. This research advocates for the adoption of the BN-CV approach to inform tailored coastal planning and management strategies, emphasizing the need for regular reassessments and sustained stakeholder engagement to build resilience against climate change impacts. Recommendations include prioritizing adaptive infrastructure in high-exposure areas like the Gold Coast, enhancing flood management in Brisbane, improving socio-economic adaptive capacity in Redland, and maintaining natural defences in Moreton Bay. This study contributes significantly to the field of coastal risk management, providing a robust tool for policymakers and coastal managers to develop more effective strategies for building coastal resilience in the face of climate change.
Bi-directional higher-order shear deformable mixed finite element formulation including couple effects for stresses of functionally graded curved 3d beams
(2024) Arıbaş, Ümit Necmettin
This paper presents a formulation based on higher-order shear deformation functions in both normal and binormal directions on the cross section to include the influence of in-plane shear stresses in the case of curved beams subjected to out-of-plane forces. Besides, another distinctive feature is the introduction of accuracy elements at the stress concentration zones to widen the range of St. Venant principle. Within this scope, a two-noded curved mixed finite element formulation with twenty-eight degree of freedoms (DOFs) in total is derived. The curved axial geometry is defined over the exact functions of the gradient of arch length and curvature. The volume fraction of functionally graded (FG) material constituents is based on the power-law distribution and the rule of mixture. The functional including the coupling effects is derived via the Hellinger Reissner formulation. The normal/shear stresses are determined over the curvatures on the section and stress equilibrium condition. Quite satisfactory converged results with respect to the solid finite elements are obtained via advantageous DOFs for the bi-directional higher-order shear deformable mixed finite elements which reduces the computational time and space. Besides, in order to increase the precision at the stress concentration zones, the length ratios of the mixed finite elements at these zones are related to the geometric features and material parameters. Finally, the influences of geometric features, material constituents and the power-law index on the stress distribution of FG spatial/planar curved beams are presented both via the bi-directional higher-order mixed finite elements and the solid finite elements. Graphical abstract: (Figure presented.)
A comprehensive analysis and comparison of SPI and SPEI for spatiotemporal drought evaluation
(2024) Abu Arra, Ahmad; Şişman, Eyüp
Assessing drought is crucial for effective water resources management and the development of mitigation strategies. Drought indices serve as indispensable tools in this evaluation process, and choosing an appropriate index is vital for accurate drought assessment. The characteristics and classification of drought depend entirely on the chosen index. Based on the existing literature, the Standardized Precipitation Index (SPI) and Standardized Precipitation Evapotranspiration Index (SPEI) are the most commonly and widely used indices, and there is a significant need for a comprehensive comparison between SPI and SPEI to understand their differences and implications for drought assessment. This research aims to compare SPI and SPEI based on drought indices, characteristics, and classifications using the innovative drought classification matrix (IDCM) for spatiotemporal drought evaluation, and the comparison process is done for events and monthly scales. Also, it aims to investigate the comparison between SPEI obtained from in situ meteorological stations and from the SPEI database. The application and the comparison are presented for Istanbul city between 1951 and 2020. The results show similar variations and high correlation (more than 0.65) between SPI and SPEI. For drought characteristics, there is no consistent relationship between SPI and SPEI at the drought event scale. The outcomes revealed that approximately 60% of the months exhibit consistent drought classifications between the two indices. Finally, it shows a significant difference between SPEI based on in situ meteorological stations and satellite data. The comparison between SPI and SPEI based on different aspects is necessary and essential for drought studies and water resources management.
Synthesis of green anode material for lithium-ion battery from orthodontic waste by fuzzy logic
(2025) Ashraf, Humza; Karahan, Billur Deniz; Şen, Zekai
For the fabrication of green batteries, instead of synthesizing the electrode materials from high-purity metal powders via primary production methods, it is of great importance to design and produce an electrode material by recovering valuable elements from existing wastes. In this article, for the first time in open literature, an electrode active material was fabricated from biomedical waste by using a combination of leaching and hydrothermal methods. Once 100% leaching efficiency was achieved, an optimization was realized in the hydrothermal parameters (filling ratios, time, and temperatures) to fabricate spherically shaped metal oxide powders with 150 nm particle size. Innovatively, fuzzy logic modeling was used for refinement of parameters. Subsequently, three verification experiments were realized at optimum conditions, defined by fuzzy logic. The repeatability as well as the accuracy of the model was confirmed. In the meantime, analysis of variance (ANOVA) technique was applied for identification of the most effective parameter for the fabrication of powders in hydrothermal conditions. A detailed mechanistic analysis about the formation of particles was also realized. Finally, the possible use of this metal oxide powder as an anode material was evaluated galvanostatically and potentiostatically. The electrode delivered a higher capacity than graphite and achieved 100-cycle tests with success. The presented approach was anticipated to constitute an example for the future, as it brought an effective perspective to material scientists about the valorization of biomedical waste in high value-added applications such as energy storage devices.
Critical drought characteristics: a new concept based on dynamic time period scenarios
(2024) Abu Arra, Ahmad; Birpınar, Mehmet Emin; Gazioğlu, Şükrü Ayhan; Şişman, Eyüp
In research on monitoring drought events, analysis is often carried out using a single period as a reference. On the other hand, changing this default period in drought calculations causes the drought index values obtained from research to differ. As a gap in the literature, this point highlights the necessity of investigating the effect of various time periods on drought characteristics. It underscores the need to propose a new concept and methodology to address this gap effectively. This research aims to analyze critical drought characteristics through dynamic time period scenarios. For the first time in the literature, drought indices and potential and critical characteristics were analyzed for various (dynamic) time periods. Drought analysis was carried out for 13 time period scenarios with 10-year intervals from a meteorological station in Durham (1872–2021) by changing the initial time condition using the Standardized Precipitation Index (SPI). The results showed that in addition to the similarities, there are significant differences between drought characteristics. For example, in some time period scenarios, a drought event was recorded during a specific period, while in other scenarios (S5–S7, S10–S13), no drought was detected during the same period, like in SPI 1. Additionally, for SPI 12, the drought duration varied significantly, lasting between 20 and 29 months, and for SPI 6, the drought duration varied between 3 and 13 months. Regarding the intensity, SPI 1 ranged between ?0.89 and ?1.33, indicating a 33% difference, and the SPI 3 intensity ranged between ?1.08 and ?1.91, indicating a 50% increase in intensity. This research significantly contributes to the field by providing a novel approach using dynamic time period scenarios to determine critical drought characteristics, offering valuable insights for water resource management, drought mitigation planning, and design purposes.
Updated talbot method for culvert design discharge prediction
(2024) Uslu, Özay; Lav, Abdullah Hilmi; Şen, Zekai
Surface runoff flows must be drained safely through culverts in ephemeral flow streams and bridges in perennial streams without any damage to the road or highway infrastructure stability. In practice, bridges cross drainage basin channels reliably, and they are more carefully planned, designed, constructed, and maintained against extreme water passages, but culverts are subject to even less frequent and intensive rainfall consequent surface runoff occurrences with higher risk potential. It is, therefore, necessary to design culverts more carefully in such a way that they drain down the upstream surface water without any critical problem to the road downstream of the road stream channels. Most of the hydrological, hydraulic, and sedimentological formulations are empirical expressions that are widely valid for locations where culverts are suitably developed based on simple bivalent logical rules between factors involved in upstream inlet locations of culverts. One of the first logic rule-based methods in the literature is Talbot’s procedural approach to culvert design. This approach is based not only on an explicit equation, but also on a set of linguistically proposed design rules that are expressed deterministically to effectively eliminate most of the ambiguities. This paper proposes a modified approach with additional logistic structural features based on a bivalent logic inference system, which is an improved version of the Talbot procedure and leads to better culvert transition surface flow prediction. The proposed method is applied to a local area in Tekirdağ City, Türkiye, where a serious train accident occurred due to a poorly maintained culvert.
Trends of meteorological and hydrological droughts and associated parameters using innovative approaches
(2024) Abu Arra, Ahmad; Alashan, Sadık; Şişman, Eyüp
Climate change and drought have profound effects on hydro-meteorological series. In addition to spatial, these effects could be on annual, seasonal, monthly, or daily temporal scales. In the literature, seasonal Mann-Kendall and Kendall Tau, Standardized Precipitation Index (SPI), Standardized Precipitation Evapotranspiration Index (SPEI), and Standardized Runoff Index are mostly used to detect seasonal effects (autumn, winter, spring, and summer), despite some restrictive assumption. Innovative Polygon Trend Analysis (IPTA) method developed from Innovative Trend Analysis (ITA) analyzes monthly effects on hydro-meteorological variables without restrictive assumptions. In this study, the IPTA method is revised and developed as Periodic Innovative Polygon Trend analysis (P-IPTA) to analyze hydro-meteorological series in periods of 1, 3, 6, 9, and 12 months instead of one-month duration. The method turns to the IPTA for one-month evaluations. Also, ITA method is improved by adding the frequencies for each drought classification (F-ITA). For the precipitation and water availability (Istanbul, Türkiye) and stream flow (Danube River, Romania) series, the P-IPTA method has been used in addition to the SPI, SPEI, and SDI methods to detect the trends in meteorological and hydrological droughts, and their associated parameters. There are generally decreasing trends, increasing drought frequencies, and decreasing wet event frequencies in the study areas. As the period lengths of the hydro-meteorological series increase, drought becomes more evident. Unlike these methods, the method results are consistent with the F-ITA SPI, SPEI, and SDI graphs and can give drought and wet periods. Similarly, the new P-IPTA method will enable researchers to investigate seasonal effects not only on hydro-meteorological series but also on any variable.
Towards sustainable coastal management: a hybrid model for vulnerability and risk assessment
(2024) Durap, Ahmet; Balas, Can Elmar
This paper presents the development of a Hybrid Model (HM) integrated with a Bayesian Network (BN) for comprehensive coastal vulnerability and risk assessment, with a focus on Konyaaltı Beach, Antalya, Turkey. The HM incorporates critical environmental parameters such as wind, waves, currents, and sediment transport to simulate conditions at vulnerable coastal areas and perform risk assessments for storm effects, flooding, and erosion. The model includes submodules for predicting coastal storms, quantifying sediment transport rates, assessing tsunami inundation severity, and categorizing storms based on beach typologies. The Adaptive Neuro-Fuzzy Inference System (ANFIS) is utilized for significant wave height predictions, enhancing the model's accuracy. The integration of hydrodynamic modeling, Bayesian networks, and ANFIS offers a robust framework for assessing coastal vulnerability and informing sustainable management practices. The study's results highlight the necessity for integrated risk management strategies, including adaptive infrastructure design, zoning and land use regulations, ecosystem-based management, and continuous monitoring and model refinement to enhance coastal resilience against dynamic environmental forces. This research provides valuable insights for mitigating the impacts of hazards on urban developments, contributing to the advancement of sustainable coastal management.
On the networks of large embeddings
(2024) Aslan, Tuğba; Khaled, Mohamed; Székely, Gergely
We define a special network that exhibits the large embeddings in any class of similar algebras. With the aid of this network, we introduce a notion of distance that conceivably counts the minimum number of dissimilarities, in a sense, between two given algebras in the class in hand; with the possibility that this distance may take the value ?. We display a number of inspirational examples from different areas of algebra, e.g., group theory and monounary algebras, to show that this research direction can be quite remarkable.
On solitary-wave solutions of Rosenau-type equations
(2024) Durán, Angel; Muslu, Gülçin Mihriye
The present paper is concerned with the existence of solitary wave solutions of Rosenau-type equations. By using two standard theories, Normal Form Theory and Concentration-Compactness Theory, some results of existence of solitary waves of three different forms are derived. The results depend on some conditions on the speed of the waves with respect to the parameters of the equations. They are discussed for several families of Rosenau equations present in the literature. The analysis is illustrated with a numerical study of generation of approximate solitary-wave profiles from a numerical procedure based on the Petviashvili iteration.
Projected changes in extreme precipitation patterns across algerian sub-regions
(2024) Hamitouche, Yasmine; Zeroual, Ayoub; Meddi, Mohamed; Assani, Ali A.; Alkama, Ramdane; Şen, Zekai; Zhang, Xinhua
Extreme precipitation events play a crucial role in shaping the vulnerability of regions like Algeria to the impacts of climate change. To delve deeper into this critical aspect, this study investigates the changing patterns of extreme precipitation across five sub-regions of Algeria using data from 33 model simulations provided by the NASA Earth Exchange Global Daily Downscaled Climate Projections (NEX-GDDP-CMIP6). Our analysis reveals a projected decline in annual precipitation for four of these regions, contrasting with an expected increase in desert areas where annual precipitation levels remain low, typically not exceeding 120 mm. Furthermore, key precipitation indices such as maximum 1-day precipitation (Rx1day) and extremely wet-day precipitation (R99p) consistently show upward trends across all zones, under both SSP245 and SSP585 scenarios. However, the number of heavy precipitation days (R20mm) demonstrates varied trends among zones, exhibiting stable fluctuations. These findings provide valuable foresight into future precipitation patterns, offering essential insights for policymakers and stakeholders. By anticipating these changes, adaptive strategies can be devised to mitigate potential climate change impacts on crucial sectors such as agriculture, flooding, water resources, and drought.
Fuzzy standardized precipitation index (FSPI) for drought early warning procedure
(Springer, 2024) Şen, Zekâi
There are several standardized meteorological, hydrological, agricultural, and environmental indices for drought classification into a set of dry categories all of which are derived from the basic concept of standardized precipitation index (SPI). Almost all these indices are based on crisp (bivalent) logic where boundary limits between neighboring categories are numbers without transboundary inclusiveness. The SPI procedure depends on the standard normal (Gaussian) probability distribution function (PDF) with zero mean and standard deviation equal to one. This paper proposed fuzzification of the SPI limits among categories for the inclusion of more than one category with different membership degrees. This method is referred to as the fuzzy SPI (FSPI) procedure, which provides drought tracing possibility and categorization. At the end for a numerical value, one can defuzzify the fuzzy result through defuzzification methods. FSPI provides preliminary warning system in terms of two or more fuzzy rule propositions and categories. Thus, one can know the logical alternatives of the drought behavior of a given hydro-meteorology variable. The application of the FSPI is presented for New Jersey State wise and Istanbul annual precipitation records.
Assessing wet and dry periods using Standardized Precipitation Index Fractal (SPIF) and polygons: A novel approach
(Multidisciplinary Digital Publishing Institute (MDPI), 2024) Şen, Zekâi
In the open literature, there are numerous studies on the normal and extreme (flood and drought) behavior of wet and dry periods based on the understanding of the standard precipitation index (SPI), which provides a series of categorizations by considering the standard normal (Gaussian) probability distribution function (PDF). The numerical meaning of each categorization assessment is quite lacking in terms of future predictions of wet and dry period duration based on historical records. This paper presents a new approach for calculating possible formations of future wet and dry period durations based on historical records through an effective fractal geometric forecasting approach. The essence of the proposed methodology is based on the number of dry periods (steps) of non-overlapping monthly duration along consecutive broken line paths in the SPI classification for wet and dry period durations. It has been observed that the plot of periods on double logarithmic paper falls along a straight line against the number of such periods, implying a power function, which is the essence of fractal geometry. Extending the empirically derived straight line provides the number of periods that may occur in the future over a range of SPI levels. This methodology is referred to as SPI fractal (SPIF), and the classic SPI classification is converted into SPIF wet and dry polygons, which provide additional information about the drought period number within a valid polygonal area, compared to the classic SPI results. The wet and dry period features of any hydro-meteorology time series are constrained in SPIF polygons. The application of the methodology was carried out on monthly rainfall records on the European side of the Istanbul Florya meteorological station in Turkey.
Cross-sectional warping and precision of the first-order shear deformation theory for vibrations of transversely functionally graded curved beams
(Springer Science and Business Media B.V., 2023) Arıbaş, Ümit Necmettin; Aydın, Mete; Atalay, Mert; Omurtag, Mehmet Hakkı
The warping may become an important factor for the precise transverse vibrations of curved beams. Thus, the first aim of this study is to specify the structural design parameters where the influence of cross-sectional warping becomes great and the first-order shear deformation theory lacks the precision necessary. The out-of-plane vibrations of the first-order shear deformation theory are compared with the warping-included vibrations as the curvature and/or thickness increase for symmetric and asymmetric transversely-functionally graded (TFG) curved beams. The second aim is to determine the influence of design parameters on the vibrations. The circular/exact elliptical beams are formed via curved mixed finite elements (MFEs) based on the exact curvature and length. The stress-free conditions are satisfied on three-dimensional (3D) constitutive equations. The variation of functionally graded (FG) material constituents is considered based on the power-law dependence. The cross-sectional warping deformations are defined over a displacement-type FE formulation. The warping-included MFEs (W-MFEs) provide satisfactory 3D structural characteristics with smaller degrees of freedom (DOFs) compared with the brick FEs. The Newmark method is used for the forced vibrations.
Pre-earthquake fuzzy logic-based rapid hazard assessment of reinforced concrete buildings
(Elsevier Ltd, 2023) Mangır, Atakan; Okumuş, Vefa
The main purpose of this paper is to present a rapid building assessment fuzzy logic (FL) modelling for risk assessment based on expert construction engineering verbal informatics. Before an earthquake, a set of input expert assessment variables are transformed into five types of hazard categorization as "no damage", "slight damage", "moderate damage", "severe damage", and "collapse". Main variables are reported by expert engineers based on visual inspection of structural components in addition to the building location's peak ground velocity (PGV) micro zonation numerical value, soil type and building's material information. Each input variable and output hazard class is fuzzified. A valid set of fuzzy rule base components is written based on input variables, each of which has an appropriate output hazard class. The fuzzy hazard assessment model has input and output variables in terms of fuzzy sets. Thus, the overall model output is in the form of a fuzzy set and then defuzzified to find the percentage of each hazard class for a single building. The application of this fuzzy logic model is presented for twenty existing reinforced concrete buildings, and the final hazard categories of these buildings are presented with interpretations and recommendations.
Innovative equivalent elastic modulus based stress calculation methodology for reinforced concrete columns
(MDPI, 2023) Şen, Zekai; Mangır, Atakan
The combination of linearity and elasticity assumptions provides classical calculation procedures for the reinforced concrete (RC) columns and beams against internal and external seismic loads. In these calculation procedures, the elasticity modulus of the concrete is taken into account by ignoring the steel reinforcement due to its small area percentage in the total cross-section area. This paper presents an innovative column stress calculation procedure considering the concrete-steel composition as the equivalent elastic modulus based on the classical Hooke's Law. This methodology takes into consideration also the elastic modulus of the steel, providing a reduction in the factor of safety. The application of the proposed method is presented for a series of RC column cross-section areas. It is observed that the proposed methodology leads to elastic modulus improvement of 6% to 27% compared to conventional calculations. The necessary flow chart for the execution of the proposed process steps and accordingly developed MATLAB program are provided for the application.
Fuzzy Inference System (FIS) model for the seismic parameters of code-based earthquake response spectra
(Multidisciplinary Digital Publishing Institute (MDPI), 2023) Mangır, Atakan
The response spectra defined in seismic design codes include crisp classifications of seismic parameters, which directly affect the spectra’s shape and greatly alter seismic design loads. The optimum design phase seismic forces have an important role in the efficiency of the construction costs and structural safety. Various parameters are used to calculate the seismic design forces, especially presented in the codes with earthquake design spectra. This study presents a rule-based fuzzy inference model with fuzzy sets to determine these parameters using fuzzy inference system (FIS) modelling, which is the most appropriate approach among the different alternatives because both the input and output variables have numerical and linguistic uncertainties in the earthquake problem. Using the seismic zone factor of the region and shear wave velocity of the soil profile as inputs, the model generates the seismic coefficients and peak ground acceleration values of the response spectra specified in the Uniform Building Code (UBC, 1997). The response spectra in this code can be easily generated with these seismic coefficients after their fuzzification. Response spectra of twenty-five different sample cases with and without the FIS model are generated, which provide comparisons for the model superiority assessment. Significant differences are observed between the crisp logic and the FIS model-generated spectra. It is suggested that the FIS model can be modified and applied to various parameters to generate response spectra in different seismic design codes.
The static and free vibration analyses of axially functionally graded elliptical beams via mixed FEM
(Golden Light Publishing, 2022) Ermiş, Merve; Akdoğan, Gökay; Kır, Oğuzhan; Arıbaş, Ümit Necmettin; Omurtag, Mehmet Hakkı
The objective of this study is to investigate the behavior of the static and free vibration analyses of axially functionally graded elliptical planar curved beams using a mixed finite element method (MFEM) based on the Timoshenko beam theory. A two-noded curved mixed finite element has 12 field variables at each node. These variables denote three displacements, three cross-sectional rotations, three forces, two bending moments, and torque, respectively. The functionally graded material is composed of ceramic-particle material and metal-matrix material. The volume fraction of ceramic and metal materials varies along the beam axis. The effective material properties (modulus of elasticity, Poisson's ratio, and density) of the functionally graded material are determined according to the rule of mixture. It is aimed in the benchmark examples to present the influence of ceramic-particle material and non-homogeneity index of material gradation, the minimum radius of the elliptical beam, and boundary condition to the results of static and free vibration analysis in detail.

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