Search results for: mixed modulus of smoothness

Authors: Tarul Garg, P. N. Agrawal

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We propose to define the q-analogue of the α-Bernstein Kantorovich operators and then introduce the q-bivariate generalization of these operators to study the approximation of functions of two variables. We obtain the rate of convergence of these bivariate operators by means of the total modulus of continuity, partial modulus of continuity and the Peetre’s K-functional for continuous functions. Further, in order to study the approximation of functions of two variables in a space bigger than the space of continuous functions, i.e. Bögel space; the GBS (Generalized Boolean Sum) of the q-bivariate operators is considered and degree of approximation is discussed for the Bögel continuous and Bögel differentiable functions with the aid of the Lipschitz class and the mixed modulus of smoothness.

Keywords: Bögel continuous, Bögel differentiable, generalized Boolean sum, K-functional, mixed modulus of smoothness

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Authors: Ruchi, A. M. Acu, Purshottam N. Agrawal

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The purpose of this paper to introduce the Durrmeyer type modification of q-generalized-Bernstein operators which include the Bernstein polynomials in the particular α = 0. We investigate the rate of convergence by means of the Lipschitz class and the Peetre’s K-functional. Also, we define the bivariate case of Durrmeyer type modification of q-generalized-Bernstein operators and study the degree of approximation with the aid of the partial modulus of continuity and the Peetre’s K-functional. Finally, we introduce the GBS (Generalized Boolean Sum) of the Durrmeyer type modification of q- generalized-Bernstein operators and investigate the approximation of the Bögel continuous and Bögel differentiable functions with the aid of the Lipschitz class and the mixed modulus of smoothness.

Keywords: Bögel continuous, Bögel differentiable, generalized Boolean sum, Peetre’s K-functional, Lipschitz class, mixed modulus of smoothness

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Authors: R. Sadeghzadegan, S. A. Naeini, A. Mirzaii

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In this article, the results of a series of carefully conducted laboratory test program were represented to determine the small strain shear modulus of sand mixed with a range of kaolinite including zero to 30%. This was experimentally achieved using a triaxial cell equipped with bender element. Results indicate that small shear modulus tends to increase, while clay content decreases and effective confining pressure increases. The exponent of stress in the power model regression analysis was not sensitive to the amount of clay content for all sand clay mixtures, while coefficient A was directly affected by change in clay content.

Keywords: small shear modulus, bender element test, plastic fines, sand

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Authors: A. Chegenizadeh, M. Keramatikerman, H. Nikraz

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Bitumen is one of the most applicable materials in pavement engineering. It is a binding material with unique viscoelastic properties, especially when it mixes with polymer. In this study, to figure out the viscoelastic behaviour of the polymer modified with bitumen (PMB), a series of dynamic shearing rheological (DSR) tests were conducted. Four percentages of lime (i.e. 1%, 2%, 4% and 5%) were mixed with PMB and tested under four different temperatures including 64ºC, 70ºC, 76ºC and 82ºC. The results indicated that complex shearing modulus (G*) increased by increasing the frequency due to raised resistance against deformation. The phase angle (δ) showed a decreasing trend by incrementing the frequency. The addition of lime percentages increased the complex modulus value and declined phase angle parameter. Increasing the temperature decreased the complex modulus and increased the phase angle until 70ºC. The decreasing trend of rutting factor with increasing temperature revealed that rutting factor improved by the addition of the lime to the PMB.

Keywords: rheological properties, DSR test, polymer mixed with bitumen (PMB), complex modulus, lime

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Authors: Zhiming Ye, Dejiang Wang, Huiling Zhao

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Development of the technology demands a higher-level research on the mechanical behavior of materials. Structural members made of bi-modulus materials have different elastic modulus when they are under tension and compression. The stress and strain states of the point effect on the elastic modulus and Poisson ratio of every point in the bi-modulus material body. Accompanied by the uncertainty and nonlinearity of the elastic constitutive relation is the complicated nonlinear problem of the bi-modulus members. In this paper, the small displacement and large displacement finite element method for the bi-modulus members have been proposed. Displacement nonlinearity is considered in the elastic constitutive equation. Mechanical behavior of slender bi-modulus beam-column under different boundary conditions and loading patterns has been simulated by the proposed method. The influence factors on the ultimate bearing capacity of slender beam and columns have been studied. The results show that as the ratio of tensile modulus to compressive modulus increases, the error of the simulation employing the same elastic modulus theory exceeds the engineering permissible error.

Keywords: bi-modulus, ultimate capacity, beam-column, nonlinearity

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Authors: Olgha Giorgishvili

Abstract:

The work is mainly concerned with the determination of modulus of deformation by laboratory method. It is known that a modulus of deformation is defining by laboratory and field methods. By laboratory method the modulus of deformation is defined in the compressive devices. Our goal is to conduct experiments by both methods and finally make to interpret the obtained results. In this article is considered the definition by new offered laboratory method of deformation modulus that is closer to the real deformation modulus. Finally, the obtained results gives the possibility to us to raise the issue of change the state norms for determining ground by laboratory method.

Keywords: building, soil mechanic, deformation moulus, compression methods

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Authors: Win-Jin Chang, Haw-Long Lee, Yu-Ching Yang

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In this study, we use the atomic-scale finite element method to investigate the mechanical behavior of the armchair- and zigzag-structured nanoporous graphene sheets with the clamped-free-free-free boundary condition under tension and shear loadings. The effect of porosity on Young’s modulus and shear modulus of nanoporous graphene sheets is obvious. For the armchair- and zigzag-structured nanoporous graphene sheets, Young’s modulus and shear modulus decreases with increasing porosity. Young’s modulus and shear modulus of zigzag graphene are larger than that of armchair one for the same porosity. The results are useful for application in the design of nanoporous graphene sheets.

Keywords: graphene, nanoporous, Young's modulus, shear modulus

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Authors: Klara Krizova, Rudolf Hela

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The paper is focused on monitoring of dependencies of different composition concretes on elastic modulus values. To obtain a summary of elastic modulus development independence of concrete composition design variability was the objective of the experiment. Essential part of this work was initiated as a reaction to building practice when questions of elastic moduli arose at the same time and which mostly did not obtain the required and expected values from concrete constructions. With growing interest in this theme the elastic modulus questions have been developing further.

Keywords: concrete, compressive strength, modulus of elasticity, EuroCode 2

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Authors: Xianjia Meng, Chuanyong Qu

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Compact bone produces fatigue damage under the inevitable physiological load. The accumulation of fatigue damage can change the bone’s micro-structure at different scales and cause the catastrophic failure eventually. However, most tests were limited to the macroscopic modulus of bone and there is a need to assess the microscopic modulus during fatigue progress. In this paper, nano-identation was used to investigate the bone specimen subjected to four point bending. The microscopic modulus of the same area were measured at different degrees of damage including fracture. So microscopic damage can be divided into three stages: first, the modulus decreased rapidly and then They fell slowly, before fracture the decline became fast again. After fracture, the average modulus decreased by 20%. The results of inner and outer planes explained the influence of compressive and tensile loads on modulus. Both the compressive and tensile moduli decreased with the accumulation of damage. They reached the minimum at ending and increased after fracture. The modulus evolution under different strains were revealed by the side. They all fell slowly and then fast with the accumulation of damage. The fractured results indicated that the elastic modulus decreased obviously at the high strain while decreased less at the low strain. During the fatigue progress, there was a significant difference in modulus at low degree of damage. However, the dispersed modulus tended to be similar at high degree of damage, but they became different again after the failure.

Keywords: fatigue damage, fracture, microscopic modulus, bone, nano-identation

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Authors: Klara Krizova, Rudolf Hela

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The topic of the article focuses on the evaluation of selected technological factors and their influence on resulting elasticity modulus of concrete. A series of various factors enter into the manufacturing process which, more or less, influences the elasticity modulus. This paper presents the results of concrete in which the influence of water coefficient and the size of maximum fraction of the aggregate on the static elasticity modulus were monitored. Part of selected results of the long-term programme was discussed in which a wide scope of various variants of proposals for the composition of concretes was evaluated.

Keywords: mix design, water-cement ratio, aggregate, modulus of elasticity

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Authors: Z. N. Haji, S. O. Oyadiji, H. Samami, O. Farrell

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The prediction of the vibration response of rubber products by analytical or numerical method depends mainly on the predefined intrinsic material properties such as Young’s modulus, damping factor and Poisson’s ratio. Such intrinsic properties are determined experimentally by subjecting a bonded rubber sample to compression tests. The compression tests on such a sample yield an apparent Young’s modulus which is greater in magnitude than the intrinsic Young’s modulus of the rubber. As a result, many analytical equations have been developed to determine Young’s modulus from an apparent Young’s modulus of bonded rubber materials. In this work, the applicability of some of these analytical equations is assessed via experimental testing. The assessment is based on testing of vulcanized nitrile butadiene rubber (NBR70) samples using tensile test and compression test methods. The analytical equations are used to determine the intrinsic Young’s modulus from the apparent modulus that is derived from the compression test data of the bonded rubber samples. Then, these Young’s moduli are compared with the actual Young’s modulus that is derived from the tensile test data. The results show significant discrepancy between the Young’s modulus derived using the analytical equations and the actual Young’s modulus.

Keywords: bonded rubber, quasi-static test, shape factor, apparent Young’s modulus

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Authors: Chongyang Ye, Rong Liu

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Compression textiles such as compression stockings (CSs) have been extensively applied for the prevention and treatment of chronic venous insufficiency of lower extremities. The involvement of multiple mechanical factors such as interface pressure, frictional force, and elastic materials make the interactions between lower limb and CSs to be complex. Determination of Poisson’s ratio and elastic moduli of CS materials are critical for constructing finite element (FE) modeling to numerically simulate a complex interactive system of CS and lower limb. In this study, a mixed approach, including an analytic model based on the orthotropic Hooke’s Law and experimental study (uniaxial tension testing and pure shear testing), has been proposed to determine Young’s modulus, Poisson’s ratio, and shear modulus of CS fabrics. The results indicated a linear relationship existing between the stress and strain properties of the studied CS samples under controlled stretch ratios (< 100%). The newly proposed method and the determined key mechanical properties of elastic orthotropic CS fabrics facilitate FE modeling for analyzing in-depth the effects of compression material design on their resultant biomechanical function in compression therapy.

Keywords: elastic compression stockings, Young’s modulus, Poisson’s ratio, shear modulus, mechanical analysis

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Authors: Muhammad Younis

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A ternary 4-point approximating non-stationary subdivision scheme has been introduced that generates the family of $C^2$ limiting curves. The theory of asymptotic equivalence is being used to analyze the convergence and smoothness of the scheme. The comparison of the proposed scheme has been demonstrated using different examples with the existing 4-point ternary approximating schemes, which shows that the limit curves of the proposed scheme behave more pleasantly and can generate conic sections as well.

Keywords: ternary, non-stationary, approximation subdivision scheme, convergence and smoothness

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Authors: O. Giorgishvili

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For calculation of foundations one of the important characteristics is the module of deformation (E0). As we all know, the main goal of calculation of the foundations of buildings on deformation is to arrange the base settling and difference in settlings in such limits that do not cause origination of cracks and changes in design levels that will be dangerous to standard operation in the buildings and their individual structures. As is known from the literature and the practical application, the modulus of deformation is determined by two basic methods: laboratory method, soil test on compression (without the side widening) and soil test in field conditions. As we know, the deformation modulus of soil determined by field method is closer to the actual modulus deformation of soil, but the complexity of the tests to be carried out and the financial concerns did not allow determination of ground deformation modulus by field method. Therefore, we determine the ground modulus of deformation by compression method without side widening. Concerning this, we introduce a new way for determination of ground modulus of deformation by laboratory order that occurs by side widening and more accurately reflects the ground modulus of deformation and more accurately reflects the actual modulus of deformation and closer to the modulus of deformation determined by the field method. In this regard, we bring a new approach on the ground deformation detection laboratory module, which is done by widening sides. The tests and the results showed that the proposed method of ground deformation modulus is closer to the results that are obtained in the field, which reflects the foundation's work in real terms more accurately than the compression of the ground deformation module.

Keywords: build, deformation modulus, foundations, ground, laboratory research

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Authors: K. Krizova

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This objective of this article is to present concrete that differs by the size of the aggregate used. The set of concrete contained six concrete recipes manufactured as traditional vibrated concrete containing identical basic components of concrete. The experiment focused on monitoring the resulting properties of hardened concrete, specifically the primary strength and modulus of the concrete elasticity and the developing parameters from 7 to 180 days were assessed.

Keywords: aggregate, cement, concrete, elasticity modulus

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Authors: Zahid Ullah, Atlas Khan

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The presented research is dedicated to an extensive examination of the regularity properties associated with a specific class of equations, namely extremely degenerate elliptic equations. This study holds significance in unraveling the complexities inherent in these equations and understanding the smoothness of their solutions. The focus is on analyzing the regularity of results, aiming to contribute to the broader field of mathematical theory. By delving into the intricacies of extremely degenerate elliptic equations, the research seeks to advance our understanding beyond conventional analyses, addressing challenges posed by degeneracy and pushing the boundaries of classical analytical methods. The motivation for this exploration lies in the practical applicability of mathematical models, particularly in real-world scenarios where physical phenomena exhibit characteristics that challenge traditional mathematical modeling. The research aspires to fill gaps in the current understanding of regularity properties within solutions to extremely degenerate elliptic equations, ultimately contributing to both theoretical foundations and practical applications in diverse scientific fields.

Keywords: investigating smoothness, extremely degenerate elliptic equations, regularity properties, mathematical analysis, complexity solutions

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Authors: M. Madigoe, R. Modiba

Abstract:

High alloyed beta (β) phase-stabilized titanium alloys are known to have a low elastic modulus comparable to that of the human bone (≈30 GPa). The β phase in titanium alloys exhibits an elastic Young’s modulus of about 60-80 GPa, which is nearly half that of α-phase (100-120 GPa). In this work, a theoretical investigation of structural stability and thermodynamic stability, as well as the elastic properties of a quaternary Ti-Nb-Ta-Zr alloy, will be presented with an attempt to lower Young’s modulus. The structural stability and elastic properties of the alloy were evaluated using the first-principles approach within the density functional theory (DFT) framework implemented in the CASTEP code. The elastic properties include bulk modulus B, elastic Young’s modulus E, shear modulus cʹ and Poisson’s ratio v. Thermodynamic stability, as well as the fraction of β phase in the alloy, was evaluated using the Thermo-Calc software package. Thermodynamic properties such as Gibbs free energy (Δ?⁰?) and enthalpy of formation will be presented in addition to phase proportion diagrams. The stoichiometric compositions of the alloy is Ti-Nbx-Ta5-Zr5 (x = 5, 10, 20, 30, 40 at.%). An optimum alloy composition must satisfy the Born stability criteria and also possess low elastic Young’s modulus. In addition, the alloy must be thermodynamically stable, i.e., Δ?⁰? < 0.

Keywords: elastic modulus, phase proportion diagram, thermo-calc, titanium alloys

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Authors: David Idiata

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This paper is directed at using the UKCP09 climate change projection tool to predict the effect of climate change on the dynamic modulus of asphalt concrete is Southern England knowing that there is a pressing challenge directly facing infrastructure in the urban cities in the world today due to climate change. Climate change causes change in the environment which in turn impacts on the long-term structural performance of structures. From the projection values obtained, it was discovered that as the temperature increases, the dynamic modulus reduces and this effect was more on the South West which have temperature range of 36.8 oC to 48.3 oC and dynamic modulus range of 2,212 MPa to 1256 MPa.

Keywords: dynamic modulus, asphalt concrete, UKCP09, Southern England

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Authors: M. Guler, E. Guler

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We report some elastic parameters of cubic fluorite type neptunium dioxide (NpO2) with a recent EAM type interatomic potential through geometry optimization calculations. Typical cubic elastic constants, bulk modulus, shear modulus, young modulus and other relevant elastic parameters were also calculated during research. After calculations, we have compared our results with the available theoretical data. Our results agree well with the previous theoretical findings of the considered quantities of NpO2.

Keywords: NpO2, elastic properties, bulk modulus, mechanical properties

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Authors: Reza Ziaie Moayed, Javad Shamsi Soosahab

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Helical piles are being used extensively in engineering applications all over the world. There are insufficient studies on the helical piles' behavior in anisotropic soils. In this paper, numerical modeling was adopted to investigate the effect of elastic modulus anisotropy on helical pile behavior resting on anisotropic sand by using a finite element limit analysis. The load-displacement behavior of helical piles under compression and tension loads is investigated in different relative densities of soils, and the effect of the ratio of horizontal elastic modulus with respect to vertical elastic modulus (EH/EV) is evaluated. The obtained results illustrate that in sandy soils, the anisotropic ratio of elastic modulus (EH/EV) has notable effect on bearing capacity of helical piles in different relative density. Therefore, it may be recommended that the effect of anisotropic condition of soil elastic modulus should be considered in helical piles behavior.

Keywords: helical piles, bearing capacity, numerical modeling, soil anisotropy

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Authors: Muhammad Swilam

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Solutions for the wrong division problem of the Extended Multi-Modulus Divider (EMMD) that occurs during modulus extension (i.e. switching the modulus value between two different ranges of division ratios), in open loop fractional dividers and fractional multiplying delay locked loop, is proposed. A detailed study for the MMD with Sigma-Delta is also presented. Moreover, extensive simulations for the divider are presented to ensure and verify its functionality and compared with the conventional dividers.

Keywords: extended multi-modulus divider (EMMD), fractional multiplying delay locked loop, open loop fractional divider, sigma delta modulator

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Authors: E. Güler, M. Güler

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We present some elastic parameters of cubic fluorite type uranium dioxide (UO2) with a recent EAM type interatomic potential through geometry optimization calculations. Typical cubic elastic constants, bulk modulus, shear modulus, young modulus and other related elastic parameters were calculated during research. After calculations, we compared our results not only with the available theoretical data but also with previous experimental results. Our results are consistent with experiments and compare well the former theoretical results of the considered parameters of UO2.

Keywords: UO2, elastic constants, bulk modulus, mechanical properties

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Authors: E. Güler, M. Güler

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We report some elastic quantities of cubic fluorite type plutonium dioxide (PuO2) with a recent EAM type interatomic potential through geometry optimization calculations. Typical cubic elastic constants, bulk modulus, shear modulus, young modulus and other related elastic quantities were calculated during present research. After present calculations, we have compared our results with the existing theoretical data of literature. Our results are consistent with previous theoretical findings of the considered parameters of PuO2.

Keywords: PuO2, elastic properties, bulk modulus, mechanical properties

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Authors: Faramarz Ashenai Ghasemi, Ismail Ghasemi, Sajad Daneshpayeh

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In this study, tensile strength and elastic modulus of nanocomposites based on polypropylene/ linear low density polyethylene/ nano titanium dioxide (PP/LLDPE/TiO2) were studied. The samples were produced using a co-rotating twin screw extruder including 0, 2, 4 Wt .% of nano particles, and 20, 40, 60 Wt.% of LLDPE. The styrene-ethylene-butylene-styrene (SEBS) was used as comptabiliser. Tensile strength and elastic modulus were evaluated. The results showed that modulus was increased by 7% with addition of nano particles in comparison to PP/LLDPE. In addition, tensile strength was decreased.

Keywords: PP/LLDPE/TiO2, nanocomposites, elastic modulus, tensile strength

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Authors: Magdi M. E. Zumrawi, Mohamed Awad

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Determination of Resilient Modulus (M_R) is quite important for characterizing materials in pavement design and evaluation. The main focus of this study is to develop a correlation that predict the resilient modulus of subgrade soils from simple and easy measured soil index properties. To achieve this objective, three subgrade soils representing typical Khartoum soils were selected and tested in the laboratory for measuring resilient modulus. Other basic laboratory tests were conducted on the soils to determine their physical properties. Several soil samples were prepared and compacted at different moisture contents and dry densities and then tested using resilient modulus testing machine. Based on experimental results, linear relationship of M_R with the consistency factor ‘F_c’ which is a combination of dry density, void ratio and consistency index had been developed. The results revealed that very good linear relationship found between the M_R and the consistency factor with a coefficient of linearity (R²) more than 0.9. The consistency factor could be used for the prediction of the M_R of compacted subgrade soils with precise and reliable results.

Keywords: Consistency factor, resilient modulus, subgrade soil, properties

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Authors: Norul Hisham Hamid, Amir Affan, Ummi Hani Abdullah, Paridah Md. Tahir, Khairul Akmal Azhar, Rahmat Nawai, W. B. H. Wan Sulwani Izzati

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The dimensional stability and static bending properties of epoxy composite reinforced with amorphous and crystalline silica were investigated. The amorphous and crystalline silica was obtained by the precipitation method from carbonisation process of the rice husk at a temperature of 600 °C and 1000 °C for 7 hours respectively. The epoxy resin was mixed with 5%, 10% and 15% concentrations of amorphous and crystalline silica. The mixture was stirred for 10 minutes and cured at 28 °C for 72 hours and oven dried at 80 °C for 72 hours. The scanning electron microscope image showed the silica sized of 10-30nm was obtained. The water absorption and thickness swelling of epoxy/amorphous silica composite was not significantly different with silica concentration ranged from 0.08% to 0.09% and 0.17% to 0.20% respectively. The maximum modulus of rupture (85 MPa) and modulus of elasticity (3284 MPa) were achieved for 10% silica concentration. For epoxy/crystalline silica composite; the water absorption and thickness swelling were also not significantly different with silica concentration, ranged from 0.08% to 0.11% and 0.16% to 0.18% respectively. The maximum modulus of rupture (47.9 MPa) and modulus of elasticity (2760 MPa) were achieved for 10% silica concentration. Overall, the water absorption and thickness swelling were almost identical for epoxy composite made from either amorphous or crystalline silica. The epoxy composite made from amorphous silica was stronger than crystalline silica.

Keywords: epoxy, composite, dimensional stability, static bending, silica

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Authors: Won Mog Choi, Seong Kyeong Hong, Seok Young Jeong

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The stress on the buried pipeline under pavement is significantly affected by vehicle loads and elastic modulus of the soil surrounding the pipeline. The correct elastic modulus of soil has to be applied to the finite element model to investigate the effect of the vehicle loads on the buried pipeline using finite element analysis. The purpose of this study is to establish the approach to calculating the correct elastic modulus of soil using the optimization process. The optimal elastic modulus of soil, which minimizes the difference between the strain measured from vehicle driving test at the velocity of 35km/h and the strain calculated from finite element analyses, was calculated through the optimization process using multi-response surface methodology. Three elastic moduli of soil (road layer, original soil, dense sand) surrounding the pipeline were defined as the variables for the optimization. Further analyses with the optimal elastic modulus at the velocities of 4.27km/h, 15.47km/h, 24.18km/h were performed and compared to the test results to verify the applicability of multi-response surface methodology. The results indicated that the strain of the buried pipeline was mostly affected by the elastic modulus of original soil, followed by the dense sand and the load layer, as well as the results of further analyses with optimal elastic modulus of soil show good agreement with the test.

Keywords: pipeline, optimization, elastic modulus of soil, response surface methodology

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Authors: Reza Ziaie Moayed, Hamidreza Rahmani

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Today, with developments in science and technology, there is an excessive potential for the use of nanomaterials in various fields of geotechnical project such as soil stabilization. This study investigates the effect of Nano-SiO₂ solution on the unconfined compression strength and Young's elastic modulus of Kaolinite. For this purpose, nano-SiO₂ was mixed with kaolinite in five different contents: 1, 2, 3, 4 and 5% by weight of the dry soil and a series of the unconfined compression test with curing time of one-day was selected as laboratory test. Analyses of the tests results show that stabilization of kaolinite with Nano-SiO₂ solution can improve effectively the unconfined compression strength of modified soil up to 1.43 times compared to  the pure soil.

Keywords: kaolinite, Nano-SiO2, stabilization, unconfined compression test, Young's modulus

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Authors: Jiri Brozovsky

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Modulus of elasticity is one of the important parameters of construction materials, which considerably influence their deformation properties and which can also be determined by means of non-destructive test methods like ultrasonic pulse method. However, measurement results of ultrasonic pulse methods are influenced by various factors, one of which is the natural frequency of the transducers. The paper states knowledge about influence of natural frequency of the transducers (54; 82 and 150kHz) on ultrasonic pulse velocity and dynamic modulus of elasticity (Young's Dynamic modulus of elasticity). Differences between ultrasonic pulse velocity and dynamic modulus of elasticity were found with the same smallest dimension of test specimen in the direction of sounding and density their value decreases as the natural frequency of transducers grew.

Keywords: calcium silicate brick, ultrasonic pulse method, ultrasonic pulse velocity, dynamic modulus of elasticity

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Authors: Mojtaba Aghamiri Esfahani, Mohammad Karkon, Seyed Majid Hosseini Nezhad, Reza Hosseini-Ara

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In this study, the effect of uncertainty in elastic modulus of a plate on free vibration response is investigated. For this purpose, the elastic modulus of the plate is modeled as stochastic variable with normal distribution. Moreover, the distance autocorrelation function is used for stochastic field. Then, by applying the finite element method and Monte Carlo simulation, stochastic finite element relations are extracted. Finally, with a numerical test, the effect of uncertainty in the elastic modulus on free vibration response of a plate is studied. The results show that the effect of uncertainty in elastic modulus of the plate cannot play an important role on the free vibration response.

Keywords: stochastic finite elements, plate bending, free vibration, Monte Carlo, Neumann expansion method.

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