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In this paper, stress gradient theory is used to model the static pull-in instability and size effect of electrostatic nanocantilevers in the presence of electrostatic and dispersion (Casimir/van der Waals) forces. The Differential transformation method (DTM) is employed to solve the nonlinear constitutive equation of the nanostructure as well as numerical methods. The basic engineering design parameters such as critical tip deflection and pull-in voltage of the nanostructure are computed. It is found that in the presence of dispersion forces, both pull-in voltage and deflection of the nanobeam increase with increasing the size effect. Compared to the pull-in voltage, the pullin deflection of the beam is less sensitive to the size effect at sub-micrometer scales. On the other hand, the size effect can increase the pull-in parameters of the nano-actuators only in sub-micrometer scales. The results indicate that the proposed analytical solutions are reliable for simulating nanostructures at sub-micrometer ranges.

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Generally reinforced concrete deep beams are used as transfer girders, pile caps, coupling beams and foundation walls. Openings are frequently provided in RC deep beams to facilitate essential services, such as ventilating ducts, water supply and drainage pipes, network access, or even movement from one room to another. Existence of opening leads to disturbance of compressive force path from the loading point to the support. Due to the lack of experiment on deep beam with opening, code provisions do not give any explicit guidance to designing these elements with opening. So this research studies the behavior of reinforced concrete deep beams with opening using finite element methods. To this end the commercial software ABAQUS/standard was used. The accuracy of model was verified with available experimental data. in two separate parts the behavior of these members was studied. First, 68 beams with opening were modeled to study the effect of size and position of opening, arrangement of web reinforcement, ratio of clear span to depth and ratio of shear span to depth. In all of these beams depth and thickness was 750 and 100 millimeter respectively. The most effective parameter on behavior and ultimate load capacity was arrangement of web reinforcement. Also the size effect on the behavior of these members was studied. So 8 beams were modeled and result indicates that by increasing size of the beams the normalized shear strength decreases. Generally reinforced concrete deep beams are used as transfer girders, pile caps, coupling beams and foundation walls. Openings are frequently provided in RC deep beams to facilitate essential services, such as ventilating ducts, water supply and drainage pipes, network access, or even movement from one room to another. Existence of opening leads to disturbance of compressive force path from the loading point to the support. Due to the lack of experiment on deep beam with opening, code provisions do not give any explicit guidance to designing these elements with opening. So this research studies the behavior of reinforced concrete deep beams with opening using finite element methods. To this end the commercial software ABAQUS/standard was used. The accuracy of model was verified with available experimental data. in two separate parts the behavior of these members was studied. First, 68 beams with opening were modeled to study the effect of size and position of opening, arrangement of web reinforcement, ratio of clear span to depth and ratio of shear span to depth. In all of these beams depth and thickness was 750 and 100 millimeter respectively. The most effective parameter on behavior and ultimate load capacity was arrangement of web reinforcement. Also the size effect on the behavior of these members was studied. So 8 beams were modeled and result indicates that by increasing size of the beams the normalized shear strength decreases.

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In this paper, the anti-plane stress analysis in an infinite elastic plane with multiple cracks is carried out by using the distributed dislocation technique. The solution is obtained for an infinite plane containing the screw dislocation via Fourier transform of biharmonic equation for the analysis of infinite plane in gradient elasticity. These solutions are used to perform integral equations for an infinite plane weakened by multiple straight cracks. Integral equations are hypersingular type which are solved numerically for density of dislocation on the cracks surfaces. The numerical method in Chebyshev series form are used to solve the hypersingular integral equations. The solution of integral equations leads to dislocation density functions. The stress intensity factor for cracks tips are formulated in terms of density of dislocation. Employing the definition of dislocation density, stress intensity factors for cracks tips are calculated. The influence of size-effect and crack location on the stress intensity factors are studied. To confirm the validity of formulations, numerical values of stress intensity factors are compared with the results in the literature. The results of the present approach are in excellent agreement with those in the literature. Some new examples with different geometrics of cracks are solved to illustrate the applicability of procedure.

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In recent decade, modeling the instability of nanostructures has attracted many attentions in nanomechanics. Nanomechanical switches are fundamental building blocks for the design of NEMS applications, such as nanotweezers and nanoscale actuators. One common type of NEMS including nano-bridge in micro mirrors is used. At nano-scales, the decreasing gap between the two electrodes makes surface traction due to molecular interaction such as van der Waals that must be taken into account in the analysis of NEMS. In this study, strain gradient theory has been used to investigate the size dependent pull-in instability of beam-type (NEMS)where is an inherent instability in them. The von-Karman nonlinear strain has been applied to derive the constitutive equation of the system. Effect of intermolecular force have been included in the nonlinear governing equations of the systems. Homotopy perturbation method (HPM) has been employed to solve the nonlinear equations. Effect of intermolecular attraction and the size dependency and the importance of coupling between them on the instability performance i.e. critical deflection and instability voltage have been discussed. According the findings of this research, one can conclude that intermolecular forces decrease pull-in voltage and size effect parameter in nano scale leads to increase of pull-in parameters. Also HPM method can be applied as efficient method to analyze beam type nano structures.

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In this paper, pull-in instability of a cantilever beam type nanoactuator made of the functionally graded material (FGM) based on higher order modified strain gradient theory investigated. It is assumed that the functionally graded beam, made of germanium and silicon, follows the volume fraction definition and law of mixtures, and its properties change as a power function through its thickness. By changing the germanium constituent volume fraction percent of the nano-beam, five different types of the nano-beams are investigated. The influences of the volume fraction index, length scale parameter and the intermolecular forces, on the pull-in instability are examined. Principle of minimum total potential energy used to derive the nonlinear governing differential equation and consistent boundary conditions which is then solved using the differential quadrature method (DQM). The present analysis is validated through direct comparisons with published other research methods and experimental results and after comparison excellent agreement has been achieved between new solution method and other experimental and numerical solution results. Besides, the results demonstrate that size effect and amount of volume fraction have a substantial impact on the pull-in instability behavior of beam-type nanoactuator.

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This paper analyzes the effect of squeeze film and size effect on dynamic response of microplate. The microplate in this work is a clamped-clamped plate, which is excited using electrostatic force. The gap between microplate and substrate filled with air. First order shear deformation theory (FSDT) and couple stress theory (CST) and considering Von Karman’s strains are used to model the equation of motion of microplate. Non-linear Reynolds equation based on Micropolar theorem is deployed to apply the size effect on the fluid. Afterward, Equations are discretized by applying couple finite element method and finite difference method. The first-order differential equations are solved utilizing Newmark’s method. One of the contribution is presenting the influences of size effect and mid-plane stretching on the microplate dynamic behavior, also the influence of different parameters on the quality factor. According to the results, mid-plane stretching effect increases the microplate rigidity. Interestingly, this effect is more dominant for voltages with higher amplitude. This paper emphasizes that considering the plate size effect will increase the rigidity of the system. Moreover, the plate size effect increases the rigidity whereas, the fluid size effect decreases the rigidity of system. Increasing the fluid’s pressure results in decrease the amplitude of oscillations in step voltage excitation which postpones the dynamic pull-in. This paper concludes that increasing the coupling parameter of fluid increases the natural frequency of microplate, whereas increasing the fluid length scale parameter decreases the natural frequency and quality factor of the system.

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In this paper, low velocity impact on nano-beam using couple stress theory was investigated. Modified couple stress theory was utilized to capture size-dependent effects. Hamilton’s principle was employed to derive governing equations and boundary conditions and then general solution was proposed. The solutions validity was confirmed by comparing present results with that of the literature. Comparing the results shows the present theory is capable to predict low velocity dynamic behavior with acceptable accuracy. The results show as mass ratio increased, natural frequencies decreased and then trend to a constant value. This limit is higher for second and third natural frequencies. Also, the natural frequencies increased when characteristic length to thickness ratio increased. It can be noted higher natural frequencies are more sensitive to variation of this ratio .Furthermore, maximum dynamic deflection raised when mass ratio increased. Moreover, a considerable result from this study is the profound effect of poison ratio on natural frequencies for nano-sized beams. As Poisson’s ratio increased, natural frequencies increased. Also, for low length scale to thickness ratio the size effect is insignificant and response trend to classic solution. Therefore, the couple stress theory can be employed to take into account size effects in low velocity impact on nano-beam problem.

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Concrete is one of the most widely used building materials for fragile behavior. The addition of fiber to concrete affects the behavior of tensile strength, tensile strength, flexural strength, modulus of elasticity, impact resistance and some other mechanical properties of concrete. For this purpose, an experimental research was carried out to provide an experimental model of the flexural fatigue life of reinforced concrete with macrosynthetic fibers by constructing concrete joists with three different thicknesses of 80, 100 and 150 mm. SN models (stress-loading) and HN (thickness-loading) was presented. The results showed that increasing the thickness of concrete samples and adding fibers to concrete mixture increases the fatigue life. Also, the addition of fibers to concrete samples measured the thickness of the sample for the stress level of 0.7 final stresses at 12.45-8.24%, for the stress level of 0.8, the final stress was 22.15-5.45%, and for the stress level of 0.9, the final stress decreased to 22.15% -10.18% Finds. Fiber-reinforced concrete is a type of concrete that is mixed with fiber. Various types of fibers are used to produce fiber-reinforced concrete, which include glass, polymer, carbon and steel. In the present research, macro-synthetic polymer fibers were used. Some of the consequences of applying macro-synthetic fibers in concrete include reduced shrinkage of fresh and hardened concrete, increased ductility, increased strength against fatigue stresses, increased durability and lifetime of concrete, improved concrete mechanical properties (tensile strength, flexural strength, etc.), control of secondary/thermal cracks of concrete, preventing the in-depth propagation of cracks, post-cracking chargeability and reduced permeability against chloride and sulfate ions .In most of the studies, the concrete sample's thickness is increased along with the increase in the beam's length; however, in the present work, only thickness of the beam samples with and without fibers was changed and other dimensions of the samples were kept constant in order to investigate merely the effect of increased thickness. Accordingly, effect of the size of macro-synthetic fiber-reinforced concrete sample at different thicknesses was assessed via fatigue life variations. The intertwisted fibers were added to the concrete mixture by 0.4 vol.%. Then, from each sample, three specimens were made. The obtained results were averaged and, then, recorded in the relevant tables. The following cases were considered as the research objectives: - Effect of sample size on fatigue life of concrete samples - Effect of adding macro-synthetic fibers on fatigue life In order to determine flexural fatigue of the concrete samples with the above-mentioned geometric properties, UTM device was used. The test was performed with constant sinusoidal loading at the frequency of 10 Hz. The input information for the test included loading curve shape, minimum and maximum loading values, loading frequency, and maximum number of loadings, all of which were defined as the input. To measure the values of stress levels in order for measuring the loading values, first, the average of the samples' flexural strength had to be determined; then, the stress levels could be calculated from the obtained results. also A cross sectional analysis of the broken sample showed that most of the sample failure was from aggregate and the mixture design was suitable.

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In structural engineering, concrete is known as a material with brittle behavior that the tensile strength of which is negligible compared to its compressive strength and show low resistance to crack propagation. Moreover, the concrete can be considered as a quasi-brittle material, which is due to the type of behavior related to the crack propagation and is also existed around the crack tip of fracture process zone (FPZ) that involves a set of microcracks. From the perspective of structural behavior, the size effect of the structure is one of the most important concepts provided by the fracture mechanics; therefore, it is important to provide an equation between concrete fracture properties such as fracture toughness (K_IC) and fracture energy (G_f) and its correlation with the size effect mechanism. The fracture energy is one of the most important characteristics for analysis of fracture behavior in concrete, evidenced to be a concrete property, showing its strength to cracking and fracture toughness. Given that the fracture energy (G_f) is sufficient to calculate the fracture behavior evaluation for the brittle materials in range of linear fracture mechanics, for the quasi-brittle materials such as concrete, this is not a sufficient parameter due to the presence of microcracks in the fracture process zone, and the length of fracture process zone (C_f) is one of the important properties of fracture in the unlimited-size structures. For determining the fracture parameters of concrete, various methods have been proposed. One of the most important methods that is presented by Bazant is the size effect method (SEM). The use of high strength concretes is increasing due to the expansion of the construction technology of these concretes. This research studies and analyzes the fracture behavior of high strength concrete (HSC) with various amounts of silica fume, along with a change in water to cement (w/c) ratio with SEM. In this experimental study, a total of 10 mixing designs have been tested. To investigate the effects of different w/c ratios in the range of HSC and the effect of silica fume, four w/c ratios of 0.24, 0.3, 0.35 and 0.4 Examined and in two w/c ratios of 0.24 and 0.35 a mix design for plain concrete without silica fume and three mix designs prepare with silica fume content of 5%, 10% and 15% by weight of cement. To determine the fracture characteristics of concrete, a total of 120 beams were tested. The results show that by decreasing the w/c ratio from 0.35 in the range of HSC, the value of initial fracture energy (G_f), the effective length of fracture processing zone (C_f) and the critical crack tip opening displacement (CTOD_c) has decreased and on the other hand the brittleness number (β) has increased. Also, by increasing the amount of silica fume in the w/c ratios of 0.35 and 0.24, the fracture energy, the length of the fracture processing zone, the fracture toughness (K_IC), the critical crack tip opening displacement has reduced, and the brittleness number has increased. The results show that by using the fracture parameters obtained from the SEM, the maximum load on the high strength concrete specimen can be predicted correctly.

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The loading rate and specimen size are two main influential factors which control the tensile and compressive strengths of Quasi-brittle materials such as concrete, ceramic and rock. Most of the studies in the past have been focused on the size effect in the static loading situations i.e. in situations in which the effect of the loading rate and inertia can be ignored. In particular, fracture mechanics size effect have received substantial attention both with respect to the physical testing and the numerical modeling. On the other hand, combined effect of the specimen size and loading rate on the rock strength has received little attention in the literature. Understanding the dynamic size effect of Quasi-brittle materials such as rock is essential for better analysis and design of rock structures. This is particularly the case when rock is subjected to the blasting loads or when it is prone to the strain bursting. Studies on the failure of rock under the coupled effect of specimen size and loading rate are far from sufficient. Due to the limitations of the laboratory test devices, limited research efforts have been conducted on the size effect of materials under dynamic loading. In this study, a 3D hybrid finite-discrete element code called CA3 was used to simulate the Split Hopkinson Pressure Bar test. The Incident and Transmitted bars were modeled by the finite element method while the Brazilian specimen was simulated using a Bonded Particle Model (BPM). The bars were assumed to beave elastically while the simulated specimen could develop micro and macro cracks which eventually could end up to complete disintegration and failure. Brazilian specimens with different sizes were numerically modeled. The specimen contained a vertical notch so that fracture mechanics size effect under high strain loading rate could be studied. The samples were subjected to different loading rate by adjusting the incoming wave in the incident bar. A micromechanical model in which the contact bond strength was allowed to vary in proportion to the relative velocity at the contact point of the involved particles was employed to capture the loading rate effect. The effect of sample size on the dynamic tensile strength of rock was explored and compared with the static size effect. The results were analyzed and discussed using the dimensional analysis approach. The numerical results suggest that the dynamic size effect on tensile strength of rock is different from the static size effect. While for small loading rates, the rock strength reduces as the specimen size increases, this is not the case when high loading rates are involved. For high loading rates, with the increase in the specimen size, the tensile strength initially increases. However, with further increase in the specimen size and the increase in the distance between the notch tips and the impact points, it appears that the inertia and loading rate effects reach to a stable situation, i.e. with further increase in the specimen size, the material strength remains constant. This interesting observation is discussed and compared with the published data in the literature.

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Concrete as the most widely used building material suffers from the inherent weakness of having high density which results in heavy structures and consequently large inertia forces during seismic excitations. A common practice to reduce the density of normal-weight concrete is to partially replace sand and gravel with natural or synthetic light-weight particles. Among them, ultra-lightweight non-absorbent closed-cell expanded polystyrene (EPS) beads can be effectively used to produce a wide range of light-weight structural and non-structural concretes with appealing physical and mechanical properties. Many empirical researches have been already conducted to reveal the key properties of this class of material such as the tensile and compressive strengths, sound and heat isolations, and durability. New findings show that, in addition to the volume content of EPS beads, the bead size can significantly alter the strengths of concrete samples. To be more precise, the bigger the size of EPS beads, the lower the strength of concrete at a constant EPS volume content. Moreover, the existing studies have shown that this size effect fades at higher EPS contents. An overview of the literature reveals that the effect of EPS bead size and volume content have not been addressed under triaxial loading conditions. Therefore, in this study, twelve different concrete mixes that differ in terms of EPS bead diameter and volume content have been prepared and tested under uniaxial compression, splitting tension, and triaxial loading conditions. Three different EPS sizes (2.25 mm, 2.75 mm, and 3.25 mm), and four EPS volume contents of 0% (witness samples), 5%, 10% and 20% are considered. The constituent materials of tested concrete samples are water, cement, river sand, superplasticizer, and EPS beads. The ratio of sand and water to cement is 2 and 0.55, respectively.  The BCB23 superplasticizer is used whose weight content is 0.6% of that of the cement. Samples are all cylinders with 5 cm in diameter and 10 cm in height and are treated in water for 28 days. The results show that increasing the volume of EPS beads would reduce the compressive and tensile strengths of concrete. Moreover, the results of uniaxial compressive tests show clear dependency to the size of EPS beads which is consistent with the results reported by other researchers. Splitting tensile test results are found different as the classical splitting mode of failure has changed to crushing mode beneath the narrow linear loading region for higher EPS contents. This phenomenon cancelled the validity of splitting test for the extraction of uniaxial tensile strength as the hypotheses of the elasticity solution for the Brazilian splitting test is not valid anymore. The failure points at the compression meridian of failure surface have been measured from the triaxial tests. The results confirm that confined strength of EPS concrete is also depends on the size of EPS beads, yet this dependency fades at higher confining stresses. This observation can be interpreted by the change of failure mechanism from local discrete cracking mode to distributed crushing mode which is also the reason behind the fade of size dependency in uniaxial compressive test at higher EPS volume contents.
 

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