Özet Metin
Anahtar Kelimeler
Özet Metin
Anahtar Kelimeler
Özet Metin
Anahtar Kelimeler
Özet Metin
Anahtar Kelimeler
Özet Metin
Anahtar Kelimeler
Özet Metin
Anahtar Kelimeler
Özet Metin
Anahtar Kelimeler
Özet Metin
Anahtar Kelimeler
Özet Metin
Anahtar Kelimeler
Özet Metin
Anahtar Kelimeler
Özet Metin
Anahtar Kelimeler
Özet Metin
Anahtar Kelimeler
Özet Metin
Anahtar Kelimeler
Özet Metin
Anahtar Kelimeler
Özet Metin
Anahtar Kelimeler
Özet Metin
Anahtar Kelimeler
Özet Metin
Anahtar Kelimeler
Özet Metin
Anahtar Kelimeler
Özet Metin
Anahtar Kelimeler
Özet Metin
Anahtar Kelimeler
Özet Metin
Anahtar Kelimeler
Özet Metin
Anahtar Kelimeler
Özet Metin
Anahtar Kelimeler
Özet Metin
Anahtar Kelimeler
Özet Metin
Anahtar Kelimeler
Özet Metin
Nanotechnology is defined as the method of producing microscopic products by processing the substance in an atomic or molecular dimension. The properties of matter in nanoscale differ from the macroscale. When the dimensions of a material are reduced, the properties remain the same at first, then minor changes occur in the material properties. When the size drops below 100 nm, dramatic changes may occur in the properties. There are two main reasons for this: First, nanomaterials have a larger surface area compared to the material produced in the larger form with the same material mass. The second reason is that in nanoscale, quantum effects are effective on the behavior of matter. Thanks to these effects, the material has brand new chemical, biological, electrical, mechanical and physical properties. Due to these new features, there has been a great demand for nanoscale objects in medicine, biomaterials, energy, textile, electronics, chemistry, machinery industries. Nanotech-nology has become a rich field of study due to the contributions of physicists, chemists, engineers, manufacturing technology workers, biologists, medical workers. Due to the potential of using nanoscale systems in a large number of engineering applications, their mechanical behavior (such as bending, vibration, buckling) and properties need to be explored in detail and clearly determined before use in new designs. In terms of mechanical analysis, one-dimensional nanostructures (carbon nanotubes and microtubes) are modeled as beams, and two-dimensional nanostructures (such as graphene layers) are modeled as plates. Different theories are used in their modeling. In beams Euler-Bernoulli beam theory, Timoshenko beam theory, or higher order beam theories (Reddy-Bickford, Levinson beam theories et al.) are widely used. For plates Kirchhoff-Love, Mindlin-Reissner, higher order plate theories (Reddy, third order plate theories et al.) are used. The mechanical properties and behavior of nano-dimensional structures can be examined using various experimental, simulation (calculation) and analytical (theoretical) methods. Experimental studies in nanoscale have some difficulties. In experimental studies, it is not possible to precisely control each parameter. Experiments are carried out in high technical facilities and the devices used must have a very high level of precision. These factors increase costs. The most widely used simulation methods are molecular dynamics simulation and Monte Carlo simulation. Although atom-level simulation methods have achieved great success in computational physics, since they require a large amount of computation, their applications are limited to simple systems with a relatively small number of molecules or atoms (a few million at most). There are also other limitations, such as time steps, constraints, boundary conditions, and temperature effects. For example, in terms of time steps, only short-lived events lasting from picoseconds to nanoseconds can be modeled. To overcome these constraints, researchers make use of continuum mecha-nics approaches. Although classical elasticity theories are used with great success in macro-sized structures, the error rate is high when compared with experimental results in micro and nano sizes. The main reason for this is that in nano and micro dimensions, material properties depend on size and geometry. In these dimensions, the small size effect is an important factor. Classical theories of elasticity cannot account for these effects, as they are dimension-independent theories. Higher-order elasticity theories have been developed to address this deficiency. These theories are modified versions of classical elasticity methods, in which material size scales are incorporated into modeling. They generalized standard constitutive equations by including higher-order derivatives of strains, stresses, and/or accelerations. These theories, which depend on size, can be grouped into three basic groups strain gradient theories, microcontinuum field theories and nonlocal elasticity theories. Among the theories of high-order elasticity, the theory of nonlocal elasticity, for which Eringen contributed greatly in its development, is the most widely used theory. In the nonlocal theory of elasticity, the stress value at any point of the body is considered to be determined by strains at all points within the body‘s volume. By this way, finite-range forces between atoms and molecules are included in the calculations. The only difference between classical theories of elasticity and nonlocal elasticity theory is constitutional equations that relate stress to strain. Equilibrium and compatibility equations are the same for both theories. The small-size effect is included in calculations using the nonlocal parameter, which is the function of two parameters related to material-specific dimensions. Nonlocal elasticity theory has two general forms, differential and integral. In this study, the displacement of prismatic nanobars using the differential form of the nonlocal elasticity theory and the large displacement theory were calculated using the two-step sequential approach method and perturbation method. These two methods used in the calculations constitute the original value of the study. In the two-step sequential approach method, the elastic curve of the bar is represented using the superposition of the two approximation curves. The first approximation curve is chosen close to the elastic curve and care is taken to ensure that certain conditions are met. These conditions include boundary conditions and independent parameter/parameters that ensure that the curve to be selected is as close as possible to the elastic curve. The displacements in the first approximation curve are assumed to be large. In the second approximation curve, displacements are considered to be small. Therefore, the equations related to the second approximation curve are linear. Since the first approximation curve is close to the elastic curve, the equilibrium equations are written according to the first approximation curve. After selecting the first approximation curve, the displacement functions of the second approximation curve can be calculated using the moment-curvature relation and additional conditions. After the required formulation was derived in Chapter 4, the method was tried on three different sample problems. The obtained results are presented graphically. In the figures, dimensionless vertical and horizontal displacements along the length of the rod and dimensionless vertical displacement at the free end according to the dimensionless load parameter are given. In the first example, it is observed that rigidity increases with the increase of the value of the dimensionless nonlocal parameter at the small values of , but the rigidity decreases at the large values of (see Figure 4.40). In the second example, the increase of the dimensionless nonlocal parameter causes a decrease in rigidity (see Figure 4.46). In the last example, the increase of dimensionless nonlocal parameter increases rigidity (see Figure 4.52). The perturbation method is studied in Chapter 5. According to the large displacement theory, moment and displacement equations have been obtained. By taking the limit of the nonlocal parameter, displacement and moment expressions have been reached for the large displacement assumption in the classical theory of elasticity. Numerical calculations were performed for two sample problems. The first example shows the general solution method in isostatic systems and the second example in hyperstatic systems. The numerical results in the examples are presented graphically using the elastic curve. The elastic curve is obtained according to the small displacement and large displacement assumptions in the classical elasticity theory and according to the large displacement assumption in the nonlocal elasticity theory. According to the nonlocal theory of elasticity, with the increase of dimensionless load parameter, it was observed that vertical displacement decreased in the first example and in the second example, vertical displacement increased. In both examples, it was determined that with the increase of dimensionless nonlocal parameter, vertical displacement decreased, that is, the stiffness increased. Both methods used in the study can be used easily on bars with different boundary conditions under the influence of various loads. When nanoscale structures are examined using classical theory of elasticity, the rigidity of these structures is small compared to experimental results. As the nonlocal elasticity theory takes into account the small size effect, it achieves results consistent with experimental data. Also the results of this study show that, when the dimensions of the system under study become smaller, nonlocal effects become non negligible and the importance of the size effect increases.
Anahtar Kelimeler
Cantilever beams, Nonlocal elasticity, Perturbation method, Large displacement theory
Özet Metin
Response of prismatic bars is investigated by using two approximation functions for the elastic curve according to large deflection and nonlocal continuum field theories. In large deflection theory, deriving closed form analytic solutions are not always possible. Even when it is possible, great mathematical difficulties arise. Solution technique implemented in this investigation uses elementary functions of mathematics and gives very accurate results compared to exact solution with significantly decreased mathematical complexity. Governing differential equation of the elastic curve is written according to large deflection and nonlocal continuum mechanics theories. Instead of solving this differential equation directly, elastic curve is approximated by using two approximation functions. The first approximation function is selected as closely as possible to the exact elastic curve. On this one, equilibrium equations and moment-curvature equation is written. Second approximation function is for correcting small displacement differences from the exact elastic curve. It is selected so as to satisfy boundary conditions and some criterions which are required to obtain an elastic curve which is as close as possible to the exact elastic curve. In the first approximation function, displacements are large whereas in the second one displacements are small. As examples, a cantilever beam and a simply supported beam is solved. Results are used for estimating magnitude of nonlocal effects. It is found that when span length decreases to nano lengths, nonlocal effects becomes more significant. On normal scale nonlocal effects are negligible. As importance of nano technology increases each day, it is beneficial to incorporate nonlocal continuum theory into mathematical models of prismatic bars on nano scale.
Anahtar Kelimeler
Large deflection theory, nonlocal continuum mechanics, nano technology, approximate method, prismati
Özet Metin
In this study static calculation of a multistorey steel housing development building which has 20 storey has been made. Static calculations has been made according to both Eurocode-3 and TS-648 standarts. In the last chapter of the thesis an evaluation presents to compare the results obtained from both standarts. In static calculations the author benefitted from Etabs computer program and in drawings the author benefitted form Autocad computer program. At earthquake and wind analysis “Standart for Buildings Which will be Construct in Disaster Regions” standart has been used. At the appendix section 10 drawings and 2 discs include static calculation datums has been presented. As a result of the calculations it has been showned that the building ensured the requirements required for both standarts and has adequate resistance for earthquake and wind forces. The outcome of the camparison between Eurocode- 3 and TS-648 which has been presented at section 8 the Eurocode-3 standart offered a more complex and economic static design opportunity than TS-648 standart.
Anahtar Kelimeler
Eurocode-3, TS-648, Static Calculation, Multistorey Steel Housing Development Building
