Sharif Digital Repository

With the development of science and industry increasingly need for seamless and high-strength rings, the attention of many researchers and industrialists paid on the ring rolling process. Then, Studying details of ring rolling process is very important. The most important issues in ring rolling process which are not sufficiently considered are: stress components distribution in ring, real amounts of friction coefficient, pressure distribution over the rollers, required power, required torque and force, and finally the minimum thickness of the ring during the process, all of these parameters have developed as analytical functions. In the present study, the minimum possible thickness of the... 

In this thesis, equations related to large deformation of a polymer were derived by considering viscoelastic effects. To express type of material behavior which includes elastoplastic and viscoelastic property at the same time, two-layer viscoplastic model was used. An axisymmetric model was used for modeling problem in finite element software. By derivation of parameters related to two layer model and entering them in finite element software and also entering other properties required to model the forming process, modeling was performed by special profile connecting input and output sections. Due to favorable properties of spline functions, profiles used in die geometry, were selected from... 

Nowadays, robots are become more common in many important applications, such as academic and industrial issues. One of the most important robots are Multi-Arm manipulators which are used in many application such as moving objects, coloring, automatic welding and etc. Working with this kind of robots needs some vital attentions like planning their moving path. It is Because of the large number of obstacles that they face with in the path. Therefore, not only robots are not allowed to collision with themselves, but also they must not touch the obstacles. In the other words, they need Path planning. Generally, the equations of these robots are nonlinear. Therefore, computers and numerical... 

Strong van der Waals (vdW) potential fields of carbon nanotubes (CNTs) makes them capable to encapsulate some nanostructures inside their hollow space, which leads to the construction of new hybrid nanostructures under specific conditions. Carbon nano-peapods, carbon nanowires and the hybrid of DNA and CNT are the main categories of hybrid nanostructures of CNT. Characteristics of hybrid nanotubes are unique and different from those of CNT. In nanostructures, the lattice spacing between individual atoms is considerable with respect to the structural dimensions. Also, the range of internal characteristic length is relatively close to external ones. So that utilizing the classical continuum... 

The present study deals with the analysis of Atomic Microscope with crack by making use of Strain Gradient Elasticity theory. Empirical observations represent that in micro dimensions, materials show behaviors, which the classic continuum mechanics theories are not able to explain. Thus, taking advantage of non-classic theories, which are capable of explaining such phenomena or behaviors in analyzing materials in micro dimensions seems necessary and of much significance. In this direction, by applying an Euler-Bernoulli beam assumption and neglecting the shear effects, governing equations and boundary conditions of the problem were obtained via taking advantage of variations in Hamilton... 

In recent years, the world has seen a great progress in micro electro-mechanical systems (MEMS). Small size, low weight, high accuracy and low energy consumption have made these devices applicable in a variety of usages. In MEMS devices, mechanical components are used for specific purposes among which one of the most widely used are micro plates. Microplates are used in the structure of many devices such as microswitchs and atomic force microscopes. Therefore, studying of static and dynamic behavior of microplates is important. As the object gets smaller (to the scale of micro and nano meters), the classic theory of mechanics of continuous media cannot predict the behavior due to its... 

The concept of generalized strains is a well-established subject in the classical continuum mechanics. The characteristics and various applications of the generalized strains have been the point of interest of many researchers in the classical continuum mechanics. The aim of this thesis is the introduction of generalized strains in the micropolar theory, as a non-classical continuum theory. A set of generalized strains is suggested for the deformation of macro-elements. Moreover, a set of generalized strains is proposed for the micro-structures. Since the rate of strains possesses a significant importance in the constitutive equations of nonlinear analysis of solids, expressions for the rate... 

The micropolar theory is a nonclassical continuum theory which considers a microstructure associated to each particle. This microstructure has three degrees of freedom and can rigidly rotate in the three dimensional space. Beside the classical or force stress tensor, in the micropolar theory the couple stress tensor is also considered.This research is devoted to deriving energy pair tensors for material strain measures in micropolar continuum. The subject of strains and their conjugate stresses is one of the major topics in the field of solid mechanics which has greatly been dealt with in the literature. This concept was introduced for investigating structural inequalities in solid... 

In this project, a size-dependent formulation is presented for mechanical analyses of inhomogeneous micro-plates based on the modified couple stress theory. The modified couple stress theory as a non-classical continuum theory has the ability to consider the small size effects in the mechanical behavior of the structures.The material properties are supposed arbitrarily to vary through the thickness of the plate. The governing differential equations of motion are derived for functionally graded plates utilizing variational approach. Based on the derived formulation, the static and free-vibration behaviors as well as buckling analysis of a rectangular functionally graded micro-plate are... 

Vibration analysis of micro-structures has been a major topic in recent years. Among them micro-plates play an important role in micro- and nano-electromechanical systems (MEMS and NEMS), e.g. micropumps, micromirrors, and microresonators. Some experimental observations revealed the size-dependent mechanical behavior in micro-scaled structures. Because of the incapability of the classical continuum theory to interpret the experimentally-detected small-scale effects in mechanical behavior of micro-scaled systems, non-classical theories should be used to deal with micron and sub-micron structures. Couple stress theory is one of the non-classical theories with only one length scale parameter. A... 

Nowadays the combination of mechanical and electronic systems in small scales is gaining attention. Micro electro-mechanical systems are widely used in various industries such as car manufacturing and electronic chips. In these devices, the most important and useful mechanical structures are beams and plates. Therefore, investigating the mechanical properties of these structures in very small scales (micro and nano) is of great importance. Decreasing the size to these scales leads to the dependence of the behavior of these structures to size. Accordingly, some theories for prediction of these behaviors have been presented, one of which is the strain gradient theory. This theory is used in... 

Due to the features like small dimensions, low manufacturing cost and low power consumption, micro-electromechanical systems (MEMS) are widely utilized in engineering applications. Many experimental investigations have indicated that the mechanical behavior of constructive microelements of these systems isn’t predictable by classical continuum theory. Therefore, to analyze the behavior of microelements, the non-classical continuum theories which can capture size effects should be utilized. On the other hand, various experimental observations have confirmed that thermoelastic damping (TED) is a dominant source of energy dissipation in microelements, in contrast to the non-small parts and... 

The analysis of nonlinear forced vibration of micro-rotors (rotating micro-shafts with disks) is carried out under loads of mass eccentricity distribution and in the presence of internal damping. For the analysis, the non-classical continuum theories of couple stress and strain gradient are employed. Vibrational behavior of micro-rotors is extremely sensitive due to the very high rotational speed, which is at the order of several millions per minute speed. The considered nonlinearity is of geometrical type due to the mid-plane stretching. First, the governing equations of motion of micro-rotors are derived by utilizing the Hamilton principle. In the next step, the Galerkin and multiple scale... 

Todays, advances in manufacturing technologies have led to design and production of micro-scale elements, including the elements employed in micro-electro-mechanical systems (MEMS). Micro-rotating systems like the micro-turbines are that kind of systems at which the high rotational speeds and the complexity of design and analysis have led to a special attention in modeling and investigating of their dynamic-vibrational behavior. In addition, in small scales, using the non-classical continuum mechanics theories such as the couple stress theory and the strain gradient theory is required to obtain the high precise results. On the other hand, attention to the torsional deformation of rotors... 

Incapability of the classical continuum mechanics theory to justify the experimental observations of the mechanical response of the small-scale structures and parts motivated the researchers to pursue the introduction and utilization of the non-classical continuum theories for analysis and design of such structures and parts. In this paper, utilizing the modified couple stress theory and the strain gradient theory as well-known and powerful non-classical continuum theories, the mechanical response, including the displacement and stress fields, for micro-rotating disks with angular acceleration is investigated. The governing differential equations of motion and the corresponding boundary... 

Micro-rotating machinery with compact energy sources and high power density has been developed in the recent decade to run portable electronic devices. To achieve efficiency targets, these miniaturized turbo-machinery must spin at elevated rotational speeds which sometimes can reach up to one million revolutions per minute. At this relatively high spinning rate, the rotordynamic behavior of these systems plays an important role in the stage of design. On the other hand, the classical continuum theory has been proven not to be able to appropriately predict the mechanical behavior of the small-scale structures. To overcome overall mentioned weakness, in this thesis the rotor of micro-engines... 

Stress tensors and their rates are fundamental quantities in modeling the behavior of materials in the field of nonlinear continuum mechanics. One of the most remarkable applications of stress rates is their presence in the rate type constitutive equations of materials.
Co-rotational rates are corresponding to the rates which are measured by an observer who is in a reference rotating coordinate system. In general, under some specific conditions for the spin of a co-rotational rate, the rate of an Eulerian tensor would be objective. In this thesis, the objective co-rotational rates of Eulerian stress tensors for isotropic elastic materials under large deformations are obtained for the... 

One of the extensively used, yet complex, structures in the industry is pre-twisted Micro/Nano beams. Studying their mechanical behavior helps to have a broader view of them. In this present study, explores and analyzes the behavior of a pre-twisted Micro/Nano beam with a quadrangular/rectangular cross-section using the strain gradient theory and modified couple stress theory. Using the calculus of variations and the Hamiltonian principle the elastodynamics governing partial differential equations of transverse deflection of the pre-twisted Micro/Nano beam with hinged-hinged boundary conditions are derived. Then the mechanical behavior of the pre-twisted Micro/Nano beam in static mode and... 

In the present study, we analyzed the mechanical behavior of micro rotating disk based on the most general form of strain gradient elasticity. According to the fact that micro rotating disks have an important role in MEMS, it is necessary to present an exact analysis of their mechanical behavior. It is noticed experimentally that materials behave stronger in deformation as they get smaller. The classical continuum theory is not capable to predict such behavior; therefore, it is essential to use one of the non-classical continuum theories to analyze the material in micro scales, which can capture this phenomenon. In this work, the strain gradient theory is utilized to derive the governing... 

In the present study, by considering the damage effects, the governing equations for elastoplastic behavior of a rotating disk are derived. Then several numerical solutions are presented for specific examples. First, by means of elastic strain energy functions along with the damage appearing in the literature and irreversible Thermodynamics laws, an analytical solution is generated for a rotating disk undergoing elastic deformations. For this purpose, the components of strain tensor are obtained in terms of the damage variable and the stress tensor components. Then, by employing the damage evolution relations mixed with the damage surface relation, damage variable is derived as a function of...