The aim of the present research is twofold. The first is to present a study on nonlinear thermo-mechanical bending and thermal postbuckling analysis of functionally graded (FG) porous ...perfect/imperfect nanobeam according to the nonlocal elasticity theory. The second, concurrent aim is to address the snap-through phenomenon in the thermally preloaded graded porous nanobeams due to lateral mechanical load. Two types of thermal loading including, uniform temperature rise and heat conduction through the thickness as well as two cases of porosity distribution, including uniform and uneven, are considered. Geometrically imperfect FG porous nanobeam with four different types of immovable boundary conditions is also taken into account. Thermo-mechanical material properties of the porous nanobeam are assumed to be position-dependent according to the modified rule of mixture. The nonlinear equilibrium equations are constructed using the Euler–Bernoulli beam model and von-Kármán type of geometrical nonlinearity. Chebyshev polynomial based Ritz method is utilized into the principle of virtual displacement to obtain the matrix representation of the nonlocal governing equations. Two different strategies, including the Newton–Raphson technique and direct displacement control scheme, are first proposed to extract the nonlinear bending and postbuckling curves of the graded nanobeam. Afterwards, to capture the snapping behavior and trace the path beyond the limit loads of the thermally preloaded nanobeam, the cylindrical arch-length technique is adopted. Numerical results are provided to explore the effect of different parameters such as the power-law index, nonlocal parameter, boundary conditions, porosity distribution, thermal loading, and imperfection amplitude on the nonlinear thermo-mechanical bending and instability of the FG nanobeam.
•Nonlocal nonlinear instability and thermo-mechanical bending of FG porous nanobeam subjected to two types of thermal preloading is studied.•On the basis of the nonlocal elasticity theory and von-Kármán nonlinearity, the governing equations are derived.•The heat conduction equation is solved for the FG porous nanobeam with uniformly and unevenly distributed porosities.•The effects of the different parameters on the nonlocal instability and thermo-mechanical bending of the graded porous nanobeam are examined.
•Tensile properties of Ti-6Al-4V under superimposed high power ultrasonic are investigated.•Yield stress reduction up to 9.52% due to acoustic softening is observed.•Ultimate strength reduction up to ...4.55% is observed.•The elongation of Ti-6Al-4V is improved up to 13% by the high power ultrasonic.•Acoustic hardening effect is not observed.
High power ultrasonic vibration is widely used for improving manufacturing processes such as machining and metal forming. High frequency mechanical vibration affects material properties and friction forces in contacting surfaces. Flow stress reduction under superimposed ultrasonic vibration is called as acoustic softening. The amount of this parameter should be determined for ultrasonic assisted metal forming processes. For determination of this parameter for workhorse Ti-6Al-4V alloy, experimental setup was designed and fabricated. Then tensile test under longitudinal ultrasonic vibration was performed for different ultrasonic powers. Results show that ultrasonic vibration has considerable effect on plastic behavior of the alloy and decreases flow stress. Also, increasing ultrasonic power leads to higher acoustic softening. Yield stress reduction up to 9.52%, ultimate stress reduction up to 4.55% and elongation up to 13% were obtained at 340W ultrasonic power. After applying ultrasonic vibrations and its termination, hardness of specimens were measured in which increase up to 9% was observed.
Corrosion fatigue refers to the process in which a metal fractures prematurely under condition of simultaneous corrosion and repeated cyclic loading. Tensile residual stresses are caused by some ...manufacturing processes that are the main reasons of decreasing in life of structures under cyclic loading and corrosive environments. Applying ultrasonic impact treatment is one of the promising and effective methods for enhancing fatigue behavior of materials. On the other hand, it has some positive effects on corrosion resistance of metals. In this work, effect of ultrasonic impact treatment on corrosion fatigue behavior of A106-B welded steel pipe, provided by gas refinery, has been investigated. It was demonstrated that more corrosion fatigue life can be achieved by application of ultrasonic impact treatment.
In the present investigation, bifurcation-type buckling characteristics of heated functionally graded (FG) annular nanoplates resting on an elastic foundation and subjected to various types of ...thermal loading are carried out by presenting an exact analytical solution for the first time. Three kinds of frequently used thermal loading, i.e. uniform temperature rise, linear and nonlinear temperature distribution through the thickness direction are considered. Thermo-mechanical properties of FG nanoplate are supposed to vary smoothly and continuously throughout the thickness based on power law model whereas the Poisson's ratio is held constant. Eringen's nonlocal elasticity theory is exploited to describe the size dependency of nanoplate. Using the principle of virtual displacements, the equilibrium equations together with corresponding boundary conditions are obtained for the thermal buckling analysis of FG annular nanoplates including size effects. The pre-buckling analysis is performed and the proper boundary conditions are chosen to assure the existence of bifurcation-type buckling. Also, the nonlocal stability equations of FG annular nanoplate are derived by using the adjacent equilibrium criterion and they are solved by applying an exact asymmetrical solution. Moreover, in following a parametric study is accompanied to examine the effects of the several parameters such as nonlocal parameter, various temperature distributions, thickness to outer radius ratio, power law index, inner to outer radius ratios and elastic medium parameters on the critical buckling temperatures of the size-dependent FG nanoplates in detail. It is found that the small scale effects and thermal loading have a significant effect on thermal stability characteristics of FG annular nanoplates.
•Asymmetrical thermal bifurcation buckling of FG annular nanoplates embedded in elastic foundation is studied.•Three types of temperature distribution including uniform, linear and nonlinear temperature distribution are considered.•Stability equations are derived by using adjacent equilibrium criterion and they are solved by applying an exact solution.•Effects of nonlocal parameter and temperature distributions on the buckling temperatures of FG nanoplates are discussed.
The bi-stability characteristics of the post-buckled plates have demonstrated extensive potential applications for energy harvesting and vibration isolation. In this article, at first, thermal ...post-buckling, nonlinear bending, and vibration behavior of the functionally graded (FG) circular nanoplates in bifurcation buckling are investigated according to nonlocal elasticity theory. Then, the nonlinear static/dynamic snapping phenomena and free vibration responses of the thermally post-buckled nanoplate subjected to static and sudden types of mechanical load are presented. For this aim, the equations of motion in conjunction with the von-Kármán nonlinearity and geometrical imperfection are established in the framework of Hamilton's principle. In addition, two distinct cases of temperature distribution as well as two types of edge conditions are taken into consideration. The equations of motion are discretized using the Chebyshev-Ritz procedure along with three different numerical algorithms. To evaluate the nonlinear dynamic snap-through buckling, the Newmark time integration scheme is adopted. Next, by means of the Budiansky-Roth criterion and the phase-plane approach, the dynamic snap-through loads are identified. A set of parametric studies is presented to provide an insight into influences of the nonlocal parameter, geometrical imperfection, gradient index, and edge supports on the static and dynamic characteristics of the nanosystem.
The current paper investigates the nonlinear thermo-mechanical instability and small/large amplitude vibration of thermally pre/post-buckled functionally graded (FG) porous circular nanoplates in ...bifurcation/limit load buckling. The thermo-mechanical properties of the graded nanoplate under uniform heating are considered to be functions of temperature according to the Touloukian model. To describe the functionally graded porous materials, two different patterns of porosity distribution are adopted in which the first pattern has a uniform distribution, but the second pattern has an uneven one. The novelty of the present study and its significance can be summarized into: (i) investigating the effect of the porosity distribution and geometrical imperfection on the nonlinear thermo-mechanical bending and small/large amplitude vibration of the temperature-dependent FG circular nanoplates during bifurcation buckling. (ii) Studying the snap-through instability and small amplitude vibration of the thermally post-buckled FG porous circular nanoplates during limit load buckling. To this aim, the nonlocal elasticity theory alongside the von-Kármán nonlinear assumption is imposed to derive the nonlinear motion equations of the geometrically imperfect FG porous circular nanoplates in the framework of Hamilton’s principle. By employing the Ritz approach together with the Chebyshev polynomial as the basic functions, the coupled nonlinear equations are discretised for both clamped and simply supported edge conditions. Next, depending on the nonlinear problem at hand, three different numerical algorithms, including the Newton-Raphson iterative method, the direct displacement control strategy, and the cylindrical arc-length technique, are implemented to assess the static and dynamic behaviour of the porous nanosystem. After validating the developed mathematical model, a comprehensive examination is performed to determine the influence of the temperature dependence of materials, porosity distribution patterns, nonlocal parameter, material gradient index, imperfection sensitivity, and edge conditions on the nonlinear bending, snap-through instability, and vibration responses of the graded circular nanoplates in the pre- and post-buckling domains of bifurcation/limit load buckling.
•Nonlinear thermal bending, postbuckling, and snap-through phenomenon due to lateral mechanical load in a thermally preloaded FG porous nanobeam under two types of thermal loading are ...investigated.•Two types of porosity distribution and geometrical imperfection of the graded nanobeam are considered.•Based on the Timoshenko beam model and von-Karman nonlinearity, the nonlinear equilibrium equations are extracted on the basis of the nonlocal elasticity theory.•Using Chebyshev-Ritz method, three different strategies, including cylindrical arch-length method, Newton-Raphson technique, and direct displacement control scheme, are proposed to extract the nonlinear thermal stability trajectories of the FG porous nanobeam.•The influences of the power-law index, two types of porosity distribution and thermal loads, nonlocal parameter, imperfection amplitude, and boundary conditions on the snap-through behavior and the nonlinear stability of the FG nanobeam are carefully discussed.
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Present paper deals with the nonlinear thermal bending response, thermal postbuckling behavior, and snap-through phenomenon due to lateral mechanical load in a thermally preloaded functionally graded (FG) porous perfect/imperfect nanobeam subjected to two types of thermal loading, including heat conduction across the thickness and uniform temperature rise. Heterogenous material properties of the porous nanobeams are assumed to be position/temperature-dependent, where dependency is obtained according to the modified rule of mixture and Touloukian formulation. Two types of porosity distribution and also geometrical imperfection of the nanobeam are considered. Assuming the Timoshenko beam model and von-Karman nonlinearity, the nonlinear equilibrium equations are extracted on the basis of the nonlocal theory of elasticity. With the establishment of the principle of virtual displacement and Chebyshev polynomial of the first kind as the basic functions, the Ritz method is utilized to obtain the matrix form of the nonlocal governing equations. Two different strategies, including the Newton-Raphson technique and direct displacement control scheme, are first proposed to extract the nonlinear bending and postbuckling trajectories of the graded porous nanobeam. Afterwards, to trace the snapping behavior beyond limit loads of the graded porous nanobeam with thermal preloading, the cylindrical arch-length scheme as a path-following method is adopted. Numerical parametric investigations are given to discuss the influences of the power-law index, two types of porosity distribution and thermal loads, size-dependent nonlocal parameter, imperfection amplitude, and boundary conditions on the snap-through behavior and the nonlinear thermal stability of the FG nanobeam.
First, modified couple stress theory is extended in the presence of thermo-mechanical loading. To this end, the generalized form of Hamilton's principle as well as constitutive relations are derived ...in general curvilinear coordinates. Then using the developed formalism, the bifurcation-type buckling of heated annular plates composed of functionally graded materials (FGMs) and resting on an elastic foundation is analytically studied. The non-classical FGM plate model contains a material length scale parameter and can interpret size effect. The adjacent equilibrium criterion is employed to derive stability equations. Thermo-mechanical properties of FGM plates are assumed to be graded across the thickness direction according to a power law form. Various types of thermal loading including uniform temperature rise, linear temperature distribution and heat conduction across the thickness are considered. A parametric study is conducted to investigate the influences of the material length scale parameter, power law index, inner and outer radii and also elastic foundation coefficients on thermal stability characteristics of FGM plates. The results reveal the existence of bifurcation-type buckling for a certain type of boundary conditions in which case the buckling patterns are asymmetric. Furthermore, the material length scale parameter and the geometry of annular FGM plates are shown to be more influential.
The present work summarizes the MED–TVC (multi effect desalination with thermal vapor compression) technique associated with the state of the art of modern desalination. In addition, a computer ...simulation model for all types of evaporation processes is presented. This program provides engineers with cost-effective tools for designing, developing and optimizing thermal desalination plants. It is the objective of this article to develop a mathematical model which would predict the influence of all factors on heat transfer coefficients, temperature and pressure, total capacity and performance ratio of the system under design and operating conditions. The transient nature of temperature during the seasons is modeled by ordinary differential equations based on mass and energy balance. Heat exchangers and thermo-compressor are designed based on the results of mass and energy balance. The validated model is further used to test the effect of variations in certain parameters in the process in order to investigate their influence on the total capacity of the plant. By means of parametric study, the computer simulation tool developed will help designers to achieve the best setting for the desalination process to minimize energy consumption. The comparison between the simulation results and experimental data well proves the program validity.
