solutions manual Antenna Theory and Design Stutzman Thiele 3rd editionDelivery is INSTANT. You can download the files IMMEDIATELY once payment is doneIf you have any questions, or would like a receive a sample chapter before your purchase, please contact us at road89395@gmail.comTable of ContentsChapter 1 Introduction 1Chapter 2 Antenna Fundamentals 23Chapter 3 Simple Radiating Systems 70Chapter 4 System Applications for Antennas 100Chapter 5 Line Sources 128Chapter 6 Wire Antennas 151Chapter 7 Broadband Antennas 218Chapter 8 Array Antennas 271Chapter 9 Aperture Antennas 344Chapter 10 Antenna Synthesis 433Chapter 11 Low-Profile Antennas and Personal Communication Antennas 465Chapter 12 Terminal and Base Station Antennas for Wireless Applications 536Chapter 13 Antenna Measurements 559Chapter 14 CEM for Antennas: The Method of Moments 587Chapter 15 CEM for Antennas: Finite Difference Time Domain Method 652Chapter 16 CEM for Antennas: High-Frequency Methods 700 Please note that the files are compressed using the program Winzip.Files ending with the extension (.pdf) can be opened using Adobe Acrobat Reader.
Solution Manual Theory Of Plasticity Chakrabarty.23
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Recently the present authors have started to investigate the plastic buckling paradox by conducting accurate finite-element modelling of buckling of cylindrical shells using both the flow theory and the deformation theory of plasticity [3, 4]. Contrary to the common belief, they showed that, by using an accurate and carefully validated geometrically nonlinear finite element modelling, a very good agreement between numerical and experimental results can be obtained also in the case of the physically sound flow theory of plasticity. Consequently, according to the performed numerical investigations in the case of axially loaded cylinders, it can be affirmed that no plastic buckling paradox actually exists. Additionally, the flow theory of plasticity, which provides a physically sound description of the behaviour of metals, can even lead to predictions of the buckling stress which are in better agreement with the corresponding test results than those provided by use of the deformation theory, in contrast with the widely accepted belief that the flow theory leads to a significant overestimation of the buckling stress while the deformation theory leads to much more accurate predictions and, therefore, is the recommended choice for use in practical applications. On the basis of these numerical investigations, it was suggested that the roots of the discrepancy lie in the simplifying assumptions which have been regularly made with respect to the buckling modes and that the adoption of the deformation theory of plasticity simply results in counterbalancing the greater stiffness induced by kinematically constraining the cylinders to follow predefined buckling modes.
Therefore the present investigation extends the analysis to the much more general case of nonproportional loading and, at the same time, makes use of an analytical treatment of the problem instead of the numerical one employed for the case of proportional loading. This makes it possible to analyse in detail the shape of the buckling modes both in the cases of the flow and of the deformation theory of plasticity.
Blachut et al. [5] conducted experimental and numerical analyses for 30 mild-steel machined cylinders, of different dimensions, subject to axial tension and increasing external pressure. Using the code BOSOR5 [7] for their numerical analyses they reported that the agreement between the two plasticity theories appeared strongly dependent on the diameter, , and the length, , of the cylindrical shell. For short cylinders (), the plastic-buckling pressure results predicted by the flow and deformation theories coincided only when the tensile axial load vanished [5]. By increasing the axial tensile load, the plastic buckling pressures predicted by the flow theory started to diverge quickly from those predicted by the deformation theory. Additionally, the flow theory failed to predict any buckling for high axial tensile load while tests confirmed the buckling occurrence. For specimens with length-to-diameter ratio ranging from 1.5 to 2.0 the results predicted by both theories were identical for a certain range of combined loading. However, for high values of applied tensile load, the predictions of the flow theory began to deviate from those of the deformation theory and became unrealistic in correspondence with large plastic strains.
Giezen et al. [6] conducted experiments and numerical analyses on two sets of tubes made of aluminium alloy 6061-T4 and subjected to combined axial tension and external pressure in order to highlight the difference in buckling predictions of both the flow theory and the deformation theory again using the code BOSOR5. These tubes have ratios equal to one. In their test two different loading paths were considered. In the first one the axial tensile load was held constant and the external pressure was increased; in the second one, the external pressure was held constant and the axial tensile load was increased. Their numerical studies showed that the buckling pressure based on the flow theory increases with increasing applied tensile load while the experimental test revealed a reduction in buckling resistance with increasing axial tension. Thus as axial tension increased the discrepancy between test results and numerical results predicted by the flow theory also significantly increased. On the other hand, results predicted by the deformation theory displayed the same trend as in the test results. However, the deformation theory significantly underpredicted the buckling pressure observed experimentally for some loading paths. Therefore, Giezen [9] concluded that, generally speaking, both plasticity theories were unsuccessful in predicting buckling load.
In conclusion, when the buckling modes are the same, and in the case of nonproportional loading, the flow and deformation theory of plasticity provide the same buckling loads. It is worth recalling that the numerical FE approach [8], which is not kinematically overconstrained by a choice of predefined harmonic buckling modes, provides results which are in line with the experimental ones in the case of proportional loading.
The deformation theory of plasticity is based on the assumption that for continued loading the state of stress is uniquely determined by the state of strain and, therefore, it is a special class of path-independent nonlinear elasticity constitutive laws.
The constitutive relationship for the deformation theory of plasticity can be obtained by extending the Ramberg-Osgood law to the case of a multiaxial stress state by means of the von Mises formulation and results in the following path-independent expression [13, 14]:where and denote the strain and stress tensors, while and denote the deviatoric and spherical parts of the stress tensor, respectively.
In the realm of the thin-shell theory, and are related to the midsurface velocities components as follows: At the onset of bifurcation different modes of deformation can be found as a solution of the rate problem. A key assumption is to characterise such modes of deformation with the following harmonic expressions for , , and :where , , and are arbitrary constants, , , and and are two positive integers. represents the number of half-waves along the generator of the cylinder and denotes the number of waves in the circumferential direction.
In the present case, for the case of the flow theory based on Prandtl-Reuss equations, it isOn the other hand, for the case of the deformation theory based on Hencky equations, it isSince the material obeys the von-Misses yield criterion, the effective stress is written, under the assumption of plane stress (i.e., ), as follows:Setting and at the point of bifurcation, it isThe ratios of the elastic modulus to the tangent modulus, , and to the secant modulus, , are expressed by the Ramberg and Osgood relationship asUnder the assumption that the cylinders are simply supported at both ends and following the same line of reasoning as in [12], the equilibrium equations at the bifurcation point lead to the following set of buckling equations in the unknown constants , , and : and a sufficient condition for bifurcation to take place is that the following characteristic equation is satisfied:where and are related to the applied average axial stress and external pressure, respectively, and is a geometry-dependent parameter as follows:It is worth noticing that (20) is obtained by neglecting the higher-order terms which involve the square and products of , and . , , , and are obtained in such a way that (20) is valid for the case of combined axial tensile stress and external pressure and the use of both flow and deformation theories of plasticity. 2ff7e9595c
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