Prismatic Bodies Research Articles

Optimization of Interference Effects on High-Rise Buildings for Different Wind Angle Using CFD Simulation

A numerical study by CFD (Computational Fluid Dynamics) simulation to obtain optimum spacing in between interfering and principal building where the interference effects are nullified and the behavior of principal building will be the same as the isolated building. The analytical result of rectangular plan shape prismatic bluff bodies are investigated in a series of Fluid Flow (CFX) analysis to study the optimum spacing in between interfering and principal building at 0° and 90° wind angle. This study highlights the Interference Factor (IF) of principal building which is similar to the an isolated building due to increasing spacing in between interfering and principal building. The plans of both the buildings are rectangular in shape and similar dimensions and principle axis. This study also highlights the IF, also found by the graphical representation of different spacing between interfering building and principal building.

Numerical Simulation of Dynamic Processes of Elastoplastic Interaction Between Three-Dimensional Heterogeneous Bodies on the Basis of Semi-Analytical Finite Element Method. Part 2. A Study of the Dynamic Deformation of Complex-Shaped Three-Dimensional Structures

Possibilities of the semi-analytical finite element method in the investigation of transient processes of the three-dimensional deformation of heterogeneous bodies of revolution and complex-shaped prismatic bodies by the action of pulsed stressing with allowance for contact interaction zones and nonlinear work of material are shown by calculations of real structures.

Structural edge delimitation from gravity anomaly data using the directional continuous wavelet transform with an example from the Basin and Range Province of the United States

In this article, we demonstrate the use of the 2D directional continuous wavelet transform (DCWT) for structural boundary delimitation. We include an example of Bouguer gravity anomaly data analysis from the Basin and Range Province of the United States. Our approach is based on mapping maxima in the modulus of the directional continuous wavelet transform for various scales. We initially validate our concept using synthetic gravity anomaly fields generated from cylindrical and prismatic model bodies (source geometries). Subsequent application of our concept to real gravity anomaly data shows that the method is versatile and robust.

Numerical evaluation of the original “Neuber’s rule” for pure out-of-plane shear loading

Neuber’s rule has become a popular analytical tool for evaluating notch root stress and strain for fatigue life estimation. The original study was based on the geometry of prismatic bodies with hyperbolic notches under pure out-of-plane shear with a nonlinear material model. From this study, the author observed that “The geometric mean of stress and strain concentration factors is equal to theoretical elastic stress concentration factor, Kt.” Although this conclusion was based on a “special deformation law,” Neuber suggested that it can be approximately extended to any stress–strain law and to tensile and bending loads replacing shear stress and strain with equivalent von Mises stress and strain and Neuber’s rule evolved. Extensive research has been conducted to evaluate and generalize Neuber’s rule for fatigue analysis. However, the applicability of Neuber’s rule to a specific situation requires consideration of the material model utilized, in addition to the notch geometry and loading conditions. This article presents a detailed finite element analysis of Neuber’s rule using out-of-plane shear loading on prismatic bodies with hyperbolic notch geometries identical to those considered by Neuber. Neuber’s nonlinear material model (special deformation law) is compared to the Ramberg–Osgood material model, and discernable differences were observed. Neuber’s observations were approximately valid for conditions congruent with his constitutive model. For the Ramberg–Osgood model, this happens to occur only for a strain hardening exponent of about 0.2. For other values of the strain hardening exponent, Neuber’s model cannot emulate the shape of the Ramberg–Osgood curve, and notch strain predictions from Neuber’s rule are less accurate.

Numerical Simulation of Dynamic Processes of Elastoplastic Interaction between Three-Dimensional Heterogeneous Bodies on the basis of Semi-Analytical Finite Element Method. Part 1. Computational Relationships of the Semi-Analytical Finite Element Method and Algorithms for the Study of Transient Processes of Dynamic Deformation of Heterogeneous Prismatic Bodies and Bodies of Revolution

On the basis of a semi-analytical finite element method, an effective approach has been developed for studying transient processes of dynamic deformation of three-dimensional heterogeneous bodies of revolution and prismatic bodies of complex shape and structure by the action of time-and space-varying pulsed stressing with allowance for the plastic properties of the material and time-varying contact interaction conditions. New types of finite elements have been created, on the basis of which computational relationships of the semi-analytical finite element method (SAFEM) for problems of dynamics have been constructed. Modified relationships of the Newmark method have been obtained, which have been formulated for the amplitude subsystems of SAFEM. Effective block iteration algorithms for the solution of large systems of nonlinear equations of SAFEM have been developed and realized.

Nonlinear effects during the tension, bend, and torsion of elastic bodies with distributed dislocations

A series of exact solutions of the problems on large deformations of three-dimensional nonlinearly elastic bodies with distributed dislocations is found. The tension-compression of the prismatic bodies with the distributed straight-linear screw dislocations is investigated. The influence of the distributed screw dislo- cations of the radial direction of the torsion and extension of the circular cylinders under large deformations is investigated. The problem on the strong bend of the rectangular bar containing distributed edge dislocations is solved. It is established that nonuniform rotation fields can occur at zero stresses in a body with continu- ously distributed dislocations.

Rigid Body Motion Conversion due to Collision

The impact phenomenon may be used for task-oriented changing of rigid body motion. When moving body encounters with some obstacle all parameters of motion are changing as a result of impact and trajectory and type of motion are also changing. In this work the conversion of translatory motion of prismatic rigid body into plane or rotation and conversion of plane motion of cylindrical body due to impact are considered. The conditions of conversion of one type of motion into another and parameters post-impact motion are studied. Problems are solved in the framework of rigid body motion, using rigid body impact theory. Studying of such phenomena is important for location of parts on industrial conveyors, feeders, etc.

A Hamiltonian state space approach to anisotropic elasticity and piezoelasticity

We present a Hamiltonian state space approach for problems of anisotropic elasticity and piezoelasticity. By means of Legendre’s transformation, the basic equations of piezoelasticity are formulated into a state equation and an output equation in terms of the state vector that comprises the generalized displacement vector and the conjugate generalized traction vector as the dual variables. The Hamiltonian features and symplectic orthogonality of the system, which are essential for the solution approach using eigenfunction expansion, are delineated at length. We show that the solution to 3D problems of a prismatic body hinges upon a 2D Hamiltonian eigensystem and the eigensolution associated with the zero eigenvalue leads to the solution to the generalized plane problem naturally. Based on the formalism, the solution to a problem of piezoelasticity is no more difficult than its elastic counterpart.

Correction schemes for self-demagnetisation

Aeromagnetic surveys collected over bodies of high susceptibility record fields that have been significantly affected by self-demagnetisation. These effects complicate interpretation as the amplitude of the magnetic response scales non-linearly with the susceptibility. Analytic modelling is only carried out for compact ellipsoidal bodies and most approaches break down in the high susceptibility limit. It therefore of interest to develop tools for understanding and modelling of self-demagnetisation effects to support geophysical exploration. We present a modelling scheme based on multiple prismatic sub-volume bodies in a 3D grid for investigating and testing self-demagnetisation effects. This scheme, and another recent iterative scheme based on multiple spherical voxels, is tested to demonstrate self-demagnetisation effects on simple bodies. The schemes are verified against the known analytic results for a spherical body and the results for a cubic body. The prismatic scheme is then used to model a dipping magnetite sheet for comparison against real data where self-demagnetisation effects are thought to be important. Finally, we demonstrate the main advantage of the correction scheme by modelling multiple magnetic bodies in a 3D grid. These correction schemes are aimed at improving current magnetic modelling techniques and providing solutions for dealing with complex and highly susceptible bodies.

Magnetic links among lava flows, tuffs and the underground plumbing system in a monogenetic volcano, derived from magnetics and paleomagnetic studies

A combined study using magnetics and paleomagnetism of the Toluquilla monogenetic volcano and associated lavas and tuffs from Valsequillo basin in Central Mexico provides evidence on a ‘magnetic’ link between the lavas, ash tuffs and the underground volcanic conduit system. Paleomagnetic analyses show that the lava and ash tuff carry reverse polarity magnetizations, which correlate with the inversely polarized dipolar magnetic anomaly over the volcano. The magnetizations in the lava and tuff show similar southward declinations and upward inclinations, supporting petrological inferences that the tuff was emplaced while still hot and indicating a temporal correlation for lava and tuff emplacement. Modeling of the dipolar anomaly gives a reverse polarity source magnetization associated with a vertical prismatic body with southward declination and upward inclination, which correlates with the reverse polarity magnetizations in the lava and tuff. The study documents a direct correlation of the paleomagnetic records with the underground magmatic conduit system of the monogenetic volcano. Time scale for cooling of the volcanic plumbing system involves a longer period than the one for the tuff and lava, suggesting that magnetization for the source of dipolar anomaly may represent a long time average as compared to the spot readings in the lava and tuff. The reverse polarity magnetizations in lava and tuff and in the underground source body for the magnetic anomaly are interpreted in terms of eruptive activity of Toluquilla volcano at about 1.3Ma during the Matuyama reverse polarity C1r.2r chron.

Study of Numeric Convergence of the Method of R − functions in Problems of Constraint Torsion

<b> </b><b> </b>This paper is devoted to the study of numeric convergence of Rvachev’s method of R − function. The method of R − function in this case is applied to the solution of the problem of constraint torsion of prismatic bodies of arbitrary section. First the problem is solved analytically when the section is rectangular and this solution is compared with results of the method of R − function. Then numeric convergence of R − function is studied, when the angles of rectangular section are rounded; it also is applied when the section has rectangular opening with rounded angles. Results compared show good agreement and convergence.

A new Ultra Precision Interferometer for absolute length measurements down to cryogenic temperatures

A new Ultra Precision Interferometer (UPI) was built at Physikalisch-Technische Bundesanstalt. As its precursor, the precision interferometer, it was designed for highly precise absolute length measurements of prismatic bodies, e.g. gauge blocks, under well-defined temperature conditions and pressure, making use of phase stepping imaging interferometry. The UPI enables a number of enhanced features, e.g. it is designed for a much better lateral resolution and better temperature stability. In addition to the original concept, the UPI is equipped with an external measurement pathway (EMP) in which a prismatic body can be placed alternatively. The temperature of the EMP can be controlled in a much wider range compared to the temperature of the interferometer's main chamber. An appropriate cryostat system, a precision temperature measurement system and improved imaging interferometry were established to permit absolute length measurements down to cryogenic temperature, demonstrated for the first time ever. Results of such measurements are important for studying thermal expansion of materials from room temperature towards less than 10 K.

Stiffness and buckling optimization of thin plates with BEM

The thickness optimization is used to maximize the stiffness or the buckling load of a Kirchhoff plate having constant volume. The shape of the plate is arbitrary and it is subjected to any type of admissible boundary conditions. The optimization consists in establishing the thickness variation law, for which either the stiffness of the plate or the buckling load is maximized. Beside the equality constraint of constant volume, the thickness variation is subjected also to inequality constraints resulting from serviceability requirements (upper and lower thickness bounds) as well as from the condition that the Kirchhoff plate theory remains valid. The latter constraint is new and it is derived herein by approximating the plate with a three-dimensional prismatic elastic body having curved upper and lower surface. The optimization problem is solved using the sequential quadratic programming algorithm. The bending and the plane stress problem of a plate with variable thickness, required for the evaluation of the objective function, are solved using the analog equation method. The thickness is approximated using integrated radial basis functions that approximate accurately not only the thickness function but also its first and second derivatives involved in the plate equation and in the constraints. Several plate optimization problems have been studied giving realistic and meaningful optimum designs without violating the validity of the thin plate theory.

Synergy of cavitation and slurry erosion in the slurry pot tester

Hydraulic machine materials are routinely tested under laboratory conditions to study the effects of slurry erosion and cavitation erosion. The material removal may occur by either of the modes or by their combined effect. To evaluate the damage in the latter case, where the damage can be severe, there is a need for a suitable test method that combines the two modes. With this objective, a new simple method is developed that combines the effect of slurry erosion and cavitation erosion. Triangular prismatic bluff bodies are used as cavitation inducers in the conventional slurry pot tester. In the slurry pot the brass test specimens are exposed to water/slurry, with and without cavitation inducers. Analysis of the wear results reveals significant variations in material loss confirming synergistic erosion damage. The new laboratory testing method can be very useful in assessing and ranking of the material performance under combined particle and cavitation erosion conditions.

Stress and Strain Locus of Perforated Plate in Inelastic Deformation—Strain-Controlled Loading Case

Plastic strain of structures having stress concentration is estimated by using the simplified method or the finite element elastic solutions. As the simplified methods used in codes and standards, we can cite Neuber’s formula in the work by American Society of Mechanical Engineers (1995, “Boiler and Pressure Vessel Code,” ASME-Code, Section 3, Division 1, Subsection NH) and by Neuber (1961, “Theory of Stress Concentration for Shear Strained Prismatic Bodies With Arbitrary Nonlinear Stress-Strain Law,” ASME, J. Appl. Mech., 28, pp.544–550) and elastic follow-up procedure in the work by Japan Society of Mechanical Engineers [2005, “Rules on Design and Construction for Nuclear Power Plants, 2005, Division 2: Fast Breeder Reactor” (in Japanese)]. Also, we will cite stress redistribution locus (SRL) method recently proposed as the other simplified method in the work by Shimakawa et al. [2002, “Creep-Fatigue Life Evaluation Based on Stress Redistribution Locus (SRL) Method,” JPVRC Symposium 2002, JPVRC/EPERC/JPVRC Joint Workshop sponsored by JPVRC, Tokyo, Japan, pp. 87–95] ad by High Pressure Institute of Japan [2005, “Creep-Fatigue Life Evaluation Scheme for Ferritic Component at Elevated Temperature,” HPIS C 107 TR 2005 (in Japanese)]. In the present paper, inelastic finite element analysis of perforated plate, whose stress concentration is about 2.2–2.5, is carried out, and stress and strain locus in inelastic range by the detailed finite element solutions is investigated to compare accuracy of the simplified methods. As strain-controlled loading conditions, monotonic loading, cyclic loading, and cyclic loading having hold time in tension under strain-controlled loading are assumed. The inelastic strain affects significantly life evaluation of fatigue and creep-fatigue failure modes, and the stress and strain locus is discussed from the detailed inelastic finite element solutions.

Generalized Hilbert transforms of the effect of single magnetic sources

The generalized Hilbert transforms of potential fields, particularly magnetic fields, provide a useful resource for improving interpretation. Even though [Formula: see text]- and [Formula: see text]-Hilbert transforms of a potential field on a plane can be approximately computed from the whole observed field, they are locally independent of the observations when working on reduced areas of the plane, and therefore, on those areas, Hilbert transforms can be combined with them to better constrain and stabilize local inversions. Extended Euler deconvolution, based on Euler’s homogeneity equation, makes extensive use of this principle. We investigated closed-form expressions for evaluating in the space domain the generalized [Formula: see text]- and [Formula: see text]-Hilbert transforms of magnetic fields generated by single point sources, given in the form of dipoles, monopoles, and Newtonian potential type sources. Apart from providing a way to calculate Hilbert transforms via equivalent sources, this approach, adding little computer effort, can be applied to solve local inverse problems as a way to improve the definition of a model previous to an inversion over a large area; the solution is modeled by point sources, and it enables matching not only the observations, but also the Hilbert transforms, thus providing stronger constraints. A synthetic example with noisy data demonstrated the resolving power of this approach in locally inverting for magnetization intensities of prismatic bodies using data windows either above or displaced from the sources. In an example from a magnetic anomaly over Sierra de San Luis, Argentina, the magnetization intensities of the basement are locally inverted for at each solution point of an extended Euler deconvolution. Results indicated a more coherent pattern when the Hilbert transforms were incorporated to the inversion, illustrating how local inversions with Hilbert transforms, which do not involve time-consuming operations, can accompany extended Euler deconvolutions to better outline characteristics of a model.

Identification of meaningful coherent structures in the wind-induced pressure on a prismatic body

The concept of coherent structure is often invoked for the qualitative analysis of the wind-induced pressure field acting on bluff bodies. Coherent structures are traditionally extracted from the measured data through the Proper Orthogonal Decomposition (or Principal Component Analysis, PCA), but serious concerns on their meaningfulness have been risen. In an attempt to mitigate these problems, the Independent Component Analysis (ICA) has been introduced and demonstrated some potentials to extract coherent structures that are consistent with the observed phenomenon in term of some features that are defined in this paper. Considering the case of the pressure measured on a square-base prism immersed in a turbulent boundary layer with a non-symmetrical configuration, PCA and ICA are applied to extract coherent structures. The role of the model order, as well as the effect of a non-homogeneous spatial discretization is investigated.

Spacetime Interpretation of Torsion in Prismatic Bodies

A non-linear theory for the plastic deformation of prismatic bodies is constructed which interpolates between Prandtl’s linear soap-film approximation and Nadai’s sand-pile model. Geometrically Prandtl’s soap film and Nadai’s wavefront are unified into a single smooth surface of constant mean curvature in three-dimensional Minkowski spacetime.

Measurement Results of the Antenna Phase Patterns Onboard Flying Spin Satellites

This paper reports measurement results of the antenna phase patterns onboard flying spin satellites during the SELENE (KAGUYA) mission period, and shows monthly variations clearly for the first time. When an antenna is loaded on a spin satellite, due to the effects of the antenna phase patterns, periodical components with the spin frequency and higher order harmonics occur and influence Doppler measurements. Because Rstar and Vstar, two subsatellites of SELENE, have octagonal prismatic bodies, the 8th, 16th, and 24th harmonics are relatively stronger than the other ones in the 2-way and 4-way Doppler data. These three harmonics' amplitudes over the entire mission longer than one year clearly varied with a period of 27.32 days (one sidereal month). The antenna phase patterns were estimated using 1-26th harmonics, whose rms variations were also with a period of 27.32 days. From the 24th harmonic and the antenna phase patterns, the spin frequency variations of Rstar and Vstar over the entire mission were estimated with an accuracy of Hz.

The problem of optimizing the torsional rigidity of a prismatic body about a cross section

Some extremal problems, related to the torsional rigidity of a homogeneous body, are investigated. The problem of optimizing the torsional rigidity of a cylindrical body about a cross section is solved by determining the variation of the region when using the one-to-one correspondence between bounded convex regions and continuous positive-homogeneous convex functions. Using this approach a formula is obtained for the torsional rigidity, and conditions are also obtained characterizing the optimum region and the maximum value of the functional.