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Federico París - One of the best experts on this subject based on the ideXlab platform.
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unique real variable expressions of the integral kernels in the somigliana stress identity covering all transversely isotropic elastic materials for 3d bem
Computer Methods in Applied Mechanics and Engineering, 2012Co-Authors: L. Távara, Vladislav Mantic, J.e. Ortiz, Federico ParísAbstract:Abstract A formulation and computational implementation of the hypersingular stress boundary integral equation for the numerical solution of three-dimensional linear elastic problems in transversely isotropic solids is developed. The formulation is based on a new closed-form real variable expression of the integral kernel S ijk giving tractions originated by an infinitesimal dislocation loop, the source of singularity work-conjugated to stress tensor. This expression is valid for any combination of material properties and for any orientation of the Radius Vector between the source and field points. The expression is based on compact expressions of U ik in terms of the Stroh eigenvalues on the plane normal to the Radius Vector. Performing double differentiation of U ik for deducing the second derivative kernel U ik , jl the stress influence function of an infinitesimal dislocation loop Σ ijkl loop are first obtained, obtaining then the integral kernel S ijk . The expressions of S ijk and of the related kernels Σ ijkl loop and U ik , jl do not suffer from the difficulties of some previous expressions, obtained by other authors in different ways, with complex valued functions appearing for some combinations of material parameters and/or with division by zero for the Radius Vector at the rotational-symmetry axis. The expressions of the above mentioned kernels have been presented in a form suitable for an efficient computational implementation. The correctness of these expressions and of their implementation in a three-dimensional collocational BEM code has been tested numerically by solving problems with known analytic solutions for different classes of transversely isotropic materials. The obtained expressions will be useful in the development of BEM codes applied to composite materials, geomechanics and biomechanics. In particular, an application to biomechanics of the BEM code developed is shown. Additionally, these expressions can be employed in the distributed dislocation technique to solve crack problems.
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Recent developments in the evaluation of the 3D fundamental solution and its derivatives for transversely isotropic elastic materials
Electronic Journal of Boundary Elements, 2012Co-Authors: Vladislav Mantic, L. Távara, J.e. Ortiz, Federico ParísAbstract:Explicit closed-form real-variable expressions of a fundamental solution and its derivatives for three-dimensional problems in transversely linear elastic isotropic solids are presented. The expressions of the fundamental solution in displacements U ik and its derivatives, originated by a unit point force, are valid for any combination of material properties and for any orientation of the Radius Vector between the source and field points. An ex- pression of U ik in terms of the Stroh eigenvalues on the oblique plane normal to the Radius Vector is used as starting point. Working from this expression of U ik , a new approach (based on the application of the rotational symmetry of the material) for deducing the first and second order derivative kernels, U ik,j and U ik,jl respectively, has been developed. The expressions of the fundamental solution and its derivatives do not suffer from the difficulties of some previous expressions, obtained by other authors in different ways, with complex valued functions appearing for some combinations of material parameters and/or with division by zero for the Radius Vector at the rotational symmetry axis. The expressions of U ik , U ik,j and U ik,jl are presented in a form suitable for an efficient computational implementation in BEM codes.
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Unique real‐variable expressions of displacement and traction fundamental solutions covering all transversely isotropic elastic materials for 3D BEM
International Journal for Numerical Methods in Engineering, 2008Co-Authors: L. Távara, Vladislav Mantic, J.e. Ortiz, Federico ParísAbstract:A general, efficient and robust boundary element method (BEM) formulation for the numerical solution of three-dimensional linear elastic problems in transversely isotropic solids is developed in the present work. The BEM formulation is based on the closed-form real-variable expressions of the fundamental solution in displacements Uik and in tractions Tik, originated by a unit point force, valid for any combination of material properties and for any orientation of the Radius Vector between the source and field points. A compact expression of this kind for Uik was introduced by Ting and Lee (Q. J. Mech. Appl. Math. 1997; 50:407–426) in terms of the Stroh eigenvalues on the oblique plane normal to the Radius Vector. Working from this expression of Uik, and after a revision of their final formula, a new approach (based on the application of the rotational symmetry of the material) for deducing the derivative kernel Uik, j and the corresponding stress kernel Σijk and traction kernel Tik has been developed in the present work. These expressions of Uik, Uik, j, Σijk and Tik do not suffer from the difficulties of some previous expressions, obtained by other authors in different ways, with complex-valued functions appearing for some combinations of material parameters and/or with division by zero for the Radius Vector at the rotational-symmetry axis. The expressions of Uik, Uik, j, Σijk and Tik have been presented in a form suitable for an efficient computational implementation. The correctness of these expressions and of their implementation in a three-dimensional collocational BEM code has been tested numerically by solving problems with known analytical solutions for different classes of transversely isotropic materials. Copyright © 2007 John Wiley & Sons, Ltd.
Po-tuan Chen - One of the best experts on this subject based on the ideXlab platform.
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Steady motions of gyrostat satellites and their stability
IEEE Transactions on Automatic Control, 1995Co-Authors: Li-sheng Wang, Kuang-yow Lian, Po-tuan ChenAbstract:The steady motions of a rigid body rotating about its maximum principal axis of inertia, while the Radius Vector lies in the direction of its minimum principal axis of inertia, is known to be stable in the sense of Lyapunov. Due in part to their stowed configuration in launch vehicles, however, satellites typically have an initial rotation about their minimum principal axis of inertia. Such rotation may be unstable in the presence of some dissipations. This paper investigates the effect of momentum wheels on the stability of steady motions. It is proved that the momentum wheels increase the effective moment of inertia of the gyrostat-satellite system about some desired axis. Stability of the steady rotation about the desired axis can be established only for the case when the moment of inertia of the axis aligned with the Radius Vector is smaller than that of the axis of linear momentum. A new set of stability criteria is obtained which includes the effects of the coupling between the orbital and attitude dynamics and may be useful in the design of attitude control systems for large spacecraft in low Earth orbit.
Joseph E. Yukich - One of the best experts on this subject based on the ideXlab platform.
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Brownian limits, local limits and variance asymptotics for convex hulls in the ball
The Annals of Probability, 2013Co-Authors: Pierre Calka, Tomasz Schreiber, Joseph E. YukichAbstract:Schreiber and Yukich [Ann. Probab. 36 (2008) 363-396] establish an asymptotic representation for random convex polytope geometry in the unit ball $\mathbb{B}^d, d\geq2$, in terms of the general theory of stabilizing functionals of Poisson point processes as well as in terms of generalized paraboloid growth processes. This paper further exploits this connection, introducing also a dual object termed the paraboloid hull process. Via these growth processes we establish local functional limit theorems for the properly scaled Radius-Vector and support functions of convex polytopes generated by high-density Poisson samples. We show that direct methods lead to explicit asymptotic expressions for the fidis of the properly scaled Radius-Vector and support functions. Generalized paraboloid growth processes, coupled with general techniques of stabilization theory, yield Brownian sheet limits for the defect volume and mean width functionals. Finally we provide explicit variance asymptotics and central limit theorems for the k-face and intrinsic volume functionals.
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Brownian limits, local limits, extreme value and variance asymptotics for convex hulls in the ball
2009Co-Authors: Pierre Calka, Tomasz Schreiber, Joseph E. YukichAbstract:The paper of Schreiber and Yukich [40] establishes an asymptotic representation for random convex polytope geometry in the unit ball $\B_d,\; d \geq 2,$ in terms of the general theory of stabilizing functionals of Poisson point processes as well as in terms of the so-called generalized paraboloid growth process. This paper further exploits this connection, introducing also a dual object termed the paraboloid hull process. Via these growth processes we establish local functional and measure-level limit theorems for the properly scaled Radius-Vector and support functions as well as for curvature measures and $k$-face empirical measures of convex polytopes generated by high density Poisson samples. We use general techniques of stabilization theory to establish Brownian sheet limits for the defect volume and mean width functionals, and we provide explicit variance asymptotics and central limit theorems for the $k$-face and intrinsic volume functionals. We establish extreme value theorems for Radius-Vector and support functions of random polytopes and we also establish versions of the afore-mentioned results for large isotropic cells of hyperplane tessellations, reducing the study of their asymptotic geometry to that of convex polytopes via inversion-based duality relations, as in Calka and Schreiber [14].
Zi-hua Weng - One of the best experts on this subject based on the ideXlab platform.
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Varying speed of light and field potential in the octonion spaces.
arXiv: General Physics, 2018Co-Authors: Zi-hua WengAbstract:The paper focuses on exploring the contribution of field potential on the speed of light. The octonions can be applied to study the physical quantities of electromagnetic and gravitational fields, including the transformation between two coordinate systems. In the octonion space, the Radius Vector can be combined with the integrating function of field potential to become one composite Radius Vector. The latter is considered as the Radius Vector in an octonion composite-space, which belongs to the function spaces. In the octonion composite-space, when there is the relative motion between two coordinate systems, it is capable of deducing the Galilean-like transformation and Lorentz-like transformation. From the two transformations, one can achieve the influence of relative speed on the speed of light (or Sagnac effect), but also the impact of electromagnetic potential on the speed of light. The study reveals that the electromagnetic potential has a direct influence on the speed of light in the optical waveguides. The paper appeals intensely to validate this inference in relevant experiments, revealing further some new physical quantities of refractive indices in the optical waveguides.
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Physical quantities and spatial parameters in the complex octonion curved space
General Relativity and Gravitation, 2016Co-Authors: Zi-hua WengAbstract:The paper focuses on finding out several physical quantities to exert an influence on the spatial parameters of complex-octonion curved space, including the metric coefficient, connection coefficient, and curvature tensor. In the flat space described with the complex octonions, the Radius Vector is combined with the integrating function of field potential to become a composite Radius Vector. And the latter can be considered as the Radius Vector in a flat composite-space (a function space). Further it is able to deduce some formulae between the physical quantity and spatial parameter, in the complex-octonion curved composite-space. Under the condition of weak field approximation, these formulae infer a few results accordant with the General Theory of Relativity. The study reveals that it is capable of ascertaining which physical quantities are able to result in the warping of space, in terms of the curved composite-space described with the complex octonions. Moreover, the method may be expanded into some curved function spaces, seeking out more possible physical quantities to impact the bending degree of curved spaces.
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Electromagnetic Force on Charged Objects with the Angular Velocity
2015Co-Authors: Zi-hua WengAbstract:The paper studies the in∞uence of angular velocity on the electromagnetic force for one rotational charged object. In the complex octonion space, the Radius Vector and the integrating function of fleld potential can be combined together to become one compounding Radius Vector. The latter may be considered as the 'Radius Vector' in the complex-octonion compounding space (one function space). The complex-octonion compounding space will be regarded as the extension of one complex-octonion compounding fleld. In the complex-octonion compounding fleld, the angular velocity will impact the compounding fleld strength, fleld source and linear momentum and so on. The study reveals that the angular velocity has a direct in∞uence on the compounding angular momentum, compounding torque, and compounding force and so forth, including the compounding force term exerting on the rotational charged object. 1. INTRODUCTION The quaternion was applied by J. C. Maxwell to research the electromagnetic theory. Nowadays some scholars studied the electromagnetic and gravitational flelds by means of the complex quater- nion. The complex quaternion space for gravitational flelds and that for electromagnetic flelds can be combined together to become one complex octonion space. As a result the physics feature of two flelds can be described simultaneously with the complex octonion (1), including the force in the presence of the gravitational fleld, electromagnetic fleld, and angular velocity. In the complex octonion space, the Radius Vector and the integrating function of fleld potential are able to be combined together to become the compounding Radius Vector, which may be con- sidered as the 'Radius Vector' in the compounding space (or one function space). In the physics, the space is the extension of the fleld (2). Similarly the compounding space will be regarded as the extension of the compounding fleld. By analogy the fleld and space should be generalized to the compounding fleld and compounding space respectively. Further it is flt for studying the impact of the angular velocity on the fleld strength and fleld source and so on, from the compounding fleld and compounding space. Making use of the complex octonion, the paper claims that there are some kinds of equilibrium states in these two flelds. The fleld potential and velocity ratio both will impact the fleld strength, fleld source, and equilibrium state. So the variation of fleld potential may alter the force or torque. This inference may flgure out the physical phenomenon relevant to the over-speed movement of stars on the fringe of a galaxy (3), although this uncertainty remains as puzzling as ever. 2. GRAVITATIONAL SOURCE
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Dense Waves in Electromagnetic and Gravitational Fields
2013Co-Authors: Zi-hua WengAbstract:The quaternion is able to describe the physical features of the electromagnetic fleld and gravitational fleld. In the quaternion space for the electromagnetic fleld, the quaternion Radius Vector combines with the integral of electromagnetic potential to become the compound- ing Radius Vector. From the quaternion operator and the compounding Radius Vector, it is able to deduce the compounding fleld strength, fleld source, and wave equation of the electromag- netic fleld. According to the compounding wave equation, the compounding fleld strength is one transverse wave, which transmission direction is perpendicular to the electric intensity and magnetic ∞ux density, and is able to impact the movements of other trial charges, and then to form the electromagnetic dense waves. The quaternion space for the gravitational fleld is inde- pendent to that for the electromagnetic fleld. In the quaternion space for the gravitational fleld, the quaternion Radius Vector combines with the integral of gravitational potential to become the compounding Radius Vector. From the quaternion operator and the compounding Radius Vector, it is able to deduce the compounding fleld strength, fleld source, and wave equation of the gravita- tional fleld. According to the compounding wave equation, the compounding fleld strength is one transverse wave, which transmitted along the orbital tangent direction, and is able to in∞uence the movements of other objects, and then to form the gravitational dense waves.
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Influence of field potential on the speed of light
arXiv: General Physics, 2009Co-Authors: Zi-hua WengAbstract:The paper discusses the affection of the scalar potential on the speed of light in the electromagnetic field, by means of the characteristics of octonion. In the octonion space, the Radius Vector is combined with the integral of field potentials to become one new Radius Vector. When the field potentials can not be neglected, the new Radius Vector will cause the prediction to departure slightly from the theoretical value of the speed of light. The results explain why the speed of light varies in diversiform optical waveguide. And there exist negative refractive indexes due to different scalar potentials in the gravitational field and electromagnetic field.
Rodney Hill - One of the best experts on this subject based on the ideXlab platform.
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Plastic anisotropy and the geometry of yield surfaces in stress space
Journal of The Mechanics and Physics of Solids, 2000Co-Authors: Rodney HillAbstract:In the context of classical anisotropic plasticity a general theorem is proved in relation to the pure geometry of convex yield surfaces in a six-dimensional Cauchy stress-space. The analysis subsequently focuses on particular yieldpoints where the local Radius Vector and surface normal represent coaxial tensors. Further detail is presented for a standard family of yield functions associated with states of generalized plane stress produced in sheet-forming operations. The overall objective is a comprehensive theoretical framework for the improved modelling of anisotropic plastic behaviour.
