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Symmetry Plane (symmetry + plane)
Selected AbstractsInclined standing contact fatigueFATIGUE & FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, Issue 7 2003B. ALFREDSSON ABSTRACT An experimental method is presented, in which a sphere is repeatedly pressed against a surface with an inclined contact load. The method is a development of the normally loaded standing contact fatigue test. Experiments are performed for three inclination angles below the angle of friction and the results are compared to those of the normally loaded standing contact fatigue test. The influence of tangential load on endurance limit load, number of cycles to crack initiation, contact mark appearance and crack behaviour in the surface as well as in cut views are evaluated. The surface crack behaviour outside the contact mark is analysed based on the cyclic contact stresses in the test specimen. The trajectories of the largest principal stresses are followed in both the surface view and in the cut view on the symmetry plane. These stress trajectories are compared to the experimental crack results. The connection between the inclined standing contact fatigue cracks and surface distress micro-cracks is also discussed. [source] Dynamic stability of a porous rectangular platePROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2006Daniel Debowski The study is devoted to a axial compressed porous-cellular rectangular plate. Mechanical properties of the plate vary across is its thickness which is defined by the non-linear function with dimensionless variable and coefficient of porosity. The material model used in the current paper is as described by Magnucki, Stasiewicz papers. The middle plane of the plate is the symmetry plane. First of all, a displacement field of any cross section of the plane was defined. The geometric and physical (according to Hook's law) relationships are linear. Afterwards, the components of strain and stress states in the plate were found. The Hamilton's principle to the problem of dynamic stability is used. This principle was allowed to formulate a system of five differential equations of dynamic stability of the plate satisfying boundary conditions. This basic system of differential equations was approximately solved with the use of Galerkin's method. The forms of unknown functions were assumed and the system of equations was reduced to a single ordinary differential equation of motion. The critical load determined used numerically processed was solved. Results of solution shown in the Figures for a family of isotropic porous-cellular plates. The effect of porosity on the critical loads is presented. In the particular case of a rectangular plate made of an isotropic homogeneous material, the elasticity coefficients do not depend on the coordinate (thickness direction), giving a classical plate. The results obtained for porous plates are compared to a homogeneous isotropic rectangular plate. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Vibration of a porouse-cellular circular platePROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2006Ewa Magnucka-Blandzi The subject of investigation is a circular porous-cellular plate under uniform pressure. Mechanical properties of the isotropic porous cellular metal vary accross the thickness of the plate. Middle plane of the plate is its symmetry plane. Fields of diseplacements and stresses with respect the nonlinear hypothesis are described. Basing on Hamilton principle three motion equations of the plate are formulated. These equations are approximately solved. The vibration problem is reduced to the second-order differential equation. Numerical investigations are realised for family of plates. Natural frequencies are determined. The obtained results are shown in Figures. To the end of the investigation comparition analyses with respect to homogeneous plates is presented. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] rac -5-Diphenylacetyl-2,2,4-trimethyl-2,3,4,5-tetrahydro-1,5-benzothiazepine and rac -5-formyl-2,2,4-trimethyl-2,3,4,5-tetrahydro-1,5-benzothiazepineACTA CRYSTALLOGRAPHICA SECTION C, Issue 11 2009Thanikasalam Kanagasabapathy rac -5-Diphenylacetyl-2,2,4-trimethyl-2,3,4,5-tetrahydro-1,5-benzothiazepine, C26H27NOS, (I), and rac -5-formyl-2,2,4-trimethyl-2,3,4,5-tetrahydro-1,5-benzothiazepine, C13H17NOS, (II), are both characterized by a planar configuration around the heterocyclic N atom. In contrast with the chair conformation of the parent benzothiazepine, which has no substituents at the heterocyclic N atom, the seven-membered ring adopts a boat conformation in (I) and a conformation intermediate between boat and twist-boat in (II). The molecules lack a symmetry plane, indicating distortions from the perfect boat or twist-boat conformations. The supramolecular architectures are significantly different, depending in (I) on C,H...O interactions and intermolecular S...S contacts, and in (II) on a single aromatic ,,, stacking interaction. [source] Energy flux in viscoelastic anisotropic mediaGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 3 2006Vlastislav, ervený SUMMARY We study properties of the energy-flux vector and other related energy quantities of homogeneous and inhomogeneous time-harmonic P and S plane waves, propagating in unbounded viscoelastic anisotropic media, both analytically and numerically. We propose an algorithm for the computation of the energy-flux vector, which can be used for media of unrestricted anisotropy and viscoelasticity, and for arbitrary homogeneous or inhomogeneous plane waves. Basic part of the algorithm is determination of the slowness vector of a homogeneous or inhomogeneous wave, which satisfies certain constraints following from the equation of motion. Approaches for determination of a slowness vector commonly used in viscoelastic isotropic media are usually difficult to use in viscoelastic anisotropic media. Sometimes they may even lead to non-physical solutions. To avoid these problems, we use the so-called mixed specification of the slowness vector, which requires, in a general case, solution of a complex-valued algebraic equation of the sixth degree. For simpler cases, as for SH waves propagating in symmetry planes, the algorithm yields simple analytic solutions. Once the slowness vector is known, determination of energy flux and of other energy quantities is easy. We present numerical examples illustrating the behaviour of the energy-flux vector and other energy quantities, for homogeneous and inhomogeneous plane P, SV and SH waves. [source] Understanding topological symmetry: A heuristic approach to its determinationJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 4 2008M. L. Contreras Abstract An algorithm based on heuristic rules for topological symmetry perception of organic structures having heteroatoms, multiple bonds, and any kind of cycle, and configuration, is presented. This algorithm identifies topological symmetry planes and sets of equivalent atoms in the structure, named symmetry atom groups (SAGs). This approach avoids both the need to explore the entire graph automorphism groups, and to encompass cycle determination, resulting in a very effective computer processing. Applications to several structures, some of them highly symmetrical such as dendrimers, are presented. © 2007 Wiley Periodicals, Inc. J Comput Chem, 2008 [source] | ||||||||||