Symmetric Notches Research Articles

Bilateral macrostomia in one of monozygotic twins

This report concerns a pair of monozygotic twins discordant for bilateral symmetrical macrostomia. Laterally placed, symmetrical notches in the vermilion borders of both upper and lower lips were apparent in the affected twin. Since the oral cavity walls develop by a differential growth and merging mechanism, this result suggests a mechanism of tissue breakdown as the cause of macrostomia. Furthermore, discordance in these monozygotic twins minimizes the importance of heredity in this malformation.

A numerical algorithm for endochronic plasticity and comparison with experiment

A numerical algorithm based on the finite element method of analysis of the boundary value problem in a continuum is presented, in the case where the plastic response of the material is given in the context of endochronic plasticity. The relevant constitutive equation is expressed in incremental form and plastic effects are accounted for by the method of an induced pseudo-force in the matrix equations. The results of the analysis are compared with observed values in the case of a plate with two symmetric notches and loaded longitudinally in its own plane. The agreement between theory and experiment is excellent.

Transient Thermal Stresses in a Circular Region with Symmetrical Circular Notches

実際の構造物では,その形状が複雑な場合が多く,このような物体における熱応力問題の解析的取扱いは困難となり,数値解法にゆだねられる場合が多い.本報は,厳密解を得ることが困難な特異形状をした物体の非定常熱応力問題を,解析的に取扱う場合の一方法を示したものであり,具体的な形状として,円弧縁によってその一部が切り取られた円形領域に,局部加熱が作用する場合について解析し,数値計算をした.

The plane-strain general yielding of notched members due to combined axial force and bending—I: Wedge-shaped notches with large flank angles

The slip-line field proposed by Green for the general yielding of notched plates in pure bending is generalized to provide solutions for the general yielding of notched plates subjected to combined bending and axial force. For symmetrically notched plates subjected to arbitrary combinations of axial force and bending moment, two constraint factors are obtained, T 1 due to the axial force and M 1 due to the bending moment. These constraint factors are shown to have a characteristic locus expressed by two parabolae in the T 1 − M 1 plane. In one extreme case where both flank angles are equal to π, i.e. a flat plate, the locus is the same as that obtained by Prager. The general yielding loci of single notched plates and plates containing symmetrical notches of the same flank angle are derived as special cases of the general problem and some practical problems involving single notches are considered.

The plane-strain general yielding of notched members due to combined axial force and bending—II: Deep circular notches

The slip-line fields proposed by Green for the plane-strain general yielding of notched plates in pure bending are generalized to provide solutions for notched plates subjected to combined axial force and bending. Deep symmetrical circular notches and single circular notches are considered. For notched plates subjected to arbitrary combinations of axial force and bending, two constraint factors are obtained, T 1 due to the axial force and M 1 due to the bending moment. These constraint factors are shown to have characteristic relationships on the T 1−M 1 plane for the single notched plate and the symmetrically notched plate. The derivations of these general yielding loci are described in detail and the statical and kinematical limitations of the slip-line fields are discussed. Finally it is demonstrated that the corresponding strain-rate vectors are normal to these loci and that, therefore, these loci can be regarded as plastic potentials.

Tension of a Strip with Symmetric Edge Cracks or Elliptical Notches

Tension of a Strip with Symmetric Edge Cracks or Elliptical Notches

A Note on Stress-Concentration Factors for Symmetric U-Shaped Notches in Tension Strips

Technical Briefs A Note on Stress-Concentration Factors for Symmetric U-Shaped Notches in Tension Strips T. Slot, T. Slot Knolls Atomic Power Laboratory, General Electric Company, Schenectady, N. Y. Search for other works by this author on: This Site PubMed Google Scholar D. F. Mowbray D. F. Mowbray Materials & Processes Laboratory, General Electric Company, Schenectady, N. Y. Search for other works by this author on: This Site PubMed Google Scholar Author and Article Information T. Slot Knolls Atomic Power Laboratory, General Electric Company, Schenectady, N. Y. D. F. Mowbray Materials & Processes Laboratory, General Electric Company, Schenectady, N. Y. J. Appl. Mech. Dec 1969, 36(4): 882-884 (3 pages) https://doi.org/10.1115/1.3564791 Published Online: December 1, 1969 Article history Received: November 26, 1968 Revised: April 7, 1969 Online: September 14, 2011

Mandibulo-facial dysostosis : (Treacher Collins syndrome) の 1 例

The term, Treacher Collins syndrome has been widely recognized as the condition which was indicated by E. Treacher Collins in 1900. First 2 cases reported by him showed symmetrical congenital notches in the outer part of each lower lids, palpebral fissures sloping downwards laterally (antimongoloid) and malar bone hypoplasia. The cases of congenital notches at the outer part of the lower lids were, however, already reported by G. A. Berry in 1889. In 1944, Franceschetti and Zwahlen who studied in detail this condition, recommended the term, dysostosis mandibulo-faciale. There after both have been used synonymously. We encountered December 6, 1967 a six-year-old girl with palpebral fissures sloping downwards laterally (antimongoloid), malar bone and maxillar hypoplasia, macrostomia and mental retardation. Our case seems to belong to the incomplete form of mandibulo-facial dysostosis (Treacher Collins syndrome).

Elastic-plastic strain and stress distribution in notched plates under plane stress

An experimental solution is presented for the plane state of stress in an elastic-plastic isotropic solid obeying the Mises yield condition. The elastic and plastic strains were determined by using birefringent coatings cemented on the surface of the model. Normal incidence of circularly polarized light yielded the difference of principal strains at the model-coating interface. Linearly polarized light gave the directions of principal strains. The values of ϵ z-principal strains, normal to the surface of the plate, were determined from an analogy relating this strain to another potential field. The values of ϵ z-strains together with data from the birefringent coatings yielded enough information for the explieit analytic solution of the elastic-plastic plane stress problem. The stress-components were determined by means of the Prandtl-Reuss stress-strain relations in a step-by-step process of loading. It was assumed that stresses and strains remained constant during each step and they only changed when the next step started. This method may have a general applicability to any plane-stress restricted plasticity problem, provided that convenient formulae are established satisfying the yield condition of the material and the associated flow rule. The method was applied to the solution of a series of plane-stress problems of restricted plasticity. Thin flat plates containing symmetrical deep notches with circular roots subjected to a uniform tension were considered and their elastoplastic stress and strain distribution was evaluated. Four cases were solved for various flank angles between 0 and 120°, the minimum width of the plates remaining constant. The influence of the flank angle on the shape of the spreading plastic zones was determined and the critical loads for incipient plastic flow were evaluated.

An elastic-plastic problem under conditions of antiplanar deformation

By antiplanar deformation is meant the state of stress in an infinitely long cylinder subjected to the action of loading which is applied in the direction of the generators and which is constant along them. The elastic-plastic problem under the condition of antiplanar deformation has already been considered in the works of Trefftz [1], Hult and McClintock [2], Neuber [3]. Paper [1] gives an exact solution of the elastic-plastic problem on the antiplanar deformation of an angle section with right-angle opening, and also of the analogous problem for a region exterior to a circular hole. The elastic-plastic problem for a half-plane with a sharp notch has been solved for small values of the loading parameter in [2]. Neuber [3] considered a strip with two symmetric sharp notches, and, moreover, for an arbitrary single-valued relation between the stresses and the strains, the solution of the problem was reduced to a system of two ordinary differential equations and for a specially selected law the solution was obtained in closed form. Below, a treatment will be given of the solution in quadratures of the static elastic-plastic problem for the exterior of an arbitrary contour wholly enclosed by the plastic zone and loaded arbitrarily (Section 2); an exact solution of the problem for the exterior of a contour consisting of segments of straight and curved lines in the case when the straight sections are free of stresses and the parts of the curved arcs, which are arbitrarily loaded, are wholly contained in the plastic zone (Section 4). The solutions of the problems of Section 4 are based mainly on the solution of a certain nonlinear boundary value problem (Section 3). Throughout this article the Prandtl diagram has been taken as the relation between the stresses and the strains.

On the Transverse Flexure of an Infinite Strip with Semicircular Notches on Both Edges

In this paper, the effects of a pair of symmetrical semicircular notches on the transverse flexure of an infinite strip under the state of plain bending are investigated by use of the Poisson-Kirchhoff theory of thin plates. The unknown coefficients included in the solution are determined by the method of perturbation. In order to clarify the effect of making the semicircular notches, the distributions of bending couples and the stress corcentration factor kb are calculated and plotted versus the ratio of notch diameter to strip width and Poisson's ratio of the plate material. The deflections of the strip are also calculated and shown graphically.

On the Transverse Flexure of an Infinite Strip with Semicircular Notches on Both Edges

In this paper, the effects of a pair of symmetrical notches on the transverse flexure of an infinite strip under the state of plain bending are investigated by the use of the Poisson-Kirchhoff theory of thin plate. The analysis is developed with the help of three fundamental solutions w00, w' and w'', and the unknown coefficients included in the function, expressing the deflection of thin plate, are determined by the method of perturbation. In order to clarify the effect of making semicircular notches, the distributions of bending couples and deflections, and the stress concentration factors are calculated and plotted versus notch diameter-strip width ratio and Poisson's ratio of the plate material.

SYMMETRIC DEFECTS IN THE LOWER LIDS ASSOCIATED WITH ABNORMALITIES OF THE ZYGOMATIC PROCESSES OF THE TEMPORAL BONES

In 1888 Berry 1 described symmetric notches in the outer portion of the lower lids in a mother whose daughter had a similar defect in one lower eyelid. Although Berry did not examine the mother's brother, the latter reputedly had a similar defect in one eye. The affected child's brother had no ocular defect but a harelip, and her older sister showed no clinical defects. In 1900 Treacher Collins 2 recorded 2 cases of symmetric congenital notching in the outer part of each lower lid associated with clinical evidence of defective development of the malar bones. The family history was negative for the condition in 1 case and was not mentioned in the other. In 1927 Isakowitz 3 described a similar case of symmetric notching of the outer portion of each lower lid. He stated the opinion that these defects were probably colobomas. Although he did not examine the father