Rounded-off Corners Research Articles

Understanding the evolution of the geometry of silicon solar cells

Today, solar cells are very familiar to the broad public, and everyone has noticed their particular geometry resembling a square with rounded-off corners. However, the rationale behind this geometry is little known. This paper presents a precise study of the geometry of silicon solar cells and its evolution since their appearance in the early 1960s. Through a parametric approach taking into account different types of constraints, it is shown that the cell geometry is the result of an optimization process depending on both technical and economic aspects. The correlation between the parametric study and historical data shows that the photovoltaic panels that we see today on our roofs have been mainly shaped by the evolution of cost constraints over the past decades.

Design of processes and products through simulation of three-dimensional extrusion

Abstract In this work, various industrial extrusion problems with high complexity are simulated by employing efficient numerical schemes such as the arbitrary Lagrangian–Eulerian FEM and mismatching refinement with domain decomposition. And a new methodology of shape optimization technique to reduce computation time for the design of the extrusion process is introduced. The mechanical properties like anisotropy of extruded products are also analyzed by the continuum approach and discussed for practical examples, and the texture development and mechanical properties in the aluminum extrusion processes are predicted by employing a rate-independent crystal plasticity model based on the smooth yield surface with rounded-off corners.

Evolution of Plastic Anisotropy during Deformation of Metal Sheets

Evolution of Plastic Anisotropy during Deformation of Metal Sheets

On the influence of the initial tension of a strip with a rectangular hole on the stress concentration caused by additional loading

The influence of the initial stretching of a simply supported plate strip containing a rectangular hole with rounded-off corners on the stress concentration around the hole caused by the bending of the strip under the action of uniformly distributed normal forces on the plane of its upper face is studied within the framework of the three-dimensional theory of elasticity under a plane-strain state. The mathematical formulation of the corresponding boundary value problems is presented. For the solution to these problems the finite element method is employed and for this purpose the validity of the constructed functional is proven. The material of the plate strip is selected as linear elastic, homogeneous and orthotropic. The numerical results are presented for the composite consisting of two alternating layers made from isotropic linear elastic materials.

Two-Dimensional Laminar Free Convection in the Cavity Having a Shape of a Square with Rounded-off Corners

Two-Dimensional Laminar Free Convection in the Cavity Having a Shape of a Square with Rounded-off Corners

Peculiarities of the artificial crack

The problem of the artificial crack was studied by assimilating the artificial crack with a rectangular hole with rounded-off corners in a plate under conditions of plane stress and subjected to a mode I loading. Various side-ratios m(a/b) of the rectangle were considered, corresponding to real cracks in applications. Using the Muskhelishvili complex stress function ϑ(z) method, combined with a convenient conformal mapping representation of the rectangular hole, the first stress invariant of the elastic field around the hole was determined, which was sufficient to evaluate the stress and strain distributions along the boundary of the hole, as well as the thickness variation of the plate around this boundary. Using the method of the equivalent or effective order of singularity [P. S. Theocaris and L. Petrou, Int. J. Fracture 31, 271–289 (1986)], virtual points inside the hole were defined at some distances from the rounded-off corners, depending on the curvatures there. The stress concentration factors and the equivalent orders of singularity at the corners yielded the equivalent stress intensity factors [P. S. Theocaris and L. Petrou, Int. J. Fracture 31, 271–289 (1986)]. The method established an exact procedure for the determination of the stress field near the rectangular slit. The theoretical results, corroborated with the experimental evidence using caustics, gave the possibility to establish the differences in the stress fields around the real crack tips and the corners of the artificial slits. Interesting results were derived bearing also on the important problem of blunting of ductile cracks.

Partially bonded rigid rounded-off corners polygonal inclusions in an elastic matrix

The plane elastostatic problem of a crack lying along the boundary of a rigid rounded-off corners polygonal inclusion embedded in an elastic matrix is theoretically studied. Using the conformal mapping method of the complex variable theory of elasticity, closed form solutions of the stress and displacement fields are obtained for a general shape rounded-off corners polygonal inclusion and biaxial applied loads at infinity. The complex stress intensity factor for complex stress singularities is defined and the local stress distribution in the neighborhood of the crack tips is given. The general solution is applied to some particular shapes of rounded-off corners polygonal inclusions and explicit formulae for the complex potentials are provided. The variation of the stress intensity factors with the angle subtended by the crack are and various combinations of the applied biaxial loads at infinity are graphically shown. The results of the stress analysis are coupled with the maximum circumferential stress criterion to obtain the fracture characteristics of the composite plate.

From the rectangular hole to the ideal crack

The problem of a rectangular hole in an infinite elastic and isotropic plate, submitted to tension at infinity, is solved for any side ratio of the hole. It is assumed that the rectangular hole has rounded-off corners, the radii of curvature of which remain many times smaller than the short sides of the rectangles. The Muskhelishvili complex stress function ϑ(z), sufficient to determine the first stress invariant needed for the solution is determined in a closed form by applying the conformal mapping method of the outside of a rectangle to the inside of a unit circle. The stress and strain distributions along the boundary of the hole, as well as inside a limited region in front of the short sides of the rectangle are accurately determined. It is proved that the method of reflected caustics is sensitive in examining the singular fields developed at the corners of the rectangles. Moreover, the minimum radii of the initial curves of the caustics are determined, outside of which the stress fields could be described by the singular solution. Experiments with reflected caustics in plexiglas plates corroborated the theoretical results.

Two approaches to the investigation of antiplane deformation of an isotropic solid with a thin elastic inclusion

An approach is proposed to the investigation of the state of stress and strain of a piecewise-homogeneous plane consisting of a matrix and a thin tunnel-like rectangular inclusion with rounded-off corners under the assumption that such a composite body is under antiplane deformation conditions. A numerical comparison is made of the results obtained in this paper and on the basis of an approximate model /1/. It is shown that they agree satisfactorily at sufficiently large distances from the vertices of the inclusion, when the inclusion is more pliable than the matrix.

The order of singularities and the stress intensity factors near corners of regular polygonal holes

A new method was developed for the calculation of the order of singularity (SO) and the respective stress intensity factor (SIF) near corners of regular polygonal holes perforated in elastic plates submitted to an overall tension at infinity. For the solution of the problem the Muskhelishvili potential function ϑ(z) was determined for an infinite plate weakened by a respective regular polygonal hole with rounded-off corners under tension. For each rounded off corner a virtual singular point was defined inside the hole along the bisector of the angle of the apex and at a distance depending on the radius of curvature of the corner. Then, the stress concentration factors (SCF) at the apices of these rounded-off corners were evaluated when their respective radii of curvature tended to zero. The corresponding stress-singularity and the SIF were afterwards derived, by correlating the SCF and the distance of the virtual singular point for each corner. By conveniently selecting the number of terms of the series development of ϑ(z) the method can approach the real values for SO and SIF to any desired degree of accuracy. A comparison of the stress field around and near a corner of a polygonal hole in an infinite plate when this corner is submitted to mode-I deformation and a V-notch in an infinite plate under tension indicated the similarities between the two affine problems.

Stress distributions and intensities at corners of equilateral triangular holes

The problem of the stress distribution in an infinite medium which was weakened by an equilateral triangular hole under tension at infinity, was studied. The triangular hole and its exterior was conformally mapped into the interior of a unit circle by using the Schwarz-Christoffel transformation. The stress function Φ(z) was defined by Muskhelishvili's complex-function theory and the conformal mapping technique. The Schwarz-Christoffel transformation was expressed as a truncated series with a finite numbers of terms. This function represents an equilateral triangle with rounded-off corners mapped into the unit circle. A change of the stress field around the triangular hole was investigated.