Eccentric Circular Hole Research Articles

Failure assessment of eccentric circular holes under compressive loading

AbstractThe present work aims to investigate the failure size effect on flattened disks containing an eccentric circular hole under mode I loading conditions. For this purpose, uniaxial compression tests are carried out on polymethyl methacrylate (PMMA) samples with holes. Depending on the hole radius and eccentricity, the energy release rate is either an increasing or decreasing function of the crack length, thus affecting the stability of crack propagation. Experimental results are interpreted and discussed through the coupled stress and energy criterion of Finite Fracture Mechanics. The approach lies on the assumption of a finite crack advance and it is implemented through the numerical estimation of the stress field and the Incremental Energy Release Rate functions. Finally, stability and crack speed propagation are discussed under the assumption of Linear Elastic Fracture Mechanics. Theoretical predictions reveal in agreement with experimental results thus demonstrating that the Coupled Criterion effectively captures the failure condition.

Prediction of the stress distributions and strength properties of 3-D braided composites with an eccentric circular hole

Due to their low delaminating tendency and high damage tolerance, 3-D braided composites are capable of being utilized in notched components. However, a few studies have investigated the mechanical properties of braided composites with open holes in multi-scale. In this paper, a multi-scale study on the mechanical properties of 3-D 4-directional braided composites with an eccentric circular hole is carried out. The equivalent elastic properties of 3-D 4-directional braided composites are calculated by the homogenization method based on the geometry of the meso unit cells. According to Lekhnitskii's theory, the local stress correction (LSC) method for computing the transverse stress around the eccentric hole is proposed. The models of meso unit cells with different braided angles are established, and the strength of the defect-free composites is predicted by the Tsai-Wu criterion. In the macroscopic view, using the point stress criterion (PSC), the average stress criterion (ASC), and numerical analysis, the strength properties of braided composites with different hole radii, braided angles, and eccentric distances are predicted. This study can be utilized to estimate the stress distributions and strength properties of 3-D braided composites with an eccentric hole and provides theoretical and simulation foundations for the problems of orthotropic materials with holes.

Born-Inversion Procedure for Shape Reconstruction of Eccentric Defects in Cylindrical Components

In this paper, a cylindrical aluminum specimen with an eccentric circular hole is prepared and ultrasonic measurements are carried out by experimental means. The measurement area is restricted to the plane perpendicular to the axis of the cylindrical component. The measured wave data are fed into the approximate correction method formula—the Born inversion procedure—and cross-sectional images are obtained. Next, a 3D shape reconstruction of the defect in the aluminum specimen is performed by stacking the cross-sectional images. After correcting the defect’s echo amplitude, the defect reconstruction effect of the 2D section and 3D defect reconstruction effect improves remarkably.

Shape Reconstruction of Eccentric Defect in Cylindrical Component by Modified Born Approximation Method

In this paper, a cylindrical aluminum sample with an eccentric circular hole was prepared, and ultrasonic measurements were carried out by experimental means. The measurement area was limited to a plane edge perpendicular to the axis of the cylindrical component. The measured waveform data were input into the formula of approximate correction method, and the section image was obtained by using a modified Born approximation (MBA) method. Then, the three-dimensional (3D) shape of the defects in the aluminum sample was reconstructed by superimposing the cross-sectional images. Results showed that the defect reconstruction effect of the two-dimensional section and the 3D defect reconstruction effect were significantly improved by the MBA method.

Interfacial cracks near an eccentric circular hole in piezoelectric bi-materials subjected to dynamic incident anti-plane shearing

Dynamic fracture analysis of piezoelectric materials with eccentric defects is an important criterion for the design of piezoelectric components. This work aims to suggest an effective method for the dynamic anti-plane shearing problem of piezoelectric bi-materials with permeable interfacial cracks near an eccentric circular hole. In the paper, Fredholm’s equations are solved via the Green’s function method and the coordinate transformation method. Based on conjunction and crack-deviation techniques, the dynamic stress intensity factors (DSIFs) at the outer and the inner tips of the left crack are expressed analytically. As cases, the effects of the eccentric distance, the piezoelectric parameters, the ratio of the crack length to the hole radius, and the dimensionless wave number of the incident wave are presented graphically.

205 偏心円孔を有する帯板の曲げ(OS2-(2),OS2 オーガナイズドセッション≪材料強度と構造設計≫)

205 偏心円孔を有する帯板の曲げ(OS2-(2),OS2 オーガナイズドセッション≪材料強度と構造設計≫)

독립좌표연성법을 이용한 편심 된 원형 구멍을 갖는 원판의 자유진동해석

This paper is concerned with the free vibration analysis of a circular plate with an eccentric circular hole by the Independent coordinate coupling method(ICCM). It was proved in the previous study that the ICCM can accurately predict the natural frequencies and mode shapes of the annular plates and can also be used for the free vibration analysis of the simply-supported circular plate with an eccentric circular hole. In this study, the clamped and free boundary conditions were considered for the circular plate. The numerical results show that the ICCM can be used effectively for the free vibration problem of circular plate with an eccentric hole compared to the finite element method.

An expression of stress concentration factor for a circular hole eccentrically located in a tensile finite-width strip of orthotropic material

An explicit expression of stress concentration factor (SCF) for a circular hole eccentrically located in a finite-width strip of orthotropic material subjected to remote tension is derived using an approximate and analytical method. The eccentricity of the hole and the ratio of the diameter to strip width are two governing geometric parameters, and their effect to the SCF is shown clearly in the expression. The formulation for the expression is consisted of two steps, first, the derivation is based on section method using balance of force and moment, respectively, second, improvement is done by empirical modification of the related coefficients based on asymptotic matching of good results obtained for some special cases. The accuracy of the final SCF expressions is adequate except the extreme case where the eccentricity of the circular hole is very large, i.e. when the hole is located very near to one side of the strip. On the other hand, when the eccentricity is taken as zero, i.e. for the simplified case of a central circular hole in a finite-width strip, the corresponding SCF expression has good accuracy. The present work is an extension of previous work for central circular hole of orthotropic material and an eccentric circular hole for isotropic material.

Stress-strain state of a flexible spherical shell with an eccentric circular hole

The stress-strain state of thin flexible spherical shells weakened by an eccentric circular hole is analyzed. The shells are made of an isotropic homogeneous material and subjected to internal pressure. A problem formulation is given, and a method of numerical solution with allowance for geometrical nonlinearity is outlined. The distribution of displacements, strains, and stresses along the hole boundary and in the region of their concentration is examined. The data obtained are compared with numerical solutions of the linear problem. The stress-strain state around the eccentric circular hole is analyzed with allowance for geometrical nonlinearity

Stresses in an Elastic Strip Having an Eccentric Circular Hole under Tension (An Analysis Using the Displacement Potential)

This paper presents an analytical solution for an infinite strip having an eccentric circular hole when the strip is subjected to tension at infinity. The analysis is based on the Papcovich-Neuber potential approach and the solution is obtained by the proper combination of harmonic function in integral forms and infinite series. The boundary conditions both on edge of the strip and on the hole are satisfied using the relations between the polar and Cartesian harmonics. The numerical results obtained are compared with those of existing solutions. A detailed stresses around the hole are illustrated for various sizes of the eccentricity and the hole.

Stress concentration factors for an eccentric circular hole in a finite-width strip or in a semi-infinite plate in tension

An explicit expression for the largest stress concentration factor (SCF) for an eccentric circular hole in a finite-width strip under remote uniform tension is formulated by approximate stress analysis and asymptotic matching with two exact limit SCF values, which are given by Kirsch and Koiter for very small and large ratios of hole radius to strip half width respectively. The explicit expression of the largest SCF for the tension semi-infinite plate with a circular hole near the free straight boundary is obtained as a special case of the first problem. The accuracy of the proposed expressions is measured by (a) comparison with data of the SCF handbook and (b) comparison with the results from finite element analysis. Corrections for the values given by Jeffery and confirmation of Koiter's exact limit value when the circular hole is very near the free straight boundary are also obtained.

STEADY THERMAL STRESS ANALYSIS IN TWO-DIMENSIONAL PROBLEMS BY THERMOELASTIC DISPLACEMENT POTENTIAL AND BOUNDARY-ELEMENT METHOD

Abstract A new numerical method to analyze steady thermal stresses in two-dimensional problems is proposed. Thermoelastic displacement potential is introduced for the analysis. The discontinuities of stresses on the boundary are investigated, and a completely analytic formulation is carried out. In order to investigate the accuracy of this method, steady thermal stress distributions in a square column and a circular cylinder with an eccentric circular hole are obtained.

Transient thermal stresses in a strip with an eccentric hole

A procedure is presented for dealing with the constraint associated with the direction of the thickness of a thin model and for obtaining transient thermal stresses under plane-stress conditions; the stresses are induced by severe thermal loads. Thermal-stress-concentration factor in an unrestrained strip with an eccentric circular hole placed near the thermally loaded edge is obtained. One straight edge of the strip is cooled and the others are insulated. Consequently, two cases for which the hole acts remarkably as a stress raiser are found.

等分布荷重を受ける有孔弾性平板の曲げに関する解析的研究 : 第 1 報 偏心円孔を有する正方形弾性平板

The purpose of this paper is to explain the bending of elastic plates with opening hole analytically in application of theory of thin plate. This analytical method used in the paper is based on a complex variable method. Part One is for square plates with eccentric circular hole. Boundary conditions treat the case of clamped edge and simply supported edge for a outward boundary, and free edge for a interior boundary. Various values obtained this analysis is quantitative sufficiently.

Bending stresses in thin circular plates with single eccentric circular holes

The bending stresses in thin circular plates having a single eccentric circular hole and small deflections are reported. The plates can have any mixture of clamped and simply supported boundaries, and can be subjected to a concentrated force uniformly distributed round the inner boundary, moments about two perpendicular axes, or uniform pressure on the plate surface. A previous paper (1)∗ has described the method of analysis using bipolar co-ordinates, and has given values for deflection and slope coefficients for varying diameter ratios and eccentricities under the loads described above. The present paper discusses the stresses found in the plates under the same conditions.

The deflection of a thin circular plate with an eccentric circular hole

A theoretical investigation of the small deflections of a thin circular plate is reported. The plate has a flat circular clamp at the outer edge and a similar clamp at the inner edge, which is placed eccentrically. These supports can be arranged to prescribe either a clamped edge or a simply supported edge, and all combinations of the two types are investigated. The plate can be subjected to a concentrated load at the centre of the inner clamp, moments about two perpendicular axes of the inner clamp, or pressure on the plate surface between the clamps. Deflections and slopes of the inner clamp have been determined, and in all cases the new values tend towards established values for the case of a central inner clamp, as the eccentricity of the inner clamp is reduced.

Stresses due to Diametral Forces in Tension on an Eccentric Hole of a Circular Disc

AbstractIn this paper, the problem of determining stresses in a circular disc with an eccentric circular hole is taken up, when the hole is subjected to two equal and opposite forces in tension along the line of centres, the outer boundary of the disc being unstressed. The solution is determined in bipolar coordinates. From the results thus obtained the stresses on a semi‐infinite plate acted upon by two equal and opposite diametral forces in tension on a circular hole in the plate in the direction of the normal to the straight boundary, the latter being kept free, have been deduced.

Stresses in a Circular Disk with an Eccentric Circular Hole Fixed at its Center and under a Tangential Force on the Outer Edge

In a previous paper, the author has reported Stresses in a Circular Disk with an Eccentric Circular Hole under Radial Forces. In this paper, the stresses in a circular disk containing an eccentric circular hole fixed at its center and under the action of a tangential force were analysed. The method of solution was the same as that used in the previous paper, and the bipolar coordinates were used in the solution. The complete stress-function in the disk with a hole is constructed in the form, in which the basic stress-function is added to the auxiliary one. From the results obtained, the solution of the problem in a semi-infinite plate under a concentrated tangential force on its straight edge and containing an unstressed circular hole was derived.

Stresses in a Circular Disk with an Eccentric Circular Hole under Radial Forces

This note gives a theoretical solution to a disk with an eccentric circular hole when it is compressed by two equal and opposite forces acting at a radius of the outer circle on the centre of inner circle. The method of solution adds to the given stress system a suitable biharmonic function, which gives no normal and tangential stress on the outer edge. The parametric coefficients involved in the solution are adjusted so as to satisfy the boundary conditions at the inner edge. Bipolar coordinates are used in the solution, by means of which explicit expressions are obtained for the parametric coefficients. Formulas of stress along the edge of circles are derived, and, in particular, the stress distributions of the inner hole are calculated.

Stresses in a Circular Disk with an Eccentric Circular Hole Fixed at its Centre and under a Tangential Force on the Outer Edge

In the previous paper the stresses in a circular disk with an eccentric circular hole under radial force were reported. This paper, however, gives a theoretical solution to a disk containing an eccentric circular hole fixed at its centre and under a tangential force on the outer edge, and the inner edge being unstressed. In this problem the bipolar coordinates are used. The Airy stress function is used as a method of solution, and the auxiliary stress function is added to the basic function which gives the stress state in the disk fixed at its centre and under a tangential force on its edge. By the numerical calculation it appears that the edge or circular hole being near the centre of disk, has larger maximum stress. The limiting case, in which the semi-infinite plate has a circular hole in the neighbourhood of its straight edge, is also discussed.