Multiple Circular Holes Research Articles

Low-frequency ultrasonic array imaging for detecting concrete structural defects in blind zones

Ultrasonic array (UA) imaging is a promising non-destructive testing (NDT) method that is extensively used for defect detection. Due to the high attenuation characteristics of ultrasonic wave propagation in concrete structures and the directivity of sensors, the total focus method (TFM) easily misses specific defects in blind zones that are far from the sensors or located at a large deflection angle. To overcome this limitation, the diffusion attenuation compensation factor and solid directivity correction factor are adopted to improve the scattered signal energy of defects that are in blind zones. On this basis, the diffusion attenuation compensation method (DACM), the solid directivity correction method (SDCM), and the diffusion attenuation compensation-based solid directivity correction method (DAC-SDCM) are proposed. These methods are applied to characterize multiple circular holes in concrete structures using the dry point contact (DPC) low-frequency UA, and the detection results are evaluated from the intensity curve and detection area of ultrasonic images. The numerical and experimental results indicate that DACM is suitable for detecting defects located at longer distances, SDCM is capable of detecting defects located at larger deflection angles, and DAC-SDCM can significantly improve the detection performance of defects that are distant and have large deflection angles. The findings demonstrate that the proposed methods can significantly improve the detection ability of defects in blind zones and broaden the application of DPC low-frequency UA in the health monitoring of concrete structures.

Vibration optimization of composite plates with multiple circular holes using two-dimensional sampling optimization method

Perforated composite plates are widely used in engineering structures, and to prevent resonance, it is important to maximize the fundamental frequency. In this paper, the Ritz method is developed to calculate the vibration frequency of laminated composite plates with multiple circular holes, and the two-dimensional sampling optimization method (2DSO) is adopted to optimize the stacking sequence for achieving maximal fundamental frequency. Accounting for a variety of boundary conditions applied to the plate contour and circular holes, Legendre polynomials are adopted as admissible functions in the Ritz method in order to predict the vibration behavior of perforated plates. Then, 2DSO uses the lamination parameter (LP) to represent the distances between different stacking sequences. By generating uniformly distributed points in the LP design space and determining their corresponding stacking sequences, several good candidate stacking sequences are identified. Subsequently, local sampling optimization is employed to find better stacking sequences around the candidate stacking sequences. Lastly, the layerwise optimization approach (LOA) is employed to refine the sampling optimum. Perforated composite plates with one, two, and four circular holes, under different boundary conditions, are optimized. Results show the accuracy of the Ritz method, and the stability and efficiency of the 2DSO algorithm.

Effect of different hole shapes on the stress intensity factor of the finite plate with edge crack

Generally, flaws or defects are formed while manufacturing the components either internally or externally. Not all such flaws are unstable under service conditions. Cracks are often developed in the structural member due to high-stress concentration factors. Fracture mechanics help us in evaluating the life and safety of structures in the presence of cracks. This is accomplished by analyzing the intensity of the crack condition by estimating certain fracture parameters. This study aims at evaluating the mode I stress intensity factor (SIF) of a finite plate with edge crack in the presence of different hole shapes. The holes are placed along and perpendicular to the crack axis. The objective is to study the effect of the size, number, and shape of holes on the mode I SIF through finite element simulation. A 2D finite plate with an edge crack submitted to tensile loading was validated against analytical results. It was found from the simulation the existence of a range of distance from the crack tip within which when the holes are placed, results in the decrease of SIF. Beyond a certain distance that is far from the crack tip, the introduction of holes does not affect the SIF. When the elliptical holes (either single or multiple) was placed along the crack axis, it reduces the SIF effectively better than the circular and square hole. On the other hand, a single square hole when placed about the vertical axis, was found to diminish the SIF effectively relative to circular and elliptical holes. Similarly, the multiple circular holes reduce the SIF significantly more than the square and elliptical holes about the vertical axis.

Experimental and Numerical Study on the Influence of Stress Concentration on the Flexural Stability of an Aluminium Hollow Tube

In recent times, particularly in applications used to build various structures for construction purposes or machines, solid sections have been gradually replaced by hollow sections due to their attractive features such as being light weight and having high specific strength. In the present investigation, an attempt was made to investigate, in detail, the flexural capability of aluminium hollow tubes (AHTs) with square cross-sections. The objective of the investigation was to study the influence of stress concentration on the flexural behaviour of the hollow tube. The stress concentration factor considered in this investigation was holes of various cross-sections and quantities. Three-point bending tests with concentrated loads were conducted on specimens of a hollow tube with different stress concentrations such as circular holes, multiple circular holes, square holes and perforations. The load was applied manually during the bending test with appropriate increments. The bending test was carried out on specimens with support spans of 110, 130, 170 and 200 mm. The output measures of the study were maximum bending load, deflection and flexural stiffness. The output measures were analysed in detail in order to recommend the type and nature of stress concentration in a hollow tube applied to structural applications to ensure the safest workability. The flexural stability of the tube was analysed by experimental and numerical procedures, and the results were validated using an analytical approach. It was found that the results of all the approaches complement each other with a low significance of error. AHTs with a circular hole, multiple circular holes and perforations were observed to have better flexural stability than other AHTs such as AHTs with square hole and plain AHTs.

Surface accuracy optimization of mechanical parts with multiple circular holes for additive manufacturing based on triangular fuzzy number

Surface accuracy directly affects the surface quality and performance of mechanical parts. Circular hole, especially spatial non-planar hole set is the typical feature and working surface of mechanical parts. Compared with traditional machining methods, additive manufacturing (AM) technology can decrease the surface accuracy errors of circular holes during fabrication. However, an accuracy error may still exist on the surface of circular holes fabricated by AM due to the influence of staircase effect. This study proposes a surface accuracy optimization approach for mechanical parts with multiple circular holes for AM based on triangular fuzzy number (TFN). First, the feature lines on the manifold mesh are extracted using the dihedral angle method and normal tensor voting to detect the circular holes. Second, the optimal AM part build orientation is determined using the genetic algorithm to optimize the surface accuracy of the circular holes by minimizing the weighted volumetric error of the part. Third, the corresponding weights of the circular holes are calculated with the TFN analytic hierarchy process in accordance with the surface accuracy requirements. Lastly, an improved adaptive slicing algorithm is utilized to reduce the entire build time while maintaining the forming surface accuracy of the circular holes using digital twins via virtual printing. The effectiveness of the proposed approach is experimentally validated using two mechanical models.

A new analytical-numerical method for calculating interacting stresses of a multi-hole problem under both remote and arbitrary surface stresses

Based on the elementary solutions and new integral equations, a new analytical-numerical method is proposed to calculate the interacting stresses of multiple circular holes in an infinite elastic plate under both remote stresses and arbitrarily distributed stresses applied to the circular boundaries. The validity of this new analytical-numerical method is verified by the analytical solution of the bi-harmonic stress function method, the numerical solution of the finite element method, and the analytical-numerical solutions of the series expansion and Laurent series methods. Some numerical examples are presented to investigate the effects of the hole geometry parameters (radii and relative positions) and loading conditions (remote stresses and surface stresses) on the interacting tangential stresses and interacting stress concentration factors. The results show that whether the interference effect is shielding (k 1) depends on the relative orientation of holes (α) and remote stresses (<∞ , <∞ ). When the maximum principal stress is aligned with the connecting line of two-hole centers and <∞ < 0.05<∞ , the plate containing two circular holes has greater stability than that containing one circular hole, and the smaller circular hole has greater stability than the bigger one. This new method not only has a simple formulation and high accuracy, but also has advantage of wide applications over common analytical methods and analytical-numerical methods in calculating the interacting stresses of a multi-hole problem under both remote and arbitrary surface stresses.

Multiple scattering analysis of flexural waves on an elastic plate with multiple circular holes

Multiple scattering analysis of flexural waves on an elastic plate with multiple circular holes

The reflection of the fundamental torsional guided wave from multiple circular holes in pipes

Localised corrosion is a major concern in the petrochemical industry, and often occurs as clusters of pits. A study of the reflection from two and three small circular holes in pipes with the fundamental torsional guided wave incident is presented. FE analyses with both part and through thickness holes at different relative positions are presented, and are a step towards estimation of the scattering behaviour of multiple and random defects. The validity of employing the superposition technique in estimating reflection coefficients is assessed. Results show that the reflection coefficient for the T(0,1) mode is dependent on absolute frequency and axial separation, and independent of circumferential position. Employing superposition is found to be valid down to defect centre to centre separation distances of two diameters in the worst case, with improved validity with shallower defects. Results from the FE analyses are validated experimentally.

Free Vibration Analysis of a Circular Plate With Multiple Circular Holes by Using Indirect BIEM and Addition Theorem

In this paper, natural frequencies and natural modes of a circular plate with multiple circular holes are theoretically derived and numerically determined by using the indirect boundary integral formulation, the addition theorem, and the complex Fourier series. Owing to the addition theorem, all kernel functions are expanded into degenerate forms and further expressed in the same polar coordinates centered at one circle where the boundary conditions are specified. Not only the computation of the principal value is avoided but also the calculation of higher-order derivatives can be easily determined. By matching boundary conditions, a coupled infinite system of linear algebraic equations is derived as an analytical model for the free vibration of a circular plate with multiple circular holes. The direct-searching approach is utilized in the truncated finite system to determine the natural frequency through singular value decomposition. After determining the unknown Fourier coefficients, the corresponding mode shapes are obtained by using the indirect boundary integral formulations. Some numerical eigensolutions are presented and then utilized to explain some physical phenomenon such as the beating and the dynamic stress concentration. Good accuracy and fast rate of convergence are the main features of the present method, thanks to the analytical approach.

Eigensolutions of a circular flexural plate with multiple circular holes by using the direct BIEM and addition theorem

The purpose of this paper is to present an analytical formulation to describe the free vibration of a circular flexural plate with multiple circular holes by using the null field integral formulation, the addition theorem and complex Fourier series. Owing to the addition theorem, all kernel functions are represented in the degenerate form and further transformed into the same polar coordinates centered at one of circles, where the boundary conditions are specified. Thus, not only the computation of the principal value for integrals is avoided but also the calculation of higher-order derivatives in the flexural plate problem can be easily determined. By matching the specified boundary conditions, a coupled infinite system of simultaneous linear algebraic equations is derived as an analytical model for the title problem. According to the direct searching approach, natural frequencies are numerically determined through the singular value decomposition (SVD) in the truncated finite system. After determining the unknown Fourier coefficients, the corresponding mode shapes are obtained by using the direct boundary integral formulations for the domain points. Several numerical results are presented. In addition, the inherent problem of spurious eigenvalue using the integral formulation is investigated and the SVD updating technique is adopted to suppress the occurrence of spurious eigenvalues. Excellent accuracy, fast rate of convergence and high computational efficiency are advantages of the present method thanks to its analytical features.

Scattering of flexural wave in a thin plate with multiple circular holes by using the multipole Trefftz method

The scattering of flexural wave by multiple circular holes in an infinite thin plate is analytically solved by using the multipole Trefftz method. The dynamic moment concentration factor (DMCF) along the edge of circular holes is determined. Based on the addition theorem, the solution of the field represented by multiple coordinate systems centered at each circle can be transformed into one coordinate system centered at one circle, where the boundary conditions are given. In this way, a coupled infinite system of simultaneous linear algebraic equations is derived as an analytical model for the scattering of flexural wave by multiple holes in an infinite plate subject to the incident flexural wave. The formulation is general and is easily applicable to dealing with the problem containing multiple circular holes. Although the number of hole is not limited in our proposed method, the numerical results of an infinite plate with three circular holes are presented in the truncated finite system. The effects of both incident wave number and the central distance among circular holes on the DMCF are investigated. Numerical results show that the DMCF of three holes is larger than that of one, when the space among holes is small and meanwhile the specified direction of incident wave is subjected to the plate.

Effect of Multiple Circular Holes on Fatigue Crack Growth Path

The mechanical fastening has some advantages in respect of the fastening strength and disassemble of the fastened parts. However, at the same time it has some dangerous factors, can cause fatigue crack initiation and propagation due to not only the static loading such as cargo and passengers but also the dynamic loading like vibrations which occur in the engines and the propellers. For this reason, the strength evaluation for the mechanical fastenings along with the sophisticated and detailed mechanical design and the safety evaluation should be executed. In this paper, we were carried out experiments to study fatigue crack growth paths in structures containing the multiple circular holes. It was investigated that how circular holes are affected on fatigue crack growth paths using the specimen consists of A5052-H112, which is widely used as the ship materials. It was found from the experimental results that the fatigue crack as if it is drawn to circular holes when crack tip approach to circular holes. However, it did not go into circular hole if there is the next circular hole. Therefore, the clarification of mechanism on the fatigue crack initiation and the propagation in structures containing the multiple circular holes can be expected in this study.

Scattering of flexural wave in thin plate with multiple holes by using the null-field integral equation approach

In this paper, a semi-analytical approach is proposed to solve the scat- tering problem of flexural waves and to determine dynamic moment concentration factors (DMCFs) in an infinitethinplatewithmultiplecircularholes. Thenull-field integral formulation is employed in conjunction with degenerate kernels, tensor transformation and Fourier series. In the proposed direct formulation, all dynamic kernels of plate are expanded into degenerate forms and further the rotated degen- erate kernels have been derived for the general exterior problem. By uniformly collocating points on the real boundary, a linear algebraic system is constructed. The results of dynamic moment concentration factors for the plate with one hole are compared with the analytical solution to verify the validity of the proposed method. For the cases of small wave number, the quasi-staticresults of a plate with one or multiple circular holes are compared with the static data of finite element method (FEM) using ABAQUS. Numerical results indicate that the DMCF of two holes is apparently larger than that of one hole when two holes are close to each other. Fictitious frequency appeared in the external problem can be suppressed by using the more number of Fourier series terms. The effect of distance between the centers of holes on dynamic moment concentration factors is also investigated by using the proposed method. Keyword: scattering,flexuralwave, dynamicmoment concentration,biHelmholtz equation, null-field boundary integral equation, degenerate kernel, Fourier series

Photodiode Peripheral Utilization Effect on CMOS APS Pixel Performance

A photodiode (PD)-type CMOS active pixel sensor (APS) pixel is comprised of a reverse-biased p-n-junction diode (PD) for photon conversion and charge storage, and a number of MOS transistors. Junction capacitance of the PD has two major components; bottom plate (area) and side wall (periphery). Both play important roles in the electro-optical performance of PD-APS pixels. This paper reports PD peripheral junction utilization effects on the pixel's electro-optical performance, full-well capacity and spectral response for an 18times 18 mum CMOS PD-APS pixel were improved by opening multiple circular holes in the PD diffusion layer. A prototype CMOS APS imager was designed, fabricated, and tested in 0.5-mum, 5 V, 2P3M CMOS process, containing a 424 times 424 pixel array with smaller sub-arrays for multiple pixel designs. Four test pixels with 7, 11, 14, and 17 circular, 1.6-mum-diameter holes were placed on one pixel array, with one control pixel for reference. Pixel characteristics, dark current, PD capacitance, quantum efficiency, sensitivity, and pixel full-well capacity were measured. It was found that increased PD junction peripheral would potentially help to improve total capacitance of the PD, with the expense of higher dark current. We also found that increased PD peripheral capacitance improves spectral response up to 12% of the PD-APS pixel, especially at short wavelengths.

Null-field integral equation approach for free vibration analysis of circular plates with multiple circular holes

In this paper, a semi-analytical approach for the eigenproblem of circular plates with multiple circular holes is presented. Natural frequencies and modes are determined by employing the null-field integral formulation in conjunction with degenerate kernels, tensor rotation and Fourier series. In the proposed approach, all kernel functions are expanded into degenerate (separable) forms and all boundary densities are represented by using Fourier series. By uniformly collocating points on the real boundary and taking finite terms of Fourier series, a linear algebraic system can be constructed. The direct searching approach is adopted to determine the natural frequency through the singular value decomposition (SVD). After determining the unknown Fourier coefficients, the cor- responding mode shape is obtained by using the boundary integral equations for domain points. The result of the annular plate, as a special case, is compared with the analytical solu- tion to verify the validity of the present method. For the cases of circular plates with an eccentric hole or multiple circu- lar holes, eigensolutions obtained by the present method are compared well with those of the existing approximate analyt- ical method or finite element method (ABAQUS). Besides, the effect of eccentricity of the hole on the natural frequency and mode is also considered. Moreover, the inherent prob- lem of spurious eigenvalue using the integral formulation is investigated and the SVD updating technique is adopted to suppress the occurrence of spurious eigenvalues. Excellent accuracy, fast rate of convergence and high computational

Simulation of Fatigue Fracture Path Prediction in Materials Containing Holes or Inclusions Using Moving Finite Element Method

It is well known that approximately 70 to 80 percent of the failure accidents that occur in complex structures that have such holes are caused by the fatigue fracture. That is, we need to know fatigue fracture path to evaluate health. In this paper, we carried out fatigue fracture path prediction simulation containing multiple circular holes or inclusions in specimens. Furthermore the effect of their existence on crack growth was examined. The simulations were conducted using the moving finite element method based on Delaunay automatic triangulation, and the numerical result of the specimens containing multiple circular holes was compared with the experimental result. In the fatigue fracture path prediction simulation, Paris's law was used to decide crack propagation length Δa and local symmetry criterion was used to decide crack propagation direction.

독립좌표연성법을 이용한 여러 개의 원형 구멍을 갖는 직사각형 평판의 자유진동해석

This paper is concerned with the vibration analysis of a rectangular plate with multiple circular holes. On the contrary to the case of rectangular plate with multiple rectangular holes, it is very difficult to perform qualitative analysis on natural vibration characteristics because of geometrical inconsistency. In this paper, we applied the Independent Coordinate Coupling Method(ICCM) to the addressed problem, which was developed to compute natural vibration characteristics of the rectangular plate with a circular hole and proven to be computationally effective. The ICCM is based on Rayleigh-Ritz method but utilizes independent coordinates for each hole domain. By matching the deflection conditions for each hole imposed on the expressions, we can easily derive the reduced mass and stiffness matrices. The resulting equation is then used for the calculation of the eigenvalue problem. The numerical results show the efficacy of the Independent Coordinate Coupling Method.

Free vibration analysis of circular plates with multiple circular holes using indirect BIEMs

In this paper, a semi-analytical approach is proposed to solve natural frequencies and natural modes for circular plates with multiple circular holes by using the indirect formulation in conjunction with degenerate kernels and Fourier series. All the kernels in the indirect formulation are expanded into degenerate form. By uniformly collocating points on the boundary, a linear algebraic system can be constructed. The direct searching approach is adopted to determine the natural frequency through singular value decomposition (SVD). After determining the unknown Fourier coefficients, the corresponding mode shape is obtained by using the indirect boundary integral formulations. The results of the annular plate, as a special case, are compared with the analytical solution to verify the validity of the present method. For the cases of circular plates with multiple circular holes, the results are also compared with those of finite element method (FEM) using ABAQUS. Besides, the effect of eccentricity of the hole on the natural frequencies is also considered. Good accuracy, high rate of convergence and computational efficiency are the main features of the present method due to the semi-analytical procedure.

Semi-analytical solution for a viscoelastic plane containing multiple circular holes

Semi-analytical solution for a viscoelastic plane containing multiple circular holes

A boundary integral method for multiple circular holes in an elastic half-plane

This paper presents a semi-analytical method for solving the problem of an isotropic elastic half-plane containing a large number of randomly distributed, non-overlapping, circular holes of arbitrary sizes. The boundary of the half-plane is assumed to be traction-free and a uniform far-field stress acts parallel to that boundary. The boundaries of the holes are assumed to be either traction-free or subjected to constant normal pressure. The analysis is based on solution of complex hypersingular integral equation with the unknown displacements at each circular boundary approximated by a truncated complex Fourier series. A system of linear algebraic equations is obtained by using a Taylor series expansion. The resulting semi-analytical method allows one to calculate the elastic fields everywhere in the half-plane. Several examples available in the literature are re-examined and corrected, and new benchmark examples with multiple holes are included to demonstrate the effectiveness of the approach.