Stress Intensity Factors for a Non-Circular Hole with Inclusion Layer Embedded in a Cracked Matrix

The failure analysis of a non-circular hole with an inclusion layer embedded in an infinite cracked matrix under a remote in-plane uniform load is presented. In this study, a series solution of stress functions for both the matrix and inclusion layer is obtained using the complex variable theory in conjunction with the method of conformal mapping. The stress intensity factor (SIF) can then be determined numerically by solving the singular integral equation (SIE) for the interaction among different crack sites, material properties, and geometries of irregular holes with an inclusion layer. In particular, the failure behavior of composite structures associated with an approximately triangular hole and an approximately square hole with inclusion layers, such as those of oxides, nitrides, and sulfides, is examined in detail. The results demonstrate that a softer layer would enhance the SIF and a stiffer layer would restrain the SIF when a crack is near the inclusion layer. It can be concluded that crack propagation would be suppressed by a stiffer layer even when a micro-defect such as a hole resides in the inclusion layer.

Experimental Investigation of Stress Distributions in 3D Printed Graded Plates with a Circular Hole

An experimental investigation is presented for the stress distributions in functionally graded plates containing a circular hole. On the basis of the authors’ previously constructed theoretical model, two kinds of graded plates made of discrete rings with increasing or decreasing Young’s modulus were designed and fabricated in virtue of multi-material 3D printing. The printed graded plates had accurate size, smooth surface, and good interface. The strains of two graded plates under uniaxial tension were measured experimentally using strain gages. The stresses were calculated within the range of linear elastic from the measured strains and compared with analytical theory. It is found that the experimental results are consistent with the theoretical results, and both of them indicate that the stress concentration around the hole reduces obviously in graded plates with radially increasing Young’s modulus, in comparison with that of perforated homogenous plates. The successful experiment in the paper provides a good basis and support for the establishment of theoretical models and promotes the in-depth development of the research field of stress concentration in functionally graded plates.

An Analytical Approach to Obtaining the Stress Field of a Cylindrical Shell with a Circular Hole under Tension

The problem of a cylindrical shell with a circular hole under uniaxial tension is considered. The main obstacle of solving this problem is the necessity to find such coefficients in the expansion of the solution into a sum of basis functions, for which this solution satisfies the boundary conditions. The study of the classical works led to understanding that none of the so far proposed approaches can be considered successfully, and the results of these approaches differ, so it is not clear, which results can be used as a basis. In the present paper, a new analytical approach to studying this issue is proposed. It allows expanding the range of applicability of the solution and gives the opportunity for the analytical study of the stress state. The idea consists in expanding each of the basis functions in a Fourier series by dividing the variables, which allows obtaining explicitly an infinite system of algebraic equations for finding coefficients. One of the important steps of this research is that the authors were able to prove which exact equation is a linear combination of the others and exclude, which made it possible to compose a reduced system for finding unknown coefficients. The proposed approach, in contrast to most classical works, does not impose mathematical restrictions on the values of the main parameter characterizing the cylindrical shell. The existing restrictions are of mechanical nature, as larger cutouts require another model. Moreover, the numerical results obtained by the new method are presented in a fairly complete manner and they are compared with the results of the classical works.

Experimental Study and Proposal to Improve the EWM Design of Cold-Formed Steel Lipped Channel Columns with Circular Holes under Axial Compression

The cold-formed steel (CFS) lipped channel section with circular holes has been widely used in low-rise and multistory building structures as the column. However, the circular hole in the web makes the lipped channel column become susceptible to buckle. A total of 54 CFS lipped channel axial compression columns with and without circular holes were used to study the buckling behavior and the effective width design method. The interaction of the local buckling and the distortional buckling were observed for the short and intermediate columns, while the slender columns were controlled by the interaction of the local buckling, distortional buckling, and flexural buckling or flexural-torsional buckling. The experimental failure loads were gradually decreased with the increase in the diameter of the circular hole for the specimens with the same section. The failure loads of the specimens with two holes were lower than those of the specimens with one hole with same section and same diameter of holes. Then, the experimental results were used to validate a nonlinear finite element model (FEM) previously developed by the authors. The validated FEM was subsequently used to obtain additional 36 numerical failure results concerning the effects of the length, the section, and the diameter and the number of the circular holes. Furthermore, the proposal to calculate the distortional buckling coefficient of the CFS lipped channel section with circular holes were put forward based on numerical analysis considering the reduction of effect of holes. Finally, a proposal to improve the effective width method (EWM) design approach for CFS lipped channel sections with circular holes under axial compression was presented. The comparisons between experimental and numerical capacities and their calculations provided by the proposed EWM design method illustrate a great application of the proposed approach.

Scattering of anti-plane waves by scalene trapezoidal boundary with embedded cavity in anisotropic material based on mapping space

Both surface motion and hole stress concentration have always been concerned in anisotropic medium. In this paper, a theoretical approach is used to study the scattering problem of circular holes under a scalene trapezoid on the surface. The mapping function that anisotropic medium to homogeneous medium is established, and the relationship between the free boundary of anisotropic medium and the mapping of homogeneous medium boundary is proved. In the space of homogeneous medium mapping, the wave displacement function is obtained by solving the equation of motion that meets the zero-stress boundary conditions by separating the variable method and the symmetric method. Based on the complex function, multi-polar coordinate method and region-matching technique, algebraic equations are established at auxiliary boundary and free boundary conditions in complex domain. Then according to sample statistics, least square method is used instead of the Fourier expansion method to solve the undetermined coefficient of the algebraic equations by discrete boundary. Numerical results shows that the continuity of the auxiliary boundary and the accuracy of the zero-stress boundary are nice, and the displacement of the free surface and the stress of the circular hole are related to the parameters of material medium, the position of the circular hole, the direction of the incident wave and the frequency content of the excitation. Finally the process of the wave propagation and scattering around trapezoid and shallow circle are shown in time domain through the inverse fourier transform.