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Analytical model for measurement of stresses using two-hole drilling

INTERNATIONAL JOURNAL OF PRESSURE VESSELS AND PIPING 2023年第1期206卷

作者： Liu, Huan Han, Dayong Deng, Lu Cao, Ran Hunan Univ Coll Civil Engn Changsha 410082 Hunan Peoples R China Powerchina Rd Bridge Grp Co Ltd Zhongshan 528403 Peoples R China Hunan Univ Hunan Prov Key Lab Damage Diag Engn Struct Changsha 410082 Hunan Peoples R China

Residual stresses have a significant effect on the strength, deformation, plasticity, and fatigue properties of materials. In general, tensile residual stresses are adverse to material performance and component life, while compressive residual stresses can improve material fatigue strength. In this study, an analytical model employing two-hole drilling (THD) is proposed for the measurement of interior stresses. Firstly, the analytical solution for the distortion of the reference hole induced by drilling an adjacent hole is derived using the complex variable method. Based on the analytical solution, the reverse procedure is established to determine the original stress state. Then, the comparative validations of the THD method with the deep hole drilling (DHD) method are performed in conjunction with the finite element (FE) simulations for the beam subjected to bending, the unloaded elastoplastic beam, and the shrink fitted assembly. Finally, parametric analysis is conducted and the results show that: the influence of drilling an adjacent hole on the reference hole rises with the increase of the hole diameters or the decrease of the hole spacing;the THD method is able to give good estimations for the stresses with linear, parabolic, and sinusoidal distributions, although the accuracy is reduced for the prediction of the longitudinal residual stress in the cold-formed section;the uncertainties in evaluated stresses ascend linearly with the increase of the measurement error in the diameter of the reference hole. Relative to the DHD method, the THD method has the merits of less damage and less equipment required and can provide an effective approach for the measurement of stresses inside materials.

关键词： Analytical model Stress measurement Hole drilling complex variable method Strain relief

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A novel complex variable solution for the stress and displacement fields around a shallow non-circular tunnel

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COMPUTERS AND GEOTECHNICS 2023年 164卷

作者： Ye, Zi Kun Ai, Zhi Yong Tongji Univ Dept Geotech Engn Minist Educ Key Lab Geotech & Underground Engn Shanghai Peoples R China

A novel complex variable solution is derived in this paper for the stress and displacement fields around a shallow non-circular tunnel. The proposed method allows explicit computations in matrix form and has advantages of considerable efficiency and high accuracy. Firstly, the stress and displacement boundary conditions for the shallow non-circular tunnel are obtained using the generalized complex variable theory and conformal mapping technique. Then, the fast Fourier transform algorithm is employed to effectively perform the Fourier series fitting for these boundary conditions, and matrix equations for the potential functions in the frequency domain are established. Later, a matrix solution for the potential functions is formulated to determine the stress and displacement fields around the shallow non-circular tunnel. Finally, select numerical analyses are conducted to verify the proposed method, discuss the key parameters in the algorithm, and reveal the effect of the acceleration strategy using FFT as well as the effect of non-circular geometries on the stress and displacement fields.

关键词： complex variable method Shallow non-circular tunnel Matrix form solution Fourier series fitting Stress and displacement fields

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Influence of fiber hollowness on the local thermo-electro-elastic field in a thermoelectric composite

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FRONTIERS IN ENERGY RESEARCH 2023年 11卷

作者： Yu, Chuanbin Liu, Haoxin Du, Chaofan Xing, Shichao Yangzhou Univ Coll Architectural Sci & Engn Yangzhou Jiangsu Peoples R China Tongling Univ Sch Mech Engn Tongling Anhui Peoples R China Tongling Univ Key Lab Construct Hydraul Robots Anhui Higher Educ Inst Tongling Anhui Peoples R China Tongling Univ Key Lab Addit Mfg Tongling City Tongling Anhui Peoples R China

The fiber geometry is one of the important parameters in the effective conversion performance and local strength of thermoelectric composites. In this study, the plane problem of a hollow fiber embedded within a non-linear thermoelectric medium in the presence of a uniform remote in-plane electric current and a uniform remote energy flux is investigated based on the complex variable method. Closed-form expressions for all the potential functions characterizing the thermoelectric field and the associated thermal stress field in both the matrix and fiber are obtained by solving the corresponding boundary value problem. Numerical examples are presented to illustrate the effect of hollowness ratio of the fiber on the local energy conversion efficiency and interfacial thermal stress concentration. It is found that a higher conversion efficiency and a lower amount of thermal stress concentration around a hollow fiber than that around a solid fiber could be achieved simultaneously by appropriate selection of the hollowness ratio of the fiber. The results can be directly used for performance optimization and reliability evaluation in design of thermoelectric composites in engineering.

关键词： thermoelectric materials complex variable method hollow fiber conversion efficiency thermal stress

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Stress analysis of perforated composite plates reinforced with carbon nanotubes with different distributions

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EMERGENT MATERIALS 2021年第6期4卷 1711-1723页

作者： Zeighami, Vahid Jafari, Mohammad Shahrood Univ Technol Fac Mech & Mechatron Engn Shahrood Iran

This study deals with calculating the resultant moments and forces around an elliptical and circular holes in a functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates. Various distributions of the reinforcement materials aligned uni-axially are investigated considering three functionally graded and uniform distributions of carbon nanotubes along thickness direction. The mechanical properties of CNTs (carbon nanotube-reinforced) are temperature- and size-dependent and are calculated by molecular dynamics simulations. Based on the gradual changes in the thickness direction and the established rule of the mixture, the effective mechanical properties of the FG-CNTRC plates are approximated. complex variable technique is used to estimate the resultant moments and forces around the elliptical and circular holes in the FG-CNTRC plate. The impacts of CNT distribution shape, the aspect ratio of hole shape, the volume fraction of CNTs, temperature dependence, and hole orientation on the resultant moments and forces around the elliptical and circular holes are investigated in detail. The highest resultant moment and force do not necessarily reduce with increasing the volume fraction of CNT;hence, the volume fraction should increase purposefully. Aligning the CNT axis with applied loading will lead to the lowest values of the highest resultant moments and forces in the holes with less elongation in a vertical direction to the nanotube axis. According to the results, the above parameters have a significant impact on the distribution of stress resultants and moments around the cutout in CNTRC plates, and the load-bearing capacity of these plates with cutouts can be improved by careful selection of these parameters.

关键词： complex variable method Potential functions Functionally graded carbon nanotube-reinforced composite The subsequent forces and moments

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Displacements and stresses around a circular tunnel in an elastic medium with pseudo-static horizontal earthquake body forces

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COMPUTERS AND GEOTECHNICS 2023年第1期162卷

作者： Jain, Hemant Kumar, Jyant Indian Inst Sci Dept Civil Engn Bengaluru 560012 India

This manuscript presents an analytical solution based on the complex variable approach for computing dis-placements and stresses around a single circular tunnel in a linear elastic medium in the presence of pseudo-static horizontal earthquake body forces. The solution has been obtained with the imposition of uniform as well as non-uniform radial displacement boundary conditions along the tunnel's periphery taking the ground volume loss (GVL) as a governing input parameter. The non-uniform radial displacements' boundary condition along the tunnel periphery has been modelled by using the Gaussian distribution function. The effects of the distribution of the tunnel's peripheral displacements, Poisson's ratio of the continuum and the depth to radius of the tunnel on the results have been examined. Necessary validation exercise, in the presence of horizontal earthquake accel-eration, has also been carried out by comparing the obtained results with that computed on the basis of the finite element method. The results were also compared with that reported in literature. It was observed that with an increase in the pseudo static acceleration, there is (i) a significant increase in the horizontal displacements, (ii) a generation of non-symmetric displacement and stress pattern, (iii) an increase in the shear stresses, and (iv) the development of high deviatoric stress zones around the tunnel periphery.

关键词： Ground settlements Elastic analysis Tunnels Earthquakes complex variable method

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Minimization of thermal stress in perforated composite plate using metaheuristic algorithms WOA, SCA and GA

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COMPOSITE STRUCTURES 2023年第Part2期304卷

作者： Jafari, Mohammad Chaleshtari, Mohammad Hossein Bayati Khoramishad, Hadi Altenbach, Holm Shahrood Univ Technol Fac Mech & Mechatron Engn Shahrood Iran Iran Univ Sci & Technol Sch Mech Engn Tehran 16846 Iran Otto von Guericke Univ Inst Mech Tech Mech Fak Maschinenbau D-39106 Magdeburg Germany

In this study, an attempt is made to achieve optimal thermal stress distribution in symmetric composite plates with non-circular holes under uniform heat flux by using metaheuristic optimization algorithms. The analytical solution is based on the thermo-elastic theory and the complex variable method. In addition, the stress analysis of laminated composite plates with circular holes is extended to non-circular holes using the appropriate mapping function. To determine the optimum thermal stress, the whale optimization algorithm (WOA) which is inspired by the lifestyle of humpback whales in nature, the sine cosine algorithm (SCA) that is inspired by the calculation of sine and cosine functions and the genetic algorithm (GA) are utilized. The effect of hole orientation, stacking sequence of laminates, bluntness and hole shape as significant parameters on optimum thermal stress distribution around the holes are studied. The laminate is made of graphite/epoxy material with stacking sequences of [0/ 90]s, [45/-45]s and [30/0/-30]s. The cost function is considered as the maximum value of thermal stress surrounding the hole. The performance of optimization algorithms is examined. It is found out that the circular shape for hole may not necessarily be the optimum geometry for all stacking sequences.

关键词： Thermal stress complex variable method Perforated laminated composites Whale optimization algorithm (WOA) Sine cosine algorithm (SCA) Genetic algorithm (GA)

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Failure behavior of horseshoe-shaped tunnel in hard rock under high stress:Phenomenon and mechanisms

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Transactions of Nonferrous Metals Society of China 2022年第2期32卷 639-656页

作者： Hao WU Guo-yan ZHAO Shao-wei MA School of Mines China University of Mining and TechnologyXuzhou 221116China School of Resources and Safety Engineering Central South UniversityChangsha 410083China

A particle flow code(PFC) was first applied to examining the mechanical response of a horseshoe-shaped opening in prismatic rock models under biaxial compression. Next, an improved complex variable method was proposed to derive the stress distribution around the opening. Lastly, a case study of tunnel failure caused by rock burst in Jinping Ⅱ Hydropower Station was further analyzed and discussed. The results manifest that a total of four types of cracks occur around the opening under low lateral confining stress, namely, the primary-tensile cracks on the roof-floor, sidewall cracks on the sidewalls, secondary-tensile cracks on the corners and shear cracks along the diagonals. As the confining stress increases, the tensile cracks gradually disappear whilst the spalling failure becomes severe. Overall, the failure phenomenon of the modelled tunnel agrees well with that of the practical headrace tunnel, and the crack initiation mechanisms can be clearly clarified by the analytical stress distribution.

关键词： horseshoe-shaped tunnel fracture behavior rock burst stress distribution complex variable method particle flow code

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Theoretical study on residual thermal stresses caused by the brazing process in annular and bilayer structures

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ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK 2023年第1期74卷 36-36页

作者： Song, Kun Li, Nian Ling, Xiang Schiavone, Peter Nanjing Tech Univ Sch Mech & Power Engn 30 Puzhu South Rd Nanjing Jiangsu Peoples R China Univ Alberta Dept Mech Engn Edmonton AB Canada

It is well-known that residual thermal stress poses a significant threat to the stability and reliability of brazed structures. However, theoretical studies focusing on the effects of residual thermal stress on even simple brazed structures remain largely absent from the literature. In this paper, we use complex variable methods to derive theoretical solutions characterizing residual stress fields for annular and bilayer structures. In addition, using a series of numerical examples, we investigate the main factors determining residual thermal stress in brazing. Our results show that both radial and hoop stress are present in the annular structure while the stress component parallel to the interface is the unique principal stress in the bilayer structure. In an annular structure in which the total thickness of materials coincides with the length of the inner radius, the residual thermal stress in the outer base material is four times higher than that of the inner base material. This is attributed to the fact that the two materials have different curvatures. In the case of a thin-wall structure in which the inner radius is ten times that of the total thickness of materials, the corresponding residual thermal stress has no more than 15% error when compared to that from the bilayer structure. Since the distortion of brazed structures is due mainly to the effects of residual thermal stress within the corresponding base materials, it would seem practical to minimize the thickness of the solder used in the brazing process.

关键词： Brazing process Residual thermal stress Analytical solution complex variable method

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Thermal stress analysis of perforated unsymmetric FG-CNTRC plate using a general analytical solution

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THIN-WALLED STRUCTURES 2022年 173卷 108956-108956页

作者： Zeighami, V Jafari, M. Shahrood Univ Technol Fac Mech & Mechatron Engn Shahrood Iran

In this study, based on the development of the complex variable method, a general solution is presented to calculate thermal stresses in unsymmetric functionally graded carbon nanotube-reinforced composite (FGCNTRC) plates weakened by a hole under uniform heat flux. The extracted equations can also be used for thermal analysis of perforated FGM plates and unsymmetric composites laminates. Due to the fact that size and temperature affect the mechanical properties of carbon nanotubes (CNT), the material properties of the unsymmetric FG-CNTRC plates are approximated based on gradual changes in the direction of thickness and extended rule of the mixture. The present analysis considers the effect of important parameters such as CNT volume fraction, CNT angle, hole aspect ratio, hole orientation, and heat flux angle on the distribution of thermal stresses and moments around elliptical and circular holes. The present comprehensive parametric study shows that the aforementioned variables have a significant effect on the thermal stresses in perforated FG-CNTRC plates. Therefore, by properly selecting their values in the design of such plates, thermal stresses can be significantly reduced.

关键词： Perforated FG-CNTRC plate complex variable method Uniform heat flux Thermal stress Unsymmetric nanocomposite plates

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Analytical stress solution for rock mass containing two holes based on an improved Schwarz alternating method

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THEORETICAL AND APPLIED FRACTURE MECHANICS 2021年 116卷 103092-103092页

作者： Tan, Lihai Ren, Ting Dou, Linming Yang, Xiaohan Cai, Xin Qiao, Ming China Univ Min & Technol Sch Mines Xuzhou 221116 Jiangsu Peoples R China Univ Wollongong Sch Civil Min & Environm Engn Wollongong NSW 2522 Australia Cent South Univ Sch Resources & Safety Engn Changsha 410083 Hunan Peoples R China

In this study, the accuracy and generality of stress calculation for a plate containing double holes via Schwarz alternating method was investigated. The original Schwarz alternating method with inverse mapping function shows a good performance in terms of the stress solution for a plate containing two arched holes. However, for a plate containing two holes with corners, evitable error may be produced during the calculation because of the unsatisfying accuracy of inverse mapping function. This error is particularly obvious in the stress calculation for a plate containing two triangular holes. To address the problem, an improved Schwarz alternating method without the consideration of inverse mapping function was proposed in this study. The coordinate transformation of points around hole boundaries is realized by an optimization method instead of the inverse mapping function, which leads to little error during the calculation and thus improves the stress solution accuracy especially for plates containing holes with corners. With the employment of the improved method, the influences of connecting angle and lateral pressure coefficient on stress solutions for plates containing double U-shaped holes were discussed. In addition, DEM simulations were further conducted to study the influence of stress characteristics on the failure patterns of rock mass. The result shows that the hoop stress linearly relates to lateral pressure coefficient in the elastic plate and fractures always initiate around hole boundaries where high stress concentrates.

关键词： complex variable method Conformal mapping Schwarz alternating method Stress analytical solution DEM numerical simulation

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