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受载空心柱下多孔半空间的接触分析

力学学报 2024年第8期56卷 2338-2350页

作者：杨勇林张亚莉马海亮丁生虎李星汪文帅宁夏大学数学统计学院宁夏数学基础学科研究中心

多孔结构具有诸多优良特性被广泛应用于航空航天、生物医疗以及各种工程装备中,而空心柱具有独特的结构常被用于承担结构载荷.因此,研究空心柱与多孔半空间的接触问题显得尤为重要.文章运用Hankel变换将轴对称接触问题转化为积分方程的... 详细信息

多孔结构具有诸多优良特性被广泛应用于航空航天、生物医疗以及各种工程装备中,而空心柱具有独特的结构常被用于承担结构载荷.因此,研究空心柱与多孔半空间的接触问题显得尤为重要.文章运用Hankel变换将轴对称接触问题转化为积分方程的求解问题,推导出表面接触应力和位移的精确表达式.发展了高斯-切比雪夫结合乘积型Bessel函数的无穷积分的数值求解方法,并退化对比验证了方法的正确性,结果表明该方法在奇异值处的计算精度和效果更佳.数值分析了表面接触应力随泊松比、孔隙率、力载荷、内径、壁厚(空心圆柱)和半径(碗形抛物柱)的变化情况,并给出了位移随孔隙率、内径、壁厚、半径及深度的变化情况.研究结果表明基体的接触区域中心产生明显的叠加变形,并且接触区域外侧的奇异性要高于内侧,所以外侧更有可能是裂纹的起始位置.此外,在较小的内径下,当空心柱壁厚与实心柱半径一致时,空心柱比实心柱所导致的基体接触区域外边缘的应力奇异性小1倍以上,并且随着孔隙率的增大该比值降低;当空心柱外径与实心柱半径一致时,空心柱比实心柱所导致的基体接触区域外边缘的应力奇异性大1倍以上,并且在大孔隙下该比值更大.研究结果对多孔材料的设计和应用具有重要的指导意义.

关键词：空心柱多孔材料轴对称接触 micro-dilatation理论积分方程方法

A Numerical Algorithm for Arbitrary Real-Order Hankel Transform

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Wuhan University Journal of Natural Sciences 2022年第1期27卷 26-34页

作者： YANG Yonglin LI Xing ding shenghu WANG Wenshuai School of Mathematics and Statistics Ningxia UniversityYinchuan 750021NingxiaChina

The Hankel transform is widely used to solve various engineering and physics problems,such as the representation of electromagnetic field components in the medium,the representation of dynamic stress intensity factors,vibration of axisymmetric infinite membrane and displacement intensity factors which all involve this type of ***,traditional numerical integration algorithms cannot be used due to the high oscillation characteristics of the Bessel function,so it is particularly important to propose a high precision and efficient numerical algorithm for calculating the integral of high *** this paper,the improved Gaver-Stehfest(G-S)inverse Laplace transform method for arbitrary real-order Bessel function integration is presented by using the asymptotic characteristics of the Bessel function and the accumulation of integration,and the optimized G-S coefficients are *** effectiveness of the algorithm is verified by numerical *** with the linear transformation accelerated convergence algorithm,it shows that the G-S inverse Laplace transform method is suitable for arbitrary real order Hankel transform,and the time consumption is relatively stable and short,which provides a reliable calculation method for the study of electromagnetic mechanics,wave propagation,and fracture dynamics.

关键词： Hankel transform large argument approximate expression of the Bessel function linear transformation accelerated convergence algorithm(LTACA) G-S inverse Laplace transform method(G-SILTM)

Cortical Bone Model with a Microcrack under Tensile Loading

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Wuhan University Journal of Natural Sciences 2022年第5期27卷 375-382页

作者： WANG Xu CHEN Yaogeng ding shenghu WANG Wenshuai LI Xing School of Mathematics and Statistics Ningxia UniversityYinchuan 750021NingxiaChina School of Science Ningxia Medical UniversityYinchuan 750004NingxiaChina

The fracture mechanics of cortical bone has received much attention in biomedical *** is a fundamental question how the material constants and the geometric parameters of the cortical bone affect the fracture behavior of the cortical *** this work,the plane problem for cortical bone with a microcrack located in the interstitial tissue under tensile loading was *** the solution for the continuously distributed edge dislocations as Green ’ s functions,the problem was formulated as singular integral equations with Cauchy *** numerical results suggest that a soft osteon promotes microcrack propagation,while a stiff osteon repels it,but the interaction effect between the microcrack and the osteon is limited near the *** study not only sheds light on the fracture mechanics behavior of cortical bone but also offers inspiration for the design of bioinspired materials in biomedical engineering.

关键词： cortical bone microcrack singular integral equation Cauchy kernel stress intensity factor

Heat Conduction in Multilayered Thermoelectric Materials with Multiple Cracks

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Acta Mechanica Solida Sinica 2018年第4期31卷 512-522页

作者： shenghu ding Yueting Zhou School of Mathematics and Statistics Ningxia University Yinchuan 750021 China School of Aerospace Engineering and Applied Mechanics Tongji University Shanghai 200092 China

Multilayer thin-film thermoelectric materials are of technological importance. This paper describes a method to analyze the heat conduction in a multilayered thermoelectric plate containing some non-collinear cracks. The material properties in one layer may be different from those in another even though each layer may still be homogeneous. Using the Fourier integral transforms, the boundary value problem is reduced to a system of general singular integral equations. The model is sufficiently general to account for any number of layers and any number of cracks. As a numerical illustration, the electric flux intensity factor, energy flux intensity factor and thermal flux intensity factor for a three-layer plate specimen with two cracks are presented. The effects of strip width on the electric flux intensity factor and thermal flux intensity factor are studied.

关键词： Multilayer Thermoelectric materials Crack Singular integral equation Intensityfactors

A Multi-Layered Model for Heat Conduction Analysis of Thermoelectric Material Strip

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Computer Modeling in Engineering & Sciences 2018年第3期114卷 335-349页

作者： shenghu ding Qingnan Liu School of Mathematics and Statistics Ningxia UniversityYinchuan750021China

A multi-layered model for heat conduction analysis of a thermoelectric material strip(TEMs)with a Griffith crack under the electric flux and energy flux load has been *** materials parameters of the TEMs vary continuously in an arbitrary *** derive the solution,the TEMs is divided into several sub-layers with different material *** mixed boundary problem is reduced to a system of singular integral equations,which are solved *** effect of strip width on the electric flux intensity factor and thermal flux intensity factor are studied.

关键词： Thermoelectric material crack singular integral equation intensity factor

Two kinds of contact problems in three-dimensional icosahedral quasicrystals

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Applied Mathematics and Mechanics(English Edition) 2015年第12期36卷 1569-1580页

作者： Xuefen ZHAO Xing LI shenghu ding School of Mathematics and Computer Science Ningxia University Xinhua College Ningxia University

Two kinds of contact problems, i.e., the frictional contact problem and the adhesive contact problem, in three-dimensional （3D） icosahedral quasicrystals are dis- cussed by a complex variable function method. For the frictional contact problem, the contact stress exhibits power singularities at the edge of the contact zone. For the adhe- sive contact problem, the contact stress exhibits oscillatory singularities at the edge of the contact zone. The numerical examples show that for the two kinds of contact problems, the contact stress exhibits singularities, and reaches the maximum value at the edge of the contact zone. The phonon-phason coupling constant has a significant effect on the contact stress intensity, while has little impact on the contact stress distribution regu- lation. The results are consistent with those of the classical elastic materials when the phonon-phason coupling constant is 0. For the adhesive contact problem, the indentation force has positive correlation with the contact displacement, but the phonon-phason cou- pling constant impact is barely perceptible. The validity of the conclusions is verified.

关键词： three-dimensional (3D) icosahedral quasicrystal Riemann-Hilbert problem,contact problem singularity complex variable function method

THE PERIODIC CRACK PROBLEM IN BONDED PIEZOELECTRIC MATERIALS

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Acta Mechanica Solida Sinica 2007年第2期20卷 171-179页

作者： ding shenghu Li Xing Department of Mathematics Shanghai Jiaotong University Shanghai 200240 China Department of Mathematics and Computer Science Ningxia University Yinchuan 750021 China

The problem of a periodic array of parallel cracks in a homogeneous piezoelectric strip bonded to a functionally graded piezoelectric material is investigated for inhomogeneous continuum. It is assumed that the material inhomogeneity is represented as the spatial variation of the shear modulus in the form of an exponential function along the direction of cracks. The mixed boundary value problem is reduced to a singular integral equation by applying the Fourier transform, and the singular integral equation is solved numerically by using the Gauss-Chebyshev integration technique. Numerical results are obtained to illustrate the variations of the stress intensity factors as a function of the crack periodicity for different values of the material inhomogeneity.

关键词： periodic array of parallel crack functionally graded piezoelectric material singular integral equation Gauss-Chebyshev integration technique

Two Kinds of Contact Problems in Dodecagonal Quasicrystals of Point Group 12 mm

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Acta Mechanica Solida Sinica 2016年第2期29卷 167-177页

作者： Xuefen Zhao Xing Li shenghu ding School of Mathematics and Computer Science Ningxia University Xinhua College Ningxia University

In this paper,two kinds of contact problems in 2-D dodecagonal quasicrystals were discussed using the complex variable function method：one is the finite frictional contact problem,the other is the adhesive contact *** analytic expressions of contact stresses in the phonon and phason fields were obtained for a flat rigid punch,which showed that：（1） for the finite frictional contact problem,the contact stress exhibited power-type singularities at the edge of the contact zone;（2） for the adhesive contact problem,the contact stress exhibited oscillatory singularities at the edge of the contact *** distribution regulation of contact stress under punch was illustrated;and the low friction property of quasicrystals was verified graphically.

关键词： 2-D dodecagonal quasicrystals contact problem singularity Riemann-Hilbert problem

Surface contact behavior of functionally graded thermoelectric materials indented by a conducting punch

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Applied Mathematics and Mechanics(English Edition) 2021年第5期42卷 649-664页

作者： Xiaojuan TIAN Yueting ZHOU Lihua WANG shenghu ding School of Aerospace Engineering and Applied Mechanics Tongji UniversityShanghai 200092China School of Mathematics and Statistics Ningxia UniversityYinchuan 750021China

The contact problem for thermoelectric materials with functionally graded properties is *** material properties,such as the electric conductivity,the thermal conductivity,the shear modulus,and the thermal expansion coefficient,vary in an exponential *** the Fourier transform technique,the electro-thermoelastic problems are transformed into three sets of singular integral equations which are solved numerically in terms of the unknown normal electric current density,the normal energy flux,and the contact ***,the complex homogeneous solutions of the displacement fields caused by the gradient parameters are simplified with the help of Euler’s *** addressing the non-linearity excited by thermoelectric effects,the particular solutions of the displacement fields can be *** effects of various combinations of material gradient parameters and thermoelectric loads on the contact behaviors of thermoelectric materials are *** results give a deep insight into the contact damage mechanism of functionally graded thermoelectric materials(FGTEMs).

关键词： thermoelectric material functionally graded property conducting punch conjugate complex root energy flux contact pressure