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 materi...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.展开更多
The fracture mechanics of cortical bone has received much attention in biomedical engineering.It is a fundamental question how the material constants and the geometric parameters of the cortical bone affect the fractu...The fracture mechanics of cortical bone has received much attention in biomedical engineering.It is a fundamental question how the material constants and the geometric parameters of the cortical bone affect the fracture behavior of the cortical bone.In this work,the plane problem for cortical bone with a microcrack located in the interstitial tissue under tensile loading was considered.Using the solution for the continuously distributed edge dislocations as Green ’ s functions,the problem was formulated as singular integral equations with Cauchy kernels.The 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 osteon.This 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.展开更多
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...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 integration.However,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 oscillation.In 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 given.The effectiveness of the algorithm is verified by numerical examples.Compared 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.展开更多
基金Project supported by the National Natural Science Foundation of China(No.10661009)the Ningxia Natural Science Foundation(No.NZ0604).
文摘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.
基金Supported by the National Natural Science Foundation of China(82060331,12062021,12062022)the Natural Science Foundation of Ningxia(2021AAC03028,2022AAC03001)。
文摘The fracture mechanics of cortical bone has received much attention in biomedical engineering.It is a fundamental question how the material constants and the geometric parameters of the cortical bone affect the fracture behavior of the cortical bone.In this work,the plane problem for cortical bone with a microcrack located in the interstitial tissue under tensile loading was considered.Using the solution for the continuously distributed edge dislocations as Green ’ s functions,the problem was formulated as singular integral equations with Cauchy kernels.The 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 osteon.This 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.
基金Supported by the National Natural Science Foundation of China(42064004,12062022,11762017,11762016)
文摘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 integration.However,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 oscillation.In 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 given.The effectiveness of the algorithm is verified by numerical examples.Compared 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.
