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characteristic tensor for Evaluation of Singular Stress Field Under Mixed-Mode Loadings

Computer Modeling in Engineering & Sciences 2020年第2期122卷 415-432页

作者： Kei Saito Tei Hirashima Ninshu Ma Hidekazu Murakawa JSOL Corporation 2-5-24 HarumiChuo-kuTokyo104-0053Japan. Osaka University 11-1 MihogaokaIbarakiOsaka567-0047Japan.

A characteristic tensor is defined using stress tensor averaged in a small circular domain at the crack tip and multiplied by the root of domain *** possesses the original stress tensor characteristics and has a simple relationship with conventional fracture-mechanics ***,it can be used to estimate stress intensity factors(SIFs)for cracks of arbitrary shape subjected to multiaxial stress loads.A characteristic tensor can also be used to estimate SIFs for kinked *** study examines the relation between a characteristic tensor and SIFs to demonstrate the correlation between the characteristic tensor and fracture-mechanics ***,a single straight crack and a kinked crack of finite length existing in a twodimensional,infinite isotropic elastic body in a plane stress state,were considered to investigate the properties of the characteristic tensor under mixed-mode *** demonstrate the practical utility of the characteristic tensor,the stress distribution obtained through finite element analysis(FEA)was used to estimate mixed-mode SIFs,and the values of estimated SIFs were compared with those obtained using an analytical *** demonstrate that SIFs estimated under mixed-mode loadings exhibit a good agreement with the analytical *** indicates that the proposed characteristictensor-based approach is effective in extracting features of singular stress fields at crack tips,and can be employed to estimate values of fracture-mechanics parameters,such as *** to its simplicity,the proposed approach can be easily incorporated in commercial FE codes for practical applications to simulate the crack-growth problem under both static and dynamic loading *** excellent applicability of the characteristic tensor greatly contributes to efficiency of the design process in industries.

关键词： characteristic tensor stress-intensity factor mixed-mode loading kinked crack.

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THE EXPLICIT SOLUTION OF HOMOGENEOUS LINEAR ORDINARY DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS

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Applied Mathematics and Mechanics(English Edition) 1992年第12期13卷 1115-1120页

作者：黄永念 Department of Mechanics Peking University Beijing

In this paper by using tensor analysis we give the explicit expressions of the solution of the initial-value problem of homogeneous linear differential equations with constant coefficients and the nth-order homogeneous linear differential equation with constant coefficients. In fact, we give the general formula for calculating the elements of the matrix exp[At] . We also give the results when the characteristic equation has the repeated roots. The present method is simpler and better than the other methods.

关键词： tensor differential equation characteristic tensor explicit solution

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