Dissertation > Mathematical sciences and chemical > Mechanics > Solid Mechanics > Strength theory > Fracture theory

Dynamic Fracture Analysis of Inhomogeneous Piezoelectric and Magneto-electro-elastic Materials by Bem

Author ZhongHongJun
Tutor LeiJun
School Beijing University of Technology
Course Engineering Mechanics
Keywords Piezoelectric/magneto-electro-elastic Layered structures Functionallygraded Dynamic fracture Boundary element method
CLC O346.1
Type Master's thesis
Year 2013
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Because of the intrinsic piezoelectric or magneto-electro-elastic coupling effect,piezoelectric and magneto-electro-elastic materials are widely used in intelligentmaterials and structures. In engineering practice, piezoelectric andmagneto-electro-elastic matetials are usually designed to be inhomogeneous structures.Such materials can be adapted to different environments conveniently and possessfavorable controllability. However, for the complicated multi-field loading conditonsand intrinsic brittleness, micro-cracks and voids are easily generated during the polingor in-service process. Under the effect of the alternating external fields, earlier failurewill occur in the presence of the micro-cracks.For the dynamic fracture problems of inhomogeneous piezoelectric andmagneto-electro-elastic materials, laminated structures, thin structures andfunctionally graded materials are taken into consideration. The main contents aresummarized as follows:(1) For piezoelectric laminated structures, a universal matrix-form displacementextrapolation formula and its explicit form are derived to determine the dynamicintensity factors of the interface crack in general anisotropic piezoelectric bi-materials.The formulas are efficient for the general cases for the poling axis of eachpiezoelectric component unparallel to the Cartesian coordinate axes. Using theexplicit extrapolation formula, the transient response of interfacial cracks inpiezoelectric bi-materials under electro-mechanical impacts is studied by time-domainBEM together with a sub-domain technique. Numerial examples present the effects ofthe poling direction, material combination and the load combination on dynamicintensity factors.(2) For piezoelectric thin structures, a semi-analytical method with multiplecoordinate transformations is derived to deal with the nearly singular integrals. Basedon this method, the dynamic responses of piezoelectric thin structures are analyzed byBEM. The comparison with the traditional BEM shows the effectiveness of thepresent method.(3) For functionally graded magneto-electro-elastic materials, the fundamentalsolutions are derived for BEM analysis. The dynamic fundamental solutions offunctionally graded magneto-electro-elastic materials for generalized plane problemsand static fundamental solutions for anti-plane problems are derived, which areimportant for the fracture analysis. (4) For magneto-electro-elastic laminated structures, an explicit extrapolationformula of dynamic intensity factors for interface cracks in transversely isotropicmagneto-electro-elastic bi-materials is derived, which is very feasible for numericalmethods.

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