The Bueckner work conjugate integrals are studied for cracks in anisotropic clastic solids.The difficulties in separating Lekhnitskii's two complex arguments involved in the integrals are overcome and explicit fun...The Bueckner work conjugate integrals are studied for cracks in anisotropic clastic solids.The difficulties in separating Lekhnitskii's two complex arguments involved in the integrals are overcome and explicit functional representa- tions of the integrals are given for several typical cases.It is found that the pseudo- orthogonal property of the eigenfunction expansion forms presented previously for isotropic cases,isotropic bimaterials,and orthotropic cases,are proved to be also valid in the present case of anisotropic material.Finally,Some useful path-independent in- tegrals and weight functions are proposed.展开更多
In this paper, a simple but inberent relation between theL-integral and the Buekner work conjugate integral is proved forcrack problems in isotropic, anisotropic, and dissimilar materi- als,respectively. It is found t...In this paper, a simple but inberent relation between theL-integral and the Buekner work conjugate integral is proved forcrack problems in isotropic, anisotropic, and dissimilar materi- als,respectively. It is found that, in the above-mentioned three cases,the L-integral, from the math- ematical point of view as well as inprinciple, arises from Betti's reciprocal theorem. This means thatthe Bueckner work conjugate integral is a more generalpath-independent integral than the others since any otherpath-independent integrals could be derived by using the Buecknerintegral while choosing a different subsidiary stress-displacementfield.展开更多
Bueckner's work conjugate integral customarily adopted for linear elastic materials is established for an interface crack in dissimilar anisotropic materials.The difficulties in separating Stroh's six complex ...Bueckner's work conjugate integral customarily adopted for linear elastic materials is established for an interface crack in dissimilar anisotropic materials.The difficulties in separating Stroh's six complex arguments involved in the integral for the dissimilar materials are overcome and thert the explicit function representations of the integral are given and studied in detail.It is found that the pseudo-orthogonal properties of the eigenfunction expansion form(EEF)for a crack presented previously in isotropic elastic cases,in isotopic bimaterial cases,and in orthotropic cases are also valid in the present dissimilar arbitrary anisotropic cases.The relation between Bueckner's work conjugate integral and the J-integral in these cases is obtained by introducing a complementary stress- displacement state.Finally,some useful path-independent integrals and weight functions are proposed for calculating the crack tip parameters such as the stress intensity factors.展开更多
基金The project supported by the National Natural Science Foundation of China(19891180)Doctorate Foundation of Xi'an Jiaotong University
文摘The Bueckner work conjugate integrals are studied for cracks in anisotropic clastic solids.The difficulties in separating Lekhnitskii's two complex arguments involved in the integrals are overcome and explicit functional representa- tions of the integrals are given for several typical cases.It is found that the pseudo- orthogonal property of the eigenfunction expansion forms presented previously for isotropic cases,isotropic bimaterials,and orthotropic cases,are proved to be also valid in the present case of anisotropic material.Finally,Some useful path-independent in- tegrals and weight functions are proposed.
文摘In this paper, a simple but inberent relation between theL-integral and the Buekner work conjugate integral is proved forcrack problems in isotropic, anisotropic, and dissimilar materi- als,respectively. It is found that, in the above-mentioned three cases,the L-integral, from the math- ematical point of view as well as inprinciple, arises from Betti's reciprocal theorem. This means thatthe Bueckner work conjugate integral is a more generalpath-independent integral than the others since any otherpath-independent integrals could be derived by using the Buecknerintegral while choosing a different subsidiary stress-displacementfield.
基金The project supported by the National Natural Science Foundation of China and the Graduate School of Xi'an Jiaotong University
文摘Bueckner's work conjugate integral customarily adopted for linear elastic materials is established for an interface crack in dissimilar anisotropic materials.The difficulties in separating Stroh's six complex arguments involved in the integral for the dissimilar materials are overcome and thert the explicit function representations of the integral are given and studied in detail.It is found that the pseudo-orthogonal properties of the eigenfunction expansion form(EEF)for a crack presented previously in isotropic elastic cases,in isotopic bimaterial cases,and in orthotropic cases are also valid in the present dissimilar arbitrary anisotropic cases.The relation between Bueckner's work conjugate integral and the J-integral in these cases is obtained by introducing a complementary stress- displacement state.Finally,some useful path-independent integrals and weight functions are proposed for calculating the crack tip parameters such as the stress intensity factors.
