The closed-form solutions of the electroelastic Eshelby's tensors can be expressed by the Eshelby's tensors of the perfectly elastic inclusion problem and the perfectly dielectric inclusion problem.

Since the closed-form solutions of the Eshelby's tensors of the perfectly elastic inclusion problem and the perfectly dielectric inclusion problem can be given by theory of elasticity and electrodynamics respectively, the electroelastic Eshelby's tensors can be gotten conveniently.

On the reduction of the dual integral equations to a Fredholm integral equation which features a closed-form kernel, solutions to the inclusion problem are computed.

The lamellar inclusion problem in plane elasticity

The localization problem (spheroidal duplex inclusion problem) is formulated with the Papkovitch-Neuber approach; this requires expansion formulae for the spheroidal potentials, which are derived in the Appendix.

The flat inclusion problem in bonded dissimilar anisotropic elastic media under longitudinal shear loading

In particular, a dynamic inclusion problem for homogeneous isotropic centrosymmetric micropolar elasticity is investigated.

The elastic inclusion problem, that is the calculation of the stress-strain field and the elastic energy of an anisotropic elastic medium with an elastic inclusion contained in it, is one of the important problems in materials science.Especially, the variation of the elastic energy of the system with the orientations of the inclusion in the medium (i. e. the orientational dependence of the elastic energy), and the orientation of the inclusion corresponding to the minimum of the...

The elastic inclusion problem, that is the calculation of the stress-strain field and the elastic energy of an anisotropic elastic medium with an elastic inclusion contained in it, is one of the important problems in materials science.Especially, the variation of the elastic energy of the system with the orientations of the inclusion in the medium (i. e. the orientational dependence of the elastic energy), and the orientation of the inclusion corresponding to the minimum of the elastic energy of the system are of great theoretical land practical significance in the investigations of the habit orientations of the phase transformations and precipitate particles, the prediction of the microcracking direction as well as the optimum distribution of the reinforcement fibers in the composites.Based on the "Point Force-Line Force Method" given by H. Y. Yang and Y.T. Chou in 1976, a general computer program is compiled, which is applicable to the numerical calculation of the elastic energy of the elliptical inclusion oriented in any direction of the anisotropic medium for the generalized plane problem. The values of the elastic energy of the elliptic inclusions with their cylinder axes along the <100>, <110> and <111> directions in cubic metals Fe, Nb and Al were computed, and the dependence of elastic energies on the orientation of cross elliptic sections, which was rotating around their cylindcr axes, has been illustrated explicitly in graphic charts.The following conclusions arc deduced from the calculation results:1. The system has its elastic energy when the inclusion is lying on the crystal planes and oriented along the crystal directions of low indexes.2. The elastic energy of the system with the inclusion subjected to pure shear strain is 1/3-1/2 of that with the inclusion subjected to principal strain.3. The elastic energy of the anisotropic system with thin plate inclusions is very small. As the elliptic index e=b/a→0 the elastic energy of the system approaches nil.4. If the boundary energy could be neglected, the new phase and the precipitate with the lowest elastic energy would take the thin plate shape and shear mode in phase transformations and precipitation.

A modified Piagetian's class inclusion task and a simplifiedclassification task were presented to prechoolers. The results indicated: 1. The ability of solving class inclusion problem was facilitatedby three factors(1)endowing general class with the common attributionsof perception, (2)highlighting the common attributions in instruction,(3) comparing sub-class with general-class by counting performance. 2. Several stages were involved in solving the class inclusionproblem: First, children around the age...

A modified Piagetian's class inclusion task and a simplifiedclassification task were presented to prechoolers. The results indicated: 1. The ability of solving class inclusion problem was facilitatedby three factors(1)endowing general class with the common attributionsof perception, (2)highlighting the common attributions in instruction,(3) comparing sub-class with general-class by counting performance. 2. Several stages were involved in solving the class inclusionproblem: First, children around the age of 4 could only compare theindividual attributions of a subclass with those of another one. Theydid not know that generality exists in individuality. Secondly, childrenbetween 5-6 could compare sub-class with general class bearing theattributions of perception, and the whole through the senses perceived.Finally children around the age of 7 and above could solve classinclusion problem in the abstract and recognize the logical relationshipbetween the part and the whole. 3. The hierarchical structure of class was shown in the 3 to4-year-olds when familiar stimuli were manipulated in a simplified task ofclassification.

The paper presents a self-consistent finite element method (SCFEM)dealing with inclusion problems. Based on self-consistent model, the average elastic properties of effective medium are calculated by the fi nite element iteration procedure. As applications of this method, the average elastic moduli for unidirectional short-fiber composites are obtained and the effect of fiber geometry on average elastic properties of composites are in-vestigated. The numerical results agree well with those of experiments....

The paper presents a self-consistent finite element method (SCFEM)dealing with inclusion problems. Based on self-consistent model, the average elastic properties of effective medium are calculated by the fi nite element iteration procedure. As applications of this method, the average elastic moduli for unidirectional short-fiber composites are obtained and the effect of fiber geometry on average elastic properties of composites are in-vestigated. The numerical results agree well with those of experiments.