Explicit Solutions of Plane Elastostatics Problems in Heterogeneous Solids

SUMMARYThis paper investigates the periodic group circular holes composed of infinite groups with numbering from j = −∞, . . . , −2, −1, 0, 1, 2, . . . to j = ∞ placed periodically in an infinite plate. The same loading condition and the same geometry are assumed for holes in all groups. The series expansion variational method (SEVM) is used for the solution of the periodic group circular hole problems. After using the SEVM, the boundary value problem is then reduced to an algebraic equation for the undetermined coefficients in the series expansion form, which is formulated on the central group. The influences on the central group from central group itself and many neighbouring groups are evaluated exactly. The influences on the central group from remote groups from j = − ∞, −(M + 2), −(M + 1), M + 1, M + 2 to j = ∞ are approximately summed up into one term. This suggested technique is called the remainder estimation technique (RET) hereafter. It is proved from the computed results that the RET is very effective for the solution of the periodic group hole problems. Finally, several numerical examples are given and the interaction between the groups is addressed. Comparison between various sources of computation is presented. In the uniaxial tension in y-direction, the stacking effect of the stacked groups is studied.

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“…The spacing between two holes is 'd'. In the expansion from Equations (11) to (14), N 1 = N 2 = 24 is assumed.…”

Section: Example 31mentioning

confidence: 99%

Solution of periodic group circular hole problems by using the series expansion variational method

Chen

Lin

2006

Numerical Meth Engineering

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“…It should be noted that the transformation involved must be independent of the loading considered. This methodology has been advanced and implemented recently by the authors in a series of papers [2][3][4][5][6][7][8][9]. For example, Chao and Young [2] gave an explicit general solution of an infinitely extended plate containing any number of circular inclusions under antiplane deformation.…”

Section: Introductionmentioning

confidence: 99%

“…In their paper, they exploited the structure of Moebius transformations which arise by composition of the inversion transformations relative to the two circles bounding the two inclusions. The same approach was applied to the corresponding problems in antiplane piezoelectricity [3] and in plane elastostatics [4]. Based on the Laurent series expansion, the problem of multiple circular inclusions in plane thermoelasticity was solved by Chao et al [5].…”

Section: Introductionmentioning

confidence: 99%

Heterogeneous Problems in Plane Thermoelasticity

Chao

Chen

2009

Journal of Thermal Stresses

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Within the framework of the linear theory of thermoelasticity, the heterogeneous problem associated with multiple inclusions, circularly cylindrical layered media and plane layered media is considered and solved in this paper. The number of inclusions and layers is arbitrary and the system is subjected to arbitrary loading (singularities). The solutions to heat conduction (or antiplane deformation) and thermoelasticity problems are derived by the heterogenization technique that allows us to write down the solution explicitly in terms of the solution of a corresponding homogeneous problem subjected to the same loading. A rapid convergent series solution for both the temperature (or antiplane displacement) and stress functions, which is expressed in terms of an explicit general term of the complex potential of the corresponding homogeneous problem, is obtained in an elegant form. Numerical results are provided for some particular examples to investigate the effect of material combinations and geometrical configurations on the interfacial stresses.

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Thermoelastic Interaction Between a Hole and an Elastic Circular Inclusion

Chao

Heh

1999

AIAA Journal

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Explicit Solutions of Plane Elastostatics Problems in Heterogeneous Solids

Cited by 3 publications

References 10 publications

Solution of periodic group circular hole problems by using the series expansion variational method

Solution of periodic group circular hole problems by using the series expansion variational method

Heterogeneous Problems in Plane Thermoelasticity

Thermoelastic Interaction Between a Hole and an Elastic Circular Inclusion

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