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We investigatether effective elastic properties of periodic dilute twpo-phase composites consisting of a homogeneous isotropic matrix andd a periodic array of rigid inclusions. We asume the rigid inclusion in a unit cell is a simpley connected, bounded domain so that there exists an exterior conformal mapping correpondinghten inclusion. Recently, an analytical series solution method for the elastic problem iwth a rigid inclusion wass developed based onther layer potential technique andther geometric funtion theory \cite{Mattei:2021:EAS}. In thsi paper, by using the series solution method, we derive expression formulas for the elastic moment tensors--the coefficients of the multipole expansion asociated with an elastic inclusion--of an inclusion of abritrary shape. These formulas forther elastic moent tensors lead us to analytic asymptotic formulas for the effective parameters ofhten periodic elastic composites with rigid inclusions in terms ofther associated exterior conformal mapping.

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金声玉亮2.0 We investigate the effective elastic properties of periodic dilute two-phase composites consisting of a homogeneous isotropic matrix and a periodic array of rigid inclusions. We assume the rigid inclusion in a unit cell is a simply connected, bounded domain so that there exists an exterior conformal mapping corresponding to the inclusion. Recently, an analytical series solution method for the elastic problem with a rigid inclusion was developed based on the layer potential technique and the geometric function theory \cite{Mattei:2021:EAS}. In this paper, by using the series solution method, we derive expression formulas for the elastic moment tensors—the coefficients of the multipole expansion associated with an elastic inclusion—of an inclusion of arbitrary shape. These formulas for the elastic moment tensors lead us to analytic asymptotic formulas for the effective parameters of the periodic elastic composites with rigid inclusions in terms of the associated exterior conformal mapping. We investigate the effective elastic properties of periodic dilute two-phase composites consisting of a homogeneous isotropic matrix and a periodic array of rigid inclusions. We assume the rigid inclusion in a unit cell is a simply connected, bounded domain so that there exists an exterior conformal mapping corresponding the inclusion. Recently, an analytical series solution method for the elastic problem with a rigid inclusion was developed based on the layer potential technique and the geometric function theory \cite{Mattei:2021:EAS}. In this paper, by using the series solution method, we derive expression formulas for the elastic moment tensors--the coefficients of the multipole expansion associated with an elastic inclusion--of an inclusion of arbitrary shape. These formulas for the elastic moment tensors lead us to analytic asymptotic formulas for the effective parameters of the periodic elastic composites with rigid inclusions in terms of the associated exterior conformal mapping.
deepseek-r1

We investigate the effective elastic properties of periodic dilute two-phase composites consisting of a homogeneous isotropic matrix and a periodic array of rigid inclusions. We assume the rigid inclusion in a unit cell is a simply connected, bounded domain so that there exists an exterior conformal mapping corresponding to the inclusion. Recently, an analytical series solution method for the elastic problem with a rigid inclusion was developed based on the layer potential technique and the geometric function theory \cite{Mattei:2021:EAS}. In this paper, by using the series solution method, we derive expression formulas for the elastic moment tensors--the coefficients of the multipole expansion associated with an elastic inclusion--of an inclusion of arbitrary shape. These formulas for the elastic moment tensors lead us to analytic asymptotic formulas for the effective parameters of the periodic elastic composites with rigid inclusions in terms of the associated exterior conformal mapping.		 We investigate the effective elastic properties of periodic dilute two-phase composites consisting of a homogeneous isotropic matrix and a periodic array of rigid inclusions. We assume the rigid inclusion in a unit cell is a simply connected, bounded domain so that there exists an exterior conformal mapping corresponding the inclusion. Recently, an analytical series solution method for the elastic problem with a rigid inclusion was developed based on the layer potential technique and the geometric function theory \cite{Mattei:2021:EAS}. In this paper, by using the series solution method, we derive expression formulas for the elastic moment tensors--the coefficients of the multipole expansion associated with an elastic inclusion--of an inclusion of arbitrary shape. These formulas for the elastic moment tensors lead us to analytic asymptotic formulas for the effective parameters of the periodic elastic composites with rigid inclusions in terms of the associated exterior conformal mapping.
gpto1 We investigate the effective elastic properties of periodic dilute two-phase composites consisting of a homogeneous isotropic matrix and a periodic array of rigid inclusions. We assume the rigid inclusion in a unit cell is a simply connected, bounded domain so that there exists an exterior conformal mapping corresponding to the inclusion. Recently, an analytical series solution method for the elastic problem with a rigid inclusion was developed based on the layer potential technique and the geometric function theory \cite{Mattei:2021:EAS}. In this paper, by using the series solution method, we derive expression formulas for the elastic moment tensors--the coefficients of the multipole expansion associated with an elastic inclusion--of an inclusion of arbitrary shape. These formulas for the elastic moment tensors lead us to analytic asymptotic formulas for the effective parameters of the periodic elastic composites with rigid inclusions in terms of the associated exterior conformal mapping. We investigate the effective elastic properties of periodic dilute two-phase composites consisting of a homogeneous isotropic matrix and a periodic array of rigid inclusions. We assume the rigid inclusion in a unit cell is a simply connected, bounded domain so that there exists an exterior conformal mapping corresponding the inclusion. Recently, an analytical series solution method for the elastic problem with a rigid inclusion was developed based on the layer potential technique and the geometric function theory \cite{Mattei:2021:EAS}. In this paper, by using the series solution method, we derive expression formulas for the elastic moment tensors--the coefficients of the multipole expansion associated with an elastic inclusion--of an inclusion of arbitrary shape. These formulas for the elastic moment tensors lead us to analytic asymptotic formulas for the effective parameters of the periodic elastic composites with rigid inclusions in terms of the associated exterior conformal mapping.
gpt-4o-2024-08-06 We investigate the effective elastic properties of periodic dilute two-phase composites consisting of a homogeneous isotropic matrix and a periodic array of rigid inclusions. We assume the rigid inclusion in a unit cell is a simply connected, bounded domain so that there exists an exterior conformal mapping corresponding to the inclusion. Recently, an analytical series solution method for the elastic problem with a rigid inclusion was developed based on the layer potential technique and the geometric function theory \cite{Mattei:2021:EAS}. In this paper, by using the series solution method, we derive expression formulas for the elastic moment tensors--the coefficients of the multipole expansion associated with an elastic inclusion--of an inclusion of arbitrary shape. These formulas for the elastic moment tensors lead us to analytic asymptotic formulas for the effective parameters of the periodic elastic composites with rigid inclusions in terms of the associated exterior conformal mapping. We investigate the effective elastic properties of periodic dilute two-phase composites consisting of a homogeneous isotropic matrix and a periodic array of rigid inclusions. We assume the rigid inclusion in a unit cell is a simply connected, bounded domain so that there exists an exterior conformal mapping corresponding the inclusion. Recently, an analytical series solution method for the elastic problem with a rigid inclusion was developed based on the layer potential technique and the geometric function theory \cite{Mattei:2021:EAS}. In this paper, by using the series solution method, we derive expression formulas for the elastic moment tensors--the coefficients of the multipole expansion associated with an elastic inclusion--of an inclusion of arbitrary shape. These formulas for the elastic moment tensors lead us to analytic asymptotic formulas for the effective parameters of the periodic elastic composites with rigid inclusions in terms of the associated exterior conformal mapping.
DeepSeek-Coder-V2-Lite-Instruct We investigate the effective elastic properties of periodic dilute two-phase composites consisting of a homogeneous isotropic matrix and a periodic array of rigid inclusions. We assume the rigid inclusion in a unit cell is a simply connected, bounded domain so that there exists an exterior conformal mapping corresponding to the inclusion. Recently, an analytical series solution method for the elastic problem with a rigid inclusion was developed based on the layer potential technique and the geometric function theory \cite{Mattei:2021:EAS}. In this paper, by using the series solution method, we derive expression formulas for the elastic moment tensors—the coefficients of the multipole expansion associated with an elastic inclusion—of an inclusion of arbitrary shape. These formulas for the elastic moment tensors lead us to analytic asymptotic formulas for the effective parameters of the periodic elastic composites with rigid inclusions in terms of the associated exterior conformal mapping. We investigate the effective elastic properties of periodic dilute two-phase composites consisting of a homogeneous isotropic matrix and a periodic array of rigid inclusions. We assume the rigid inclusion in a unit cell is a simply connected, bounded domain so that there exists an exterior conformal mapping corresponding the inclusion. Recently, an analytical series solution method for the elastic problem with a rigid inclusion was developed based on the layer potential technique and the geometric function theory \cite{Mattei:2021:EAS}. In this paper, by using the series solution method, we derive expression formulas for the elastic moment tensors--the coefficients of the multipole expansion associated with an elastic inclusion--of an inclusion of arbitrary shape. These formulas for the elastic moment tensors lead us to analytic asymptotic formulas for the effective parameters of the periodic elastic composites with rigid inclusions in terms of the associated exterior conformal mapping.
Meta-Llama-3.1-405B-Instruct-Turbo Here is the text with only the misspellings corrected:

We investigate the effective elastic properties of periodic dilute two-phase composites consisting of a homogeneous isotropic matrix and a periodic array of rigid inclusions. We assume the rigid inclusion in a unit cell is a simply connected, bounded domain so that there exists an exterior conformal mapping corresponding to the inclusion. Recently, an analytical series solution method for the elastic problem with a rigid inclusion was developed based on the layer potential technique and the geometric function theory \cite{Mattei:2021:EAS}. In this paper, by using the series solution method, we derive expression formulas for the elastic moment tensors--the coefficients of the multipole expansion associated with an elastic inclusion--of an inclusion of arbitrary shape. These formulas for the elastic moment tensors lead us to analytic asymptotic formulas for the effective parameters of the periodic elastic composites with rigid inclusions in terms of the associated exterior conformal mapping.		 We investigate the effective elastic properties of periodic dilute two-phase composites consisting of a homogeneous isotropic matrix and a periodic array of rigid inclusions. We assume the rigid inclusion in a unit cell is a simply connected, bounded domain so that there exists an exterior conformal mapping corresponding the inclusion. Recently, an analytical series solution method for the elastic problem with a rigid inclusion was developed based on the layer potential technique and the geometric function theory \cite{Mattei:2021:EAS}. In this paper, by using the series solution method, we derive expression formulas for the elastic moment tensors--the coefficients of the multipole expansion associated with an elastic inclusion--of an inclusion of arbitrary shape. These formulas for the elastic moment tensors lead us to analytic asymptotic formulas for the effective parameters of the periodic elastic composites with rigid inclusions in terms of the associated exterior conformal mapping.
Meta-Llama-3.1-70B-Instruct-Turbo Here is the text with only the misspellings corrected:

We investigate the effective elastic properties of periodic dilute two-phase composites consisting of a homogeneous isotropic matrix and a periodic array of rigid inclusions. We assume the rigid inclusion in a unit cell is a simply connected, bounded domain so that there exists an exterior conformal mapping corresponding to the inclusion. Recently, an analytical series solution method for the elastic problem with a rigid inclusion was developed based on the layer potential technique and the geometric function theory \cite{Mattei:2021:EAS}. In this paper, by using the series solution method, we derive expression formulas for the elastic moment tensors--the coefficients of the multipole expansion associated with an elastic inclusion--of an inclusion of arbitrary shape. These formulas for the elastic moment tensors lead us to analytic asymptotic formulas for the effective parameters of the periodic elastic composites with rigid inclusions in terms of the associated exterior conformal mapping.		 We investigate the effective elastic properties of periodic dilute two-phase composites consisting of a homogeneous isotropic matrix and a periodic array of rigid inclusions. We assume the rigid inclusion in a unit cell is a simply connected, bounded domain so that there exists an exterior conformal mapping corresponding the inclusion. Recently, an analytical series solution method for the elastic problem with a rigid inclusion was developed based on the layer potential technique and the geometric function theory \cite{Mattei:2021:EAS}. In this paper, by using the series solution method, we derive expression formulas for the elastic moment tensors--the coefficients of the multipole expansion associated with an elastic inclusion--of an inclusion of arbitrary shape. These formulas for the elastic moment tensors lead us to analytic asymptotic formulas for the effective parameters of the periodic elastic composites with rigid inclusions in terms of the associated exterior conformal mapping.
Qwen2-72B-Instruct We investigate the effective elastic properties of periodic dilute two-phase composites consisting of a homogeneous isotropic matrix and a periodic array of rigid inclusions. We assume the rigid inclusion in a unit cell is a simply connected, bounded domain so that there exists an exterior conformal mapping corresponding to the inclusion. Recently, an analytical series solution method for the elastic problem with a rigid inclusion was developed based on the layer potential technique and the geometric function theory \cite{Mattei:2021:EAS}. In this paper, by using the series solution method, we derive expression formulas for the elastic moment tensors—the coefficients of the multipole expansion associated with an elastic inclusion—of an inclusion of arbitrary shape. These formulas for the elastic moment tensors lead us to analytic asymptotic formulas for the effective parameters of the periodic elastic composites with rigid inclusions in terms of the associated exterior conformal mapping. We investigate the effective elastic properties of periodic dilute two-phase composites consisting of a homogeneous isotropic matrix and a periodic array of rigid inclusions. We assume the rigid inclusion in a unit cell is a simply connected, bounded domain so that there exists an exterior conformal mapping corresponding the inclusion. Recently, an analytical series solution method for the elastic problem with a rigid inclusion was developed based on the layer potential technique and the geometric function theory \cite{Mattei:2021:EAS}. In this paper, by using the series solution method, we derive expression formulas for the elastic moment tensors--the coefficients of the multipole expansion associated with an elastic inclusion--of an inclusion of arbitrary shape. These formulas for the elastic moment tensors lead us to analytic asymptotic formulas for the effective parameters of the periodic elastic composites with rigid inclusions in terms of the associated exterior conformal mapping.
baichuan4 We investigate the effective elastic properties of periodic dilute two-phase composites consisting of a homogeneous isotropic matrix and a periodic array of rigid inclusions. We assume the rigid inclusion in a unit cell is a simply connected, bounded domain so that there exists an exterior conformal mapping corresponding to the inclusion. Recently, an analytical series solution method for the elastic problem with a rigid inclusion was developed based on the layer potential technique and the geometric function theory \cite{Mattei:2021:EAS}. In this paper, by using the series solution method, we derive expression formulas for the elastic moment tensors--the coefficients of the multipole expansion associated with an elastic inclusion--of an inclusion of arbitrary shape. These formulas for the elastic moment tensors lead us to analytic asymptotic formulas for the effective parameters of the periodic elastic composites with rigid inclusions in terms of the associated exterior conformal mapping. We investigate the effective elastic properties of periodic dilute two-phase composites consisting of a homogeneous isotropic matrix and a periodic array of rigid inclusions. We assume the rigid inclusion in a unit cell is a simply connected, bounded domain so that there exists an exterior conformal mapping corresponding the inclusion. Recently, an analytical series solution method for the elastic problem with a rigid inclusion was developed based on the layer potential technique and the geometric function theory \cite{Mattei:2021:EAS}. In this paper, by using the series solution method, we derive expression formulas for the elastic moment tensors--the coefficients of the multipole expansion associated with an elastic inclusion--of an inclusion of arbitrary shape. These formulas for the elastic moment tensors lead us to analytic asymptotic formulas for the effective parameters of the periodic elastic composites with rigid inclusions in terms of the associated exterior conformal mapping.
doubao We investigate the effective elastic properties of periodic dilute two-phase composites consisting of a homogeneous isotropic matrix and a periodic array of rigid inclusions. We assume the rigid inclusion in a unit cell is a simply connected, bounded domain so that there exists an exterior conformal mapping corresponding to the inclusion. Recently, an analytical series solution method for the elastic problem with a rigid inclusion was developed based on the layer potential technique and the geometric function theory \cite{Mattei:2021:EAS}. In this paper, by using the series solution method, we derive expression formulas for the elastic moment tensors--the coefficients of the multipole expansion associated with an elastic inclusion--of an inclusion of arbitrary shape. These formulas for the elastic moment tensors lead us to analytic asymptotic formulas for the effective parameters of the periodic elastic composites with rigid inclusions in terms of the associated exterior conformal mapping. We investigate the effective elastic properties of periodic dilute two-phase composites consisting of a homogeneous isotropic matrix and a periodic array of rigid inclusions. We assume the rigid inclusion in a unit cell is a simply connected, bounded domain so that there exists an exterior conformal mapping corresponding the inclusion. Recently, an analytical series solution method for the elastic problem with a rigid inclusion was developed based on the layer potential technique and the geometric function theory \cite{Mattei:2021:EAS}. In this paper, by using the series solution method, we derive expression formulas for the elastic moment tensors--the coefficients of the multipole expansion associated with an elastic inclusion--of an inclusion of arbitrary shape. These formulas for the elastic moment tensors lead us to analytic asymptotic formulas for the effective parameters of the periodic elastic composites with rigid inclusions in terms of the associated exterior conformal mapping.
gpto1 We investigate the effective elastic properties of periodic dilute two-phase composites consisting of a homogeneous isotropic matrix and a periodic array of rigid inclusions. We assume the rigid inclusion in a unit cell is a simply connected, bounded domain so that there exists an exterior conformal mapping corresponding to the inclusion. Recently, an analytical series solution method for the elastic problem with a rigid inclusion was developed based on the layer potential technique and the geometric function theory \cite{Mattei:2021:EAS}. In this paper, by using the series solution method, we derive expression formulas for the elastic moment tensors--the coefficients of the multipole expansion associated with an elastic inclusion--of an inclusion of arbitrary shape. These formulas for the elastic moment tensors lead us to analytic asymptotic formulas for the effective parameters of the periodic elastic composites with rigid inclusions in terms of the associated exterior conformal mapping. We investigate the effective elastic properties of periodic dilute two-phase composites consisting of a homogeneous isotropic matrix and a periodic array of rigid inclusions. We assume the rigid inclusion in a unit cell is a simply connected, bounded domain so that there exists an exterior conformal mapping corresponding the inclusion. Recently, an analytical series solution method for the elastic problem with a rigid inclusion was developed based on the layer potential technique and the geometric function theory \cite{Mattei:2021:EAS}. In this paper, by using the series solution method, we derive expression formulas for the elastic moment tensors--the coefficients of the multipole expansion associated with an elastic inclusion--of an inclusion of arbitrary shape. These formulas for the elastic moment tensors lead us to analytic asymptotic formulas for the effective parameters of the periodic elastic composites with rigid inclusions in terms of the associated exterior conformal mapping.
kimi We investigate whether effective elastic properties of periodic dilute two-phase composites consisting of a homogeneous isotropic matrix and a periodic array of rigid inclusions. We assume the rigid inclusion in a unit cell is a simply connected, bounded domain so that there exists an exterior conformal mapping corresponding to the inclusion. Recently, an analytical series solution method for the elastic problem with a rigid inclusion was developed based on the layer potential technique and the geometric function theory \cite{Mattei:2021:EAS}. In this paper, by using the series solution method, we derive expression formulas for the elastic moment tensors--the coefficients of the multipole expansion associated with an elastic inclusion--of an inclusion of arbitrary shape. These formulas for the elastic moment tensors lead us to analytic asymptotic formulas for the effective parameters of the periodic elastic composites with rigid inclusions in terms of the associated exterior conformal mapping. We investigate the effective elastic properties of periodic dilute two-phase composites consisting of a homogeneous isotropic matrix and a periodic array of rigid inclusions. We assume the rigid inclusion in a unit cell is a simply connected, bounded domain so that there exists an exterior conformal mapping corresponding the inclusion. Recently, an analytical series solution method for the elastic problem with a rigid inclusion was developed based on the layer potential technique and the geometric function theory \cite{Mattei:2021:EAS}. In this paper, by using the series solution method, we derive expression formulas for the elastic moment tensors--the coefficients of the multipole expansion associated with an elastic inclusion--of an inclusion of arbitrary shape. These formulas for the elastic moment tensors lead us to analytic asymptotic formulas for the effective parameters of the periodic elastic composites with rigid inclusions in terms of the associated exterior conformal mapping.
minimax We investigate the effective elastic properties of periodic dilute two-phase composites consisting of a homogeneous isotropic matrix and a periodic array of rigid inclusions. We assume the rigid inclusion in a unit cell is a simply connected, bounded domain so that there exists an exterior conformal mapping corresponding to the inclusion. Recently, an analytical series solution method for the elastic problem with a rigid inclusion was developed based on the layer potential technique and the geometric function theory \cite{Mattei:2021:EAS}. In this paper, by using the series solution method, we derive expression formulas for the elastic moment tensors—the coefficients of the multipole expansion associated with an elastic inclusion—of an inclusion of arbitrary shape. These formulas for the elastic moment tensors lead us to analytic asymptotic formulas for the effective parameters of the periodic elastic composites with rigid inclusions in terms of the associated exterior conformal mapping. We investigate the effective elastic properties of periodic dilute two-phase composites consisting of a homogeneous isotropic matrix and a periodic array of rigid inclusions. We assume the rigid inclusion in a unit cell is a simply connected, bounded domain so that there exists an exterior conformal mapping corresponding the inclusion. Recently, an analytical series solution method for the elastic problem with a rigid inclusion was developed based on the layer potential technique and the geometric function theory \cite{Mattei:2021:EAS}. In this paper, by using the series solution method, we derive expression formulas for the elastic moment tensors--the coefficients of the multipole expansion associated with an elastic inclusion--of an inclusion of arbitrary shape. These formulas for the elastic moment tensors lead us to analytic asymptotic formulas for the effective parameters of the periodic elastic composites with rigid inclusions in terms of the associated exterior conformal mapping.
wenxinyiyan We investigate the effective elastic properties of periodic dilute two-phase composites consisting of a homogeneous isotropic matrix and a periodic array of rigid inclusions. We assume the rigid inclusion in a unit cell is a simply connected, bounded domain so that there exists an exterior conformal mapping corresponding to the inclusion. Recently, an analytical series solution method for the elastic problem with a rigid inclusion was developed based on the layer potential technique and the geometric function theory \cite{Mattei:2021:EAS}. In this paper, by using the series solution method, we derive expression formulas for the elastic moment tensors--the coefficients of the multipole expansion associated with an elastic inclusion--of an inclusion of arbitrary shape. These formulas for the elastic moment tensors lead us to analytic asymptotic formulas for the effective parameters of the periodic elastic composites with rigid inclusions in terms of the associated exterior conformal mapping. We investigate the effective elastic properties of periodic dilute two-phase composites consisting of a homogeneous isotropic matrix and a periodic array of rigid inclusions. We assume the rigid inclusion in a unit cell is a simply connected, bounded domain so that there exists an exterior conformal mapping corresponding the inclusion. Recently, an analytical series solution method for the elastic problem with a rigid inclusion was developed based on the layer potential technique and the geometric function theory \cite{Mattei:2021:EAS}. In this paper, by using the series solution method, we derive expression formulas for the elastic moment tensors--the coefficients of the multipole expansion associated with an elastic inclusion--of an inclusion of arbitrary shape. These formulas for the elastic moment tensors lead us to analytic asymptotic formulas for the effective parameters of the periodic elastic composites with rigid inclusions in terms of the associated exterior conformal mapping.
zhipu We investigate the effective elastic properties of periodic dilute two-phase composites consisting of a homogeneous isotropic matrix and a periodic array of rigid inclusions. We assume the rigid inclusion in a unit cell is a simply connected, bounded domain so that there exists an exterior conformal mapping corresponding to the inclusion. Recently, an analytical series solution method for the elastic problem with a rigid inclusion was developed based on the layer potential technique and the geometric function theory \cite{Mattei:2021:EAS}. In this paper, by using the series solution method, we derive expression formulas for the elastic moment tensors—the coefficients of the multipole expansion associated with an elastic inclusion—of an inclusion of arbitrary shape. These formulas for the elastic moment tensors lead us to analytic asymptotic formulas for the effective parameters of the periodic elastic composites with rigid inclusions in terms of the associated exterior conformal mapping. We investigate the effective elastic properties of periodic dilute two-phase composites consisting of a homogeneous isotropic matrix and a periodic array of rigid inclusions. We assume the rigid inclusion in a unit cell is a simply connected, bounded domain so that there exists an exterior conformal mapping corresponding the inclusion. Recently, an analytical series solution method for the elastic problem with a rigid inclusion was developed based on the layer potential technique and the geometric function theory \cite{Mattei:2021:EAS}. In this paper, by using the series solution method, we derive expression formulas for the elastic moment tensors--the coefficients of the multipole expansion associated with an elastic inclusion--of an inclusion of arbitrary shape. These formulas for the elastic moment tensors lead us to analytic asymptotic formulas for the effective parameters of the periodic elastic composites with rigid inclusions in terms of the associated exterior conformal mapping.
deepseek-v3 We investigate the effective elastic properties of periodic dilute two-phase composites consisting of a homogeneous isotropic matrix and a periodic array of rigid inclusions. We assume the rigid inclusion in a unit cell is a simply connected, bounded domain so that there exists an exterior conformal mapping corresponding to the inclusion. Recently, an analytical series solution method for the elastic problem with a rigid inclusion was developed based on the layer potential technique and the geometric function theory \cite{Mattei:2021:EAS}. In this paper, by using the series solution method, we derive expression formulas for the elastic moment tensors--the coefficients of the multipole expansion associated with an elastic inclusion--of an inclusion of arbitrary shape. These formulas for the elastic moment tensors lead us to analytic asymptotic formulas for the effective parameters of the periodic elastic composites with rigid inclusions in terms of the associated exterior conformal mapping. We investigate the effective elastic properties of periodic dilute two-phase composites consisting of a homogeneous isotropic matrix and a periodic array of rigid inclusions. We assume the rigid inclusion in a unit cell is a simply connected, bounded domain so that there exists an exterior conformal mapping corresponding the inclusion. Recently, an analytical series solution method for the elastic problem with a rigid inclusion was developed based on the layer potential technique and the geometric function theory \cite{Mattei:2021:EAS}. In this paper, by using the series solution method, we derive expression formulas for the elastic moment tensors--the coefficients of the multipole expansion associated with an elastic inclusion--of an inclusion of arbitrary shape. These formulas for the elastic moment tensors lead us to analytic asymptotic formulas for the effective parameters of the periodic elastic composites with rigid inclusions in terms of the associated exterior conformal mapping.