運用蓋拉金積分法解非均質物體之彈性力場
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Date
1995-11-01
Authors
李永明
屠名正
孫玉柱
Journal Title
Journal ISSN
Volume Title
Publisher
逢甲大學
Abstract
在以往研究非均質物體彈性力場的文獻中，基體大多是無限大的，本文則使用蓋拉金積分法，求解三維有限區域基體，含一個或多個球體、橢圓體雜物之非均質物體之彈性力場。本文所解問題之邊界條件為固定值之應變場，而冗長的數學運算則由數值程式配合 Mathematica 軟體來執行。本文也研究不同相介質的機械性質比，夾雜物之體積分率及長寬比等，對彈性力場整體與局部之影響。 經過詳細的分析，下列兩種效應非常顯著（ 1 ）在不同介質界面附近的彈性力場， 會因夾雜物存在而受到干擾，（ 2 ）在不同介質界面間，會有應力集中的現象。
In the related literatures of the elastic field in the heterogeneous bodies, the matrix domain is almost infinite. However, the Galerkin integral method is used in this study to solve the elastic field for the finite heterogeneous bodies with either one or multiple spherical or ellipsoidal inclusions. A constant strain field is imposed on the external boundary. The lengthy algebra operations are carried out by the numerical program called Mathematical. The global and the local effects of the ratio of mechanical properties between two phases, the volume fraction ratio of the inclusion and the aspect ratio on the elastic field are examined. Through detailed study, the two effects below are very obvious, (1) the elastic fields are disturbed by the inclusion in the vicinity of the interfacial boundary, and (2) stress concentration occurs at the interface between two phases.
In the related literatures of the elastic field in the heterogeneous bodies, the matrix domain is almost infinite. However, the Galerkin integral method is used in this study to solve the elastic field for the finite heterogeneous bodies with either one or multiple spherical or ellipsoidal inclusions. A constant strain field is imposed on the external boundary. The lengthy algebra operations are carried out by the numerical program called Mathematical. The global and the local effects of the ratio of mechanical properties between two phases, the volume fraction ratio of the inclusion and the aspect ratio on the elastic field are examined. Through detailed study, the two effects below are very obvious, (1) the elastic fields are disturbed by the inclusion in the vicinity of the interfacial boundary, and (2) stress concentration occurs at the interface between two phases.