METODA ELEMEN BATAS UNTUK ANALISIS PROBLEM MEDIUM INFINITE DAN SEMI-INFINITE ELASTIS DUA DIMENSI
Classic elasticity theory is usually used to determine stresses and displacements in semi-infinite or infinite medium. Another approach to determine stresses and displacements in those mediums can be done by using numerical method, called Boundary Element Method (BEM). <br /> This thesis expl...
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| Format: | Theses |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/2783 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | Classic elasticity theory is usually used to determine stresses and displacements in semi-infinite or infinite medium. Another approach to determine stresses and displacements in those mediums can be done by using numerical method, called Boundary Element Method (BEM). <br />
This thesis explains about using BEM to solve elasticity problems concerning the cases of infinite and semi-infinite problems, especially the cases that usually find in geotechnical problems. Kelvin solutions for infinite problem and Melan solutions for semi-infinite problem from elasticity theory are used as a base for calculation using BEM.For semi-infinite problem the technique developed by Mindlin is used, i.e.: determining a horizontal plane boundary free from tractions.Bettis reciprocal theorem is used to determine Somigliana identity and then forming a boundary integral equation. The boundary integral equation is calculated numerically by making discretization around the boundary of a domain. This technique is usually called as Boundary Element Method (BEM). The calculation of boundary integral equation will produce displacements or tractions which was not known around the boundary in the beginning. After the boundary's displacements or tractions are known, the internal point dispacements and stresses can be calculated by using Somigliana's identity.The particularity of BEM is that it reduces the dimension of the problem by one, so that it simplifies the problem, however, it needs quite complicated mathematical formulation.By using BEM infinite and semi-infinite problems can be solved easier rather than Finite Element Method. Because Finite Element Method is good for solving closed domain problems, while BEM can be used for closed or open domain.Some examples of.infinite and semi-infinite problems (usually find in geotechnical problems) were attempted to solve using BEM with constant elements. Using constant elements do not always produce good result. It is suggested to use high order elements, such as linear element. |
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