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"KARIŞIK" MLPG SONLU HACİMLER YÖNTEMİ İLE MLS YAKLAŞTIRMASI KULLANILARAK TEMAS PROBLEMİNİN ÇÖZÜMÜ

SOLUTION OF CONTACT PROBLEM USING "MIXED" MLPG FINITE VOLUME METHOD WITH MLS APPROXIMATIONS

Journal Name:

  • Journal of Naval Sciences And Engineering

Publication Year:

  • 2016

Key Words:

Keywords (Original Language):

Author Name
Abstract (2. Language): 
Meshless methods are became an alternative to most popular numerical methods used to solve engineering problems such as Finite Difference and Finite Element Methods. Because of element free nature, problems are solved using meshless methods depending on the general geometry and conditions of the problem. Mixed Meshless Local Petrov-Galerkin (MLPG) approach is based on writing the local weak forms of PDEs. Moving least squares (MLS) is used as the interpolation schemes. In this study contact analysis problem is modelled using Meshless Finite Volume Method (MFVM) with MLS interpolation and solved for beam contact problem. Meshless discretization and linear complementary equation of the 2-D frictionless contact problems are described first. Then the problem is converted to a linear complementary problem (LCP) and solved using Lemke’s algorithm. An elastic cantilever beam contact to a rigid foundation is considered as an example problem.
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Abstract (Original Language): 
Ağsız yöntemler son yıllarda Sonlu Farklar ve Sonlu Elemanlar Yöntemleri gibi mühendislik problemlerini çözmek için kullanılan en popüler sayısal yöntemlere alternatif haline gelmiş durumdadır. Ağsız yöntemlerin eleman bağımsız yapısı gereği problemlerin çözümleri yalnızca çözümün yapılacağı geometri ve problemin koşullarına bağlıdır. Karışık Ağsız Yerel Petrov-Galerkin (MLPG) yaklaşımı Kısmi Diferansiyel Denklemlerin (PDEs) yerel zayıf formlarının yazılması temeline dayanmaktadır. Hareketli En Küçük Kareler (MLS) yöntemi interpolasyon şeması olarak kullanılmaktadır. Bu çalışmada Ağsız Sonlu Hacimler Yöntemi (MFVM) ile MLS interpolasyon şeması birlikte kullanılarak temas analizi problemi modellenmiş ve kiriş temas problemi için çözülmüştür. Ağsız ayrıklaştırma ve 2-D sürtünmesiz temas problemlerinin doğrusal tamamlayıcı denklemleri ilk olarak açıklanmıştır. Daha sonra problem doğrusal tamamlayıcı probleme (LCP) dönüştürülmüş ve Lemke algoritması kullanılarak çözülmüştür. Örnek problem olarak rijit bir temele temas halindeki elastik bir konsol kiriş problemi ele alınmıştır.
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REFERENCES

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