Dairesel Plakların Sonlu Farklar Yöntemiyle Çözülmesi

Abstract

Bu çalışmada var olan bir dairesel plak üzerinde sonlu farklar yöntemi uygulanmaya çalışılmıştır. Dairesel plağı en iyi temsil edecek şekil bulunmaya çalışılmış ve elde edilen yeni şekil sonlu farklar yöntemiyle çözülerek belirli noktalardaki yer değiştirmeler ve moment değerleri elde edilmiştir. Elde edilen yer değiştirmeler ve moment değerleri gerçek sonuçlarla kıyaslanarak yapılan yaklaşımın ne derece doğru olduğu gösterilmiştir. Elde edilen yeni şekil farklı biçimlerde bölünerek sonlu farklar yöntemi uygulanmış ve her iki şekildeki sonuçlar arasındaki bulunmuştur. Bu fark bir grafik üzerine dökülmüş ve eldeki sonuçlar açık bir şekilde gösterilmiştir.

Fixed circular plate with uniformly load was main topic of this study. A circular plate was transformed two form for making the problem more easier in this study. Circularity of plate were annihilated and new formswere used for solution. A new first form of plate is solved and deflection of some point of new first form is determined by dividing uniformly. In first form, circular plate were divided with six horizontal and vertical line uniformly to be solved clearly.Results of this approximation were found out and showed on a graphic. After the first approximation and results, circular plate were divided with eight horizontal and vertical line uniformly When Finite Difference Method was applied second form of plate and equations of deflections were solved, new results of determined points on plate were found easily. Deflections of second form were showed on the same graphic. Exact solution of circular pilates were needed to compare with results of Finite Difference Method. Fixed circular plate with uniform load was solved by using boundary conditions and equation of plate and exact solution were gained. Deflections of determined points on circular plate was demonstrated on the same graphic. When the graphic was analyzed, it is clear that results of Finite Difference Method and exact solution were close to each others. Results of second new form were more close than first new form. This study demonstrated that circular plates can solve by using Finite Difference Method.