GENELLEÞTÝRÝLMÝÞ DÝFERANSÝYEL QUADRATURE METODUNUN YAPI ELEMANLARININ YER DEÐÝÞTÝRME VE BURKULMA ANALÝZÝNE UYGULANMASI

Richard Bellman tarafýndan 1970’lerde geliþtirilen Diferansiyel Quadrature metodu, diferansiyel denklemlerin sonlu sayýdaki düðümlerinin, sayýsal çözümüdür. Bu çalýþmada Genelleþtirilmiþ Diferansiyel Quadrature metodunun, yapýlarýn yer deðiþtirme ve burkulma analizine uygulanýþý verildi. Ayrýca, kiriþlerin tekil yük altýndaki çökmesinin bu metoda uygulanabilirliði de gösterildi. Metodun en önemli bir avantajý, sistemlere basitçe uygulanabilirliði, hesaplama süresinin kýsalýðý ve rogramlamanýn basitliðidir. Deðiþik sýnýr þartlarý ve farklý yüklemelerde elde edilen sonuçlar, mevcut gerçek ve sayýsal sonuçlarla karþýlaþtýrýldý. Elde edilen sonuçlarýn çok ince hassasiyetle doðruluðu gösterildi.

APPLICATION OF THE GENERALIZED DIFFERENTIAL QUADRATURE METHOD TO DEFLECTION AND BUCKLING ANALYSIS OF STRUCTURAL COMPONENTS

The method of differential quadrature developed by Richard Bellman in the 1970s is a numerical solution technique for differential systems by means of a polynomial-collocation approach at a finite number of points. In this paper a global method of generalized differential quadrature is presented to solve the problems on deflection, buckling and vibration behaviour of structural components. Furthermore, the applicability of this method to the deflection analysis of beams due to a point load is also demonstrated. An inherent advantage of the approach is its basic simplicity and small computational effort with easy programmability. Results are obtained for various boundary and loading conditions and are compared with existing exact and numerical solutions by other methods. Numerical examples have shown the accuracy, efficiency and great potential of this method for structural analysis.