Polinomal Diferansiyel Quadrature (PDQ) Metodu ile Dikdörtgen Plakların Statik, Dinamik ve Burkulma Hesabı

Abstract

Çalışmada Homojen ve izotrop dikdörtgen plakların iki ve üç boyutlu eğilme, burkulma ve serbest titreşim analizi diferansiyel quadrature metoduyla yapılmıştır. Diferansiyel quadrature metodundaki ağırlık katsayıları; kuvvet, Chebyshev ve Lagrange polinomları ile hesaplanmıştır. Plak diferansiyel denklemleri yani yönetici denklemler (esas denklemler ve sınır koşulları) diferansiyel quadrature metodu vasıtasıyla çözüm bölgesindeki düğüm noktalarında bilinmeyen fonksiyon değerleri olarak tanımlanmış bir lineer denklem takımına veya standart özdeğer problemine indirgenmiştir. Elde edilen sonuçlar literatürde mevcut değerler ile karşılaştırmalı olarak sunulmuştur. Sonuçlar mühendislik analizi kapsamında yeter hassasiyette bulunmuştur.

Keywords

• Stabilite, Burkulma, Plak, Polinomal Diferansiyel Quadrature

Static, Dynamic and Buckling Analysis of Rectangular Plates by the Method of Polynomial based Differential Quadrature (PDQ)

Abstract

In the study, two and three-dimensional bending, buckling, and free vibration analysis of homogenous and isotropic rectangular plates are made by the method of differential quadrature. The weighting coefficients for differential quadrature are obtained using the power, Chebyshev and Lagrange polynomials. The governing differential equations (constitutive equations and boundary conditions) are reduced to a linear algebraic equations or a standard eigenvalue equation in terms of the unknown function values at the grid points in the field domain via differential quadrature method. The obtained results are then compared with the other results in the related literature. It is found that the obtained results are suitable in point of view the engineering analysis concept.

Keywords

• Stability, Buckling, Plate, Polinomial Differential Quadrature

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