Ata MUĞAN, Hakan ERSOY

Tekil değerlerin ayrıştırılması (TDA) yöntemi ile duyarlılık analizi

Bu çalışmada, lineer cebirin araçlarından olan Tekil Değerlere Ayrıştırma "TDA" (Singular Value Decomposition, SVD) metodu, yapısal sistemlerin tasarım duyarlılığı analizlerine uygulanarak TDA'ya dayalı duyarlılık analizi yöntemi geliştirilmiştir. Bir yapısal sistemin tekil değerlerinin şekillendirilmesi, aynı zamanda sistem cevabının belirlenmesi anlamına gelmektedir. Buradan hareketle, geliştirilen TDA 'ya dayalı duyarlılık analizi yöntemi ile mevcut klasik tasarım duyarlılığı metodlarının statik, dinamik analizler, çoklu yükleme hali ve yapısal gürbüzlük gibi alanlarda karşılaştırmaları yapılmış ve yöntemin performansı sayısal örnekler üzerinde denenmiştir. Yöntemin belli alanlarda klasik metodlara göre daha fazla bilgi açığa çıkarmasının yanı sıra, hesaplamalı alanda işlemci süresi ve hafıza kullanımında büyük avantajlara sahip olduğu görülmektedir.

Design sensitivity analyses of structures based on singular value decomposition

In this study, the singular value decomposition (SVD) is employed for design sensitivity analyses of structures. As the squares of singular values are the bounds of power, energy and power spectral density ratios between the input and output vectors, shaping the singular values of a structure, is equivalent to shaping the response of the structure. Comparison is made of the proposed sensitivity analysis based upon the SVD -with static and dynamic responses, and eigenvalue design sensitivity analyses. The issues such as structural robustness, worst loading case and multiple load cases are studied. As shown, design sensitivity analyses based upon the SVD can give good insight into static and dynamic response characteristics of structures. Several numerical examples are also presented to illustrate the proposed approach. As a result, the SVD based analysis is compared with the classical techniques yield more information and computationally advantageous particularly in case of multiple load cases, finding worst case loading and sensitivity bounds of a structure. Another advantage of this method is that it is well suited for finite element method equations which is the most popular method among computational methods especially in modeling continuous structures. That's why the proposed method can be applied to sensitivity and optimization algorithms of well-known commercial analysis softwares such as Ansys, Nastran etc.

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