Performance Analysis of Zhao and Durbin Numerical Inversion Methods of Laplace Transform

N.A.

Article Details

Performance Analysis of Zhao and Durbin Numerical Inversion Methods of Laplace Transform

Authors:

N.A.

Publisher:

Cukurova University

Main Topics:

Makine Mühendisliği (Diğer) | Kompozit ve Hibrit Malzemeler

Journal:

Çukurova Üniversitesi Mühendislik Fakültesi Dergisi Vol.38 Issue 2, pp.507-513

Document Type:

Article

Publication Date:

7/2023

Document Language:

English

Document ID (Org No.):

2001293591

pISSN:

2757-9255

Keywords:

Abstract:

 The Laplace transform is essential to satisfy the independence of time for the analysis of the transient response of the composite or functionally-graded materials. The time independent boundary value problem may be solved then either by numerically or analytically. The solutions should be inverted to the physical plane using inverse Laplace transform. Therefore, the selected numerical inversion method may be crucial to obtain the high accuracy throughout the whole analysis steps. In the present study, Zhaos Method I, Zhaos Method II, Durbins Method and Modified Durbins Method are applied to dynamic loading conditions. The analysis results show that the accurate and stable solutions even for long time inversion have been obtained by Modified Durbins Method and Zhaos Methods. However, compared with the methods of Zhaos, the computational and programing load of Durbins Methods are minimum.

 The Laplace transform is essential to satisfy the independence of time for the analysis of the transient response of the composite or functionally-graded materials. The time independent boundary value problem may be solved then either by numerically or analytically. The solutions should be inverted to the physical plane using inverse Laplace transform. Therefore, the selected numerical inversion method may be crucial to obtain the high accuracy throughout the whole analysis steps. In the present study, Zhaos Method I, Zhaos Method II, Durbins Method and Modified Durbins Method are applied to dynamic loading conditions. The analysis results show that the accurate and stable solutions even for long time inversion have been obtained by Modified Durbins Method and Zhaos Methods. However, compared with the methods of Zhaos, the computational and programing load of Durbins Methods are minimum.

 The Laplace transform is essential to satisfy the independence of time for the analysis of the transient response of the composite or functionally-graded materials. The time independent boundary value problem may be solved then either by numerically or analytically. The solutions should be inverted to the physical plane using inverse Laplace transform. Therefore, the selected numerical inversion method may be crucial to obtain the high accuracy throughout the whole analysis steps. In the present study, Zhaos Method I, Zhaos Method II, Durbins Method and Modified Durbins Method are applied to dynamic loading conditions. The analysis results show that the accurate and stable solutions even for long time inversion have been obtained by Modified Durbins Method and Zhaos Methods. However, compared with the methods of Zhaos, the computational and programing load of Durbins Methods are minimum.

 Laplace dönüşümü kompozit ya da fonksiyonel derecelendirilmiş malzemelerin dinamik analizlerinde, zamana olan bağımlılığı ortadan kaldırmak için önemli bir yöntemdir. Zamandan bağımsız sınır değer problemleri analitik ya da sayısal olarak çözülebilir. Elde edilen sonuçlar fiziksel uzaya ters Laplace dönüşümü ile çevirilir. Bu yüzden seçilecek olan ters dönüşüm yöntemi tüm analiz adımlarında yüksek doğruluk elde edilmesi bakımından oldukça önemli olabilir. Bu çalışmada, Zhao Method I, Zhao Method II, Durbin Method ve Düzeltilmiş Durbin Methodları dinamik yükleme koşulları için uygulanmıştır. Analiz sonuçları, uzun süreli çözümlemelerde bile Düzeltilmiş Durbin ve Zhao Methodları ile güvenli ve stabil sonuçlar elde edildiğini göstermiştir. Fakat, Zhao Methodları ile kıyaslandığında Düzeltilmiş Durbin Methodunun programlama ve hesaplama yükü çok daha azdır.

Article Details

Performance Analysis of Zhao and Durbin Numerical Inversion Methods of Laplace Transform

Authors:

N.A.

Publisher:

Cukurova University

Main Topics:

Makine Mühendisliği (Diğer) | Kompozit ve Hibrit Malzemeler

Journal:

Çukurova Üniversitesi Mühendislik Fakültesi Dergisi Vol.38 Issue 2, pp.507-513

Document Type:

Article

Publication Date:

7/2023

Document Language:

English

Document ID (Org No.):

2001293591

pISSN:

2757-9255

Numerical inversion

Laplace transform

Transient analysis

Composite materialsSayısal ters dönüşüm

Laplace dönüşümü

Transient analiz

Kompozit malzemeler

Issues

Article Details

Authors: N.A.

Publisher: Cukurova University

Main Topics: Makine Mühendisliği (Diğer) | Kompozit ve Hibrit Malzemeler

Journal: Çukurova Üniversitesi Mühendislik Fakültesi Dergisi Vol.38 Issue 2, pp.507-513

Document Type: Article

Publication Date: 7/2023

Document Language: English

Document ID (Org No.): 2001293591

pISSN: 2757-9255

Issues

Authors:

N.A.

Publisher:

Cukurova University

Main Topics:

Makine Mühendisliği (Diğer) | Kompozit ve Hibrit Malzemeler

Journal:

Çukurova Üniversitesi Mühendislik Fakültesi Dergisi Vol.38 Issue 2, pp.507-513

Document Type:

Article

Publication Date:

7/2023

Document Language:

English

Document ID (Org No.):

2001293591

pISSN:

2757-9255