Title page for ETD etd-06182010-181920


Type of Document Dissertation
Author Slemp, Wesley Campbell Hop
Author's Email Address wslemp@vt.edu
URN etd-06182010-181920
Title Integrated Sinc Method for Composite and Hybrid Structures
Degree PhD
Department Aerospace and Ocean Engineering
Advisory Committee
Advisor Name Title
Kapania, Rabesh K. Committee Chair
Batra, Romesh C. Committee Member
Brown, Alan J. Committee Member
Patil, Mayuresh J. Committee Member
Philen, Michael K. Committee Member
Keywords
  • Meshless Methods
  • Composite Materials
  • Hybrid Materials
  • Functionally Graded Materials
  • Integrated Sinc Method
  • Interlaminar Stresses
  • Cohesive Zone Modeling
  • Numerical Indefinite Integration
  • Collocation Method
  • Local Petrov-Galerkin Method
Date of Defense 2010-06-04
Availability unrestricted
Abstract
Composite materials and hybrid materials such as fiber-metal laminates, and functionally graded materials are increasingly common in application in aerospace structures. However, adhesive bonding of dissimilar materials makes these materials susceptible to delamination. The use of integrated Sinc methods for predicting interlaminar failure in laminated composites and hybrid material systems was examined. Because the Sinc methods first approximate the highest-order derivative in the governing equation, the in-plane derivatives of in-plane strain needed to obtain interlaminar stresses by integration of the equilibrium equations of 3D elasticity are known without post-processing. Interlaminar stresses obtained with the Sinc method based on Interpolation of Highest derivative were compared for the first-order and third-order shear deformable theories, the refined zigzag beam theory and the higher-order shear and normal deformable beam theory. The results indicate that the interlaminar stresses by the zigzag theory compare well with those obtained by a 3D finite element analysis, while the traditional equivalent single layer theories perform well for some laminates.

The philosophy of the Sinc method based on Interpolation of Highest Derivative was extended to create a novel weak form based approach called the Integrated Local Petrov-Galerkin Sinc Method. The Integrated Local Petrov-Galerkin Sinc Method is easily utilized for boundary-value problem on non-rectangular domains as demonstrated for analysis of elastic and elastic-plastic plane-stress panels with elliptical notches. The numerical results showed excellent accuracy compared to similar results obtained with the finite element method.

The Integrated Local Petrov-Galerkin Sinc Method was used to analyze interlaminar debonding of composite and fiber-metal laminated beams. A double-cantilever beam and a fixed-ratio mixed mode beam were analyzed using the Integrated Local Petrov-Galerkin Sinc Method and the results were shown to correlate well with those by the finite element method. An adaptive Sinc point distribution technique was implemented for the delamination analysis which significantly improved the methods accuracy for the present problem. Delamination of a GLARE, plane-strain specimen was also analyzed using the Integrated Local Petrov-Galerkin Sinc Method. The results correlate well with 2D, plane-strain analysis by the finite element method, including interlaminar stresses obtained by through-the-thickness integration of the equilibrium equations of 3D elasticity.

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