The Effect of Anisotropy on the Structure Optimization Using BEM-GSS and BEM-NGGP Algorithms | Chapter 09 | Advances in Mathematics and Computer Science Vol. 1
Aims: A shape optimization technique is developed, using
the boundary element method, for two-dimensional anisotropic structures to
study the effects of anisotropy on the displacements and stresses, then
minimize weight while satisfying certain constraints upon stresses and
geometry.
Study Design: Original
Research Paper.
Place and Duration of Study: Jamoum University College, Mathematics Department,
between June 2016 and July 2017.
Methodology: The shape design sensitivity analysis of a
two-dimensional anisotropic structure using a singular formulation of the
boundary element method is investigated to study the effects of anisotropy on
the displacements and stresses. An Implicit differentiation technique of the
discretized boundary integral equations is performed to produce terms that
contain derivatives of the fundamental solutions employed in the analysis. This
technique allows the coupling between optimization technique and numerical
boundary element method (BEM) to form an optimum shape design algorithm that
yields shape design sensitivities of the displacement and stress fields for
anisotropic materials with very high accuracy. The fundamental solutions of
displacements and tractions in terms of complex variables employed in the
analysis. The boundary element method was developed and implemented for use
with the golden-section search (GSS) algorithm and neutrosophic goal geometric
programming (NGGP) algorithm as a numerical optimization technique for
minimizing weight while satisfying all of the constraints.
Results: The proposed method has been verified by using the
two-dimensional plate with an elliptical hole as the numerical example. The
numerical results show that the proposed method is suitable and effective tool
for the computer implementation of the solution.
Conclusion: From the research that has been performed, it is
possible to conclude that the optimal shape of the two-dimensional plate with
an elliptical hole is crucial when elastic field is sensitive to boundary
shape. Also from this knowledge of the effects of anisotropy on the
displacements and stresses, we can design various anisotropic structures to
meet specific engineering requirements and utilize within which to place new
information can be more effective.
Author Details:
Mohamed Abdelsabour Fahmy
Faculty of Computer and Informatics, Suez Canal University, New Campus, 4.5 Km, Ring Road, El Salam District, 41522 Ismailia, Egypt.
Faculty of Computer and Informatics, Suez Canal University, New Campus, 4.5 Km, Ring Road, El Salam District, 41522 Ismailia, Egypt.
Jamoum
University College, Umm Al-Qura University, Alshohdaa 25371, Jamoum, Makkah,
Saudi Arabia
View Volume: https://doi.org/10.9734/bpi/amacs/v1
Comments
Post a Comment