DRBEM Sensitivity Analysis and Shape Optimization of Rotating Magneto-Thermo-Viscoelastic FGA Structures Using DRBEM-GSS and DRBEM-NGGP Algorithms | Chapter 05 | Advances in Mathematics and Computer Science Vol. 1
Aims: A practicalshape optimization technique is
developed, using the dual reciprocity boundary element method (DRBEM) with the
golden-section search algorithm based on uniform bicubic B-splines, for
rotating magneto-thermo-viscoelastic functionally graded anisotropic (FGA) structures
subjected to a moving heat source in the context of the Green and Naghdi theory
of type III.
Study Design: Original Research Paper.
Place and Duration of Study: Jamoum University College, Mathematics Department,
between July 2016 and August 2017.
Methodology: An implicit-implicit staggered algorithm was
proposed for use with the DRBEM to obtain the final DRBEM coupled linear system
of equations for displacements and temperature that describe the
magneto-thermo-viscoelastic structural analysis problem. An implicit
differentiation of the discretized dual reciprocity boundary integral equation
with respect to design variables is used to calculate shape displacement
sensitivities of anisotropic materials with very high accuracy. This method
allows the coupling between optimization technique and a dual reciprocity
boundary element method. The feasible direction method was developed and implemented for use with the
one-dimensional golden-section search technique based on uniform bicubic B-splines,
as a numerical optimization method for minimizing weight while satisfying all
of the constraints. The DRBEM was developed and implemented for use with the golden-section
search (DRBEM-GSS) algorithm and also implemented with the neutrosophic goal geometric
programming (DRBEM-NGGP) algorithm as a numerical optimization techniques for
minimizing weight while satisfying all of the constraints.
Results: The optimum shape design of fillet in tension bars
used as the numerical example in order to verify the formulation and the
implementation of the proposed technique. The numerical results show our
technique is efficient and precise.
Conclusion: From the research that has been performed, it is
possible to conclude that the optimal shape of the top half of the fillet under
stress constraint based on magneto-thermo-viscoelasticity is crucial when
magneto-thermoviscoelastic field is sensitive to boundary shape. Also from this
knowledge of the variation of the displacements and temperature sensitivities with
time for magneto-thermo-viscoelastic FGA structures, we can design various
magneto-thermoviscoelastic 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 Computers and Informatics, Suez Canal University, New Campus, 4.5 Km, Ring Road, El Salam District, 41522 Ismailia, Egypt. and Jamoum University College, Umm Al-Qura
University, Alshohdaa 25371, Jamoum, Makkah, Saudi Arabia
View Volume: https://doi.org/10.9734/bpi/amacs/v1
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