DRBEM Sensitivity Analysis and Shape Optimization of Rotating Magneto-Thermo-Viscoelastic FGA Structures Using DRBEMGSS and DRBEM-NGGP Algorithms

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 magnetothermo-
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 (DRBEMGSS)
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 magnetothermoviscoelastic
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.