# 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.

AuthorÂ  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