Skip to content
Research Article Open access CC BY 4.0

DRBEM Sensitivity Analysis and Shape Optimization of Rotating Magneto-Thermo-Viscoelastic FGA Structures Using Golden-Section Search Algorithm Based on Uniform Bicubic B-Splines

Mohamed Abdelsabour Fahmy

Journal of Advances in Mathematics and Computer Science · pp. 1–20 · Published 2 Jan 2018

10.9734/JAMCS/2017/38677

Abstract

Aims: A practicalshape optimization technique is developed, using thedual 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. 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.

Dual reciprocity boundary element method Shape Optimization Design sensitivity analysis Implicit differentiation method Feasibledirection method Functionally graded anisotropic structures Golden-section search algorithm.

References (37)

  1. 1 A generalized dynamical theory of thermoelasticity [DOI]
  2. 2 ON UNDAMPED HEAT WAVES IN AN ELASTIC SOLID [DOI]
  3. 3 The Dual Reciprocity Boundary Element Method [DOI]
  4. 4 Boundary element techniques in engineering [DOI]
  5. 5 Boundary Element Methods for Engineers and Scientists [DOI]
  6. 6 The dual reciprocity boundary element formulation for nonlinear diffusion problems [DOI]
  7. 7 Topology optimization of thermoelastic structures: mean compliance minimization or elastic strain energy minimization [DOI]
  8. 8 Transient magneto-thermoviscoelastic plane waves in a non-homogeneous anisotropic thick strip subjected to a moving heat source [DOI]
  9. 9 An unconditionally stable staggered algorithm for transient finite element analysis of coupled thermoelastic problems [DOI]
  10. 10 Computer implementation of the BEM dual reciprocity method for the solution of general field equations [DOI]
  11. 11 Nonlinear transient thermal stress and elastic wave propagation analyses of thick temperature-dependent FGM cylinders, using a second-order point-collocation method [DOI]
  12. 12 Shape optimization of a cyclone separator using multi-objective surrogate-based optimization [DOI]
  13. 13 A TIME-STEPPING DRBEM FOR MAGNETO-THERMO-VISCOELASTIC INTERACTIONS IN A ROTATING NONHOMOGENEOUS ANISOTROPIC SOLID [DOI]
  14. 14 A time-stepping DRBEM for the transient magneto-thermo-visco-elastic stresses in a rotating non-homogeneous anisotropic solid [DOI]
  15. 15 Topology optimization using B-spline finite elements [DOI]
  16. 16 Implicit–explicit time integration DRBEM for generalized magneto-thermoelasticity problems of rotating anisotropic viscoelastic functionally graded solids [DOI]
  17. 17 Generalized Magneto-Thermo-Viscoelastic Problems of Rotating Functionally Graded Anisotropic Plates by the Dual Reciprocity Boundary Element Method [DOI]
  18. 18 The effect of initial stress and inhomogeneity on the thermoelastic stresses in a rotating anisotropic solid [DOI]
  19. 19 The Effect of Rotation and Inhomogeneity on the Transient Magneto-Thermoviscoelastic Stresses in an Anisotropic Solid [DOI]
  20. 20 Transient Magneto-Thermo-Elastic Stresses in an Anisotropic Viscoelastic Solid with and Without a Moving Heat Source [DOI]
  21. 21 A Three-Dimensional Generalized Magneto-Thermo-Viscoelastic Problem of a Rotating Functionally Graded Anisotropic Solids with and Without Energy Dissipation [DOI]
  22. 22 A Comuputerized DRBEM model for generalized magneto-thermo-visco-elastic stress waves in functionally graded anisotropic thin film/substrate structures [DOI]
  23. 23 NUMERICAL MODELING OF TRANSIENT MAGNETO-THERMO-VISCOELASTIC WAVES IN A ROTATING NONHOMOGENEOUS ANISOTROPIC SOLID UNDER INITIAL STRESS [DOI]
  24. 24 Transient magneto-thermo-viscoelastic stresses in a rotating nonhomogeneous anisotropic solid with and without a moving heat source [DOI]
  25. 25 A Time-Stepping DRBEM for 3D Anisotropic Functionally Graded Piezoelectric Structures Under the Influence of Gravitational Waves [DOI]
  26. 26 The dual reciprocity boundary element method for spontaneous ignition [DOI]
  27. 27 Meshless approach to shape optimization of linear thermoelastic solids [DOI]
  28. 28 Electro-thermo-mechanical behaviors of FGPM spheres using analytical method and ANSYS software [DOI]
  29. 29 The propagation of thermal stresses in an infinite elastic slab [DOI]
  30. 30 Analysis of nonlinear, dynamic coupled thermoviscoelasticity problems by the finite element method [DOI]
  31. 31 Dynamic fracture behavior of functionally graded magnetoelectroelastic solids by BIEM [DOI]
  32. 32 Multi-dimensional optimization of functionally graded material composition using polynomial expansion of the volume fraction [DOI]
  33. 33 Topology optimization of structures with gradient elastic material [DOI]
  34. 34 Transient magnetothermoelastic waves in a viscoelastic half-space produced by ramp-type heating of its surface [DOI]
  35. 35 Shape optimization of two-dimensional thermoelastic structures using boundary integral equation formulation [DOI]
  36. 36 Optimization of fluid-structure systems by eigenvalues gap separation with sensitivity analysis [DOI]
  37. 37 Three-dimensional design optimization using the boundary integral equation method [DOI]

Cited by 15

Modeling and Optimization of Anisotropic Viscoelastic Porous Structures Using CQBEM and Moving Asymptotes Algorithm

Mohamed Abdelsabour Fahmy · Arabian Journal for Science and Engineering · 2018

A New Computerized Boundary Element Model for Three-Temperature Nonlinear Generalized Thermoelastic Stresses in Anisotropic Circular Cylindrical Plate Structures

Mohamed Abdelsabour Fahmy · Dynamical Systems Theory · 2020

Design optimization for a simulation of rotating anisotropic viscoelastic porous structures using time-domain OQBEM

Mohamed Abdelsabour Fahmy · Mathematics and Computers in Simulation · 2019

Showing 3 of 15 known citations — external sources report more than can currently be individually listed.

Related research

Article metrics

Real usage data collected on this platform.

4

Page views

0

PDF downloads

0

Outbound clicks

15

Citations

Views over time

Views by country

Approximate, from request IP at view time — not citizenship or institution. Countries with fewer than 5 views are grouped as "Other".

Traffic sources

Referring site, by host.

Views and downloads exclude known bots/crawlers. Citations combines this platform's own DOI-resolved index with each external source's own reported total — see Cited by above for individually listed citing works. Last refreshed 0 seconds ago.