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A Predictor-corrector Time-Stepping Drbem for Shape Design Sensitivity and Optimization of Multilayer FGA Structures

Mohamed Abdelsabour Fahmy


The main objective of this paper is to propose a practical shape optimization technique based on a predictor-corrector implicit-implicit staggered algorithm, which was implemented for use with the time-stepping dual reciprocity boundary element method (DRBEM) to obtain the final coupled linear system of equations for temperature and displacements that describe the magneto-thermoelastic structural analysis problem of initially stressed multilayered functionally graded anisotropic (FGA) structures in the context of the Green and Naghdi theory of type III.

An implicit differentiation method, which allows the coupling between optimization method and a dual reciprocity boundary element method, is used to calculate temperature and displacements sensitivities with respect to design variables with very high accuracy. The feasible direction method was developed and implemented for use with the one-dimensional golden section search method as a numerical optimization method for minimizing the weight objective function of the structure while satisfying all of the constraints. The optimum shape design of the link plate for selected anisotropic materials, used as the numerical example in order to demonstrate the validity of the proposed technique. The numerical results show that the optimal shape of the link plate under stress constraint is sensitive to boundary shape. The results also show that our technique is efficient and precise.

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