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Ph.D.
(Engineering & Technology)
STRUCTURAL OPTIMIZATION BY COUPLING MESHFREE
METHOD AND FINITE ELEMENT METHOD

Ph.D. Scholar : Rohit Gaurangkumar Ramanbhai
Research Supervisor : Dr. Vikram B. Patel

Regi. No.: 15146051007
Abstract :
In this research work, an innovative numerical technique for optimizing structural shapes
using the couple Meshless Method (MM)-Finite Element Method (FEM) and the
stochastic optimization algorithm is used. In shape optimization, the interior and exterior
boundaries of a structure are varied to produce the most optimal geometric
configuration. As a result, structures are lighter, more reliable, and more cost-effective.
Thus, it has remained an active research area in the field of product design and
development since the early 1970s.

For structural analysis in shape optimization, coupled MM-FEM has been used to
eradicate well-known issues related to traditional FEM. These issues include frequent
remeshing in case of large shape variations. Moreover, the FEM solution does not
continue across the element boundaries. The coupled MM-FEM technique provides a
better solution in terms of solution accuracy within permissible computation time.
Additionally, it is also possible to address the issue of imposing essential boundary
conditions (EBCs). The ramp function is used as a coupling technique to achieve
continuity at the interface elements.

For the present study, Swarm Intelligence (SI) based particle swarm optimization (PSO)
algorithm is used. A population-based stochastic optimization approach eliminates the
computational burden, complexity, and errors associated with design sensitivity analyses
(DSA). For boundary representation, Akima spline interpolation was used, due to its higher
stability and smoothness over the Cubic spline. Through numerical examples of
cantilever and fixed-fixed beams in 2D linear elastics with behavior constraints on
displacement, the effectiveness, validity, and performance of the proposed technique are
demonstrated. In the coupled Element Free Galerkin (EFG)-FE and PSO technique, the
influence of various design variables and h-refinement on the optimum shape and
objective function value is investigated for cantilever beam and fixed-fixed beam. A
comparison is made between the proposed techniques and other existing techniques, as
well as the FEM, to establish their validity and demonstrate their effectiveness.

Key words: Shape optimization, Meshless Methods (MMs), Coupled Element Free
Galerkin (EFG) method-Finite Element (FE) Method, Ramp function, Particle Swarm
Optimization (PSO) 06