Abstract:
This thesis presents the efficient topology optimization methods constructed within the state-of-the-art polygon scaled boundary finite element (SBFE) framework. The SBFE approach enables the discrete model construction of structures comprising of arbitrary curve geometry lying in 2D and/or 3D spaces. More explicitly, incorporated with quadtree (in 2D) and octree (3D) mesh refinements the automatic adaptive mesh scheme run within the polygon SBFE framework provides the cost-effective model generation allowing hanging nodes. These distinctive features present the developed SBFE approach well suiting as an underlying modeling framework for the topology design optimization of solids. The bi-directional evolutionary structural optimization (BESO) algorithm is integrated with the digital image-based processes, where a novel convolution-filtered technique refines the intensity between solid and void areas. This leads to the fast convergence of accurate optimal layout (distribution of materials) of the design structures. The applications of the combined BESO and SBFE method are illustrated though the optimal topology designs of structures under not only statically (time-independent) but also dynamically (time-dependent) applied load regimes. The latter applies a (single-step) high-order time integration technique that accurately approximates the dynamic responses of design structures. What is more is its nontrivial extension to the optimal topology design of structures under limited natural frequencies. Finally, the use of material interpolation techniques built on an unified BESO and SBFE framework allows the extension of the above applications to the challenging design problems with multi-phase material conditions.
