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Topology optimization of polymorphic structures and mechanisms using global and multicriteria optimization

Kaminakis Nikolaos

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Summary

Topology optimization solves the basic engineering design problem of distributing a limited amount of material in a design space in order to form a structure or a mechanism that works in an optimal way. One of the most interesting applications is the synthesis of compliant mechanisms. A compliant mechanism is a flexible monolithic structure that transforms an external load to motion along a specific direction and the same time is stiff enough to bear with the applied forces. Multipurpose compliant mechanisms are structures with all the above features that are able to deliver two or more different motions depending on the applied load case. In this thesis a new hybrid algorithm is developed and used for the calculation of optimum structures and flexible mechanisms, which combines features of applicable global optimization, to avoid local minima, and classic topology optimization algorithms.Topology optimization is used as a conceptual design tool for structures, compliant mechanisms and auxetical materials, etc. Following classical developments, several multiobjective topology optimization problems are first formulated. From numerical experiments it was noticed that when topology optimization starts from initial random material distributions, the resulted structures are different, meaning that local minima arise. Therefore, a hybrid algorithm utilizing the advantages of global optimization techniques, is proposed. The hybrid scheme uses topology optimization as the evaluation tool of the previously mentioned global optimization algorithms. The majority of materials in nature when stretched in one direction, get thinner in the normal to loading direction, and vice versa. The opposite effect take place in auxetic materials. Auxetic materials are artificial microstructures with properties that may not be found in nature. Their mechanical properties are defined by their structure rather than their composition. The feature that describes them as auxetic, is the negative Poisson's ratio. This auxetic behavior occurs due to their specific internal structure and the way it deforms when the sample is uniaxially loaded. The design of auxetic materials can follow similar techniques to the compliant mechanism and is presented as an application which leads to new designs of auxetic microstrucures. Their effectiveness as well as their response to nonlinearities, are verified using numerical homogenization tools and CAD/CAE software.

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