Topology optimization of flexible structures under static and dynamic loads - Modelling and Testing

Abstract

This thesis investigates the use of topology optimization in optimal design of flexible structures under static and dynamic loading. These structures should work properly under such loads. The good performance of such structures can be achieved by optimal design of them especially using topology optimization method. Initially the moving iso-surface threshold (MIST) method is extended for topology optimization of multi-layer bending plates/shells under static loading. Multiple layer-wise objective functions and volume constraints are employed in the optimization formulations. Extension of MIST method for multi-layer plates, gives opportunity to develop a 2.5D MIST method to derive optimal layout of known stiffened or sandwiched stiffeners. In the case of flexible structure under dynamic loading and for a multi-layer structure consists of a base, a damping and a constraining layer, the MIST method is extended to optimally design damping/or base layer to maximize multiple modal damping ratios. In addition in this thesis, for a graded structure with multi volume fractions and constraints having viscous or hysteretic damping subject to harmonic loadings, MIST method is extended to optimally distribute material to achieve minimum dynamic compliance for SISO and MIMO optimization problems. The other contribution in this thesis is the extension of unit load method for dynamic problems to find displacement of a chosen DOF of a cellular structure with multi-volume fractions and constraints under arbitrary dynamic loading and having damping. Based on this approach, MIST method is extended to solve optimization problems of minimizing displacement of a chosen DOF or minimizing power spectral density of a signal in a finite time interval by optimal design of under design structure. For all of the proposed procedures, numerical examples and for some of them experimental analysis are presented to validate and explain the efficiency of these methods.