A static-dynamic topology-sizing optimisation method is presented. The solution is based on a sequential Mixed-Integer Linear Programming solution and aims to minimise the mass of a structure subjected to concurrent constraints on static and dynamic response. It is shown that the classical problem of the dynamics of lightweight sandwich structures may be mitigated through core topology and face sheet thickness combinations, retaining the static load carrying capacity while presenting stringent dynamic properties at a low mass penalty. A numerical example, in the form of a load carrying sandwich beam which is excited at different frequencies, is used to demonstrate the method.

This paper presents a novel 3D lattice metastructure featuring customizable elastic moduli in all three dimensions, achieved through distorted Kelvin cells. These structures are fabricated using thermoplastic polyurethane (TPU) materials through selective laser sintering (SLS) additive manufacturing techniques. Static compression tests reveal significant recoverable deformations and near-zero Poisson effects. Numerical simulations indicate that distorted Kelvin cells (DKCs) exhibit lower transmission in the longitudinal direction compared to standard Kelvin cells within the frequency range of interest. Additionally, DKCs demonstrate increased coupling between longitudinal and transverse directions at resonant frequencies. Parametric studies explore various lattice sizes, face configurations (closed or open), twisting angles, and matrix materials. Optimization studies, focusing on different twisting angles on each pair's faces, aim to minimize the response under 400 Hz, showcasing the potential for tuning these structures for specific applications.

A method is proposed that allows for the concurrent optimization of core topology and face sheet thickness of a sandwich beam under compliance constraints. The problem is solved using a novel mixed-linear extension of the Topology Optimization of Binary Structure (TOBS) topology optimization method aiming to minimize the total mass of the beam. The method has been demonstrated on a clamped beam example and the results have been compared to results from topology optimization of the core with a range of a priori fixed face sheet thicknesses. It is shown that the new method, starting from a fully populated core, finds a minimum mass that is lower than but in the neighbourhood of the best results from the topology optimization with fixed face sheet thicknesses. By varying the compliance constraint it is shown that the core topology approaches an ideal corrugated geometry as the compliance constraint is relaxed. The trends observed in the results are compared to analytical models for an idealized core.

Given the increasing importance of sustainability in product design, tools for designing products with low environmental impact are important for tackling problems in the future. One important measure of environmental impact is life cycle energy (LCE), which uses the cumulative amount of energy a product consumes over its’ lifetime as a proxy for environmental impact. In this work, the core topology and face sheet thickness of a sandwich beam are optimized for different material compositions with the goal to minimize the life cycle energy of the beam. A constraint on the mean compliance of the beam is used as a proxy for functional requirements. The problem is solved using a mixed-integer programming extension of the established Topology Optimization of Binary Structures (TOBS) method. Numerical examples indicate that the method is able to find feasible minimum LCE solutions with varying topologies and face sheet thicknesses.

In the vehicle industry it is common to find structures that are required to carry mechanical loads while not experiencing large vibrations when subjected to dynamic loads. An important design tool to achieve this is topology optimization. In the presented work, a mixed-integer programming extension to the established Topology Optimization of Binary Structures (TOBS) method is used to concurrently optimize core topology and face sheet thickness of a sandwich beam subjected to static and time-harmonic loading. The proposed method allows for optimization of the core topology without the face sheet thickness being known a priori. The static and dynamic compliance are used as measures of the response to static and time-harmonic loading and the goal of the optimization is to minimize the mass of the beam subjected to constraints on the compliances. The beam is optimized for different excitation frequencies. The results show that the method is able to find solutions with low mass that satisfy both static and dynamic constraints.

In this paper mass minimization of hysteretically damped structures subjected to static and time-harmonic loading is studied via the Topology Optimization of Binary Structures (TOBS) method. Elements are removed or added to the finite element model of a structure in every iteration based on the solution to an integer linear program (ILP). The ILP is constructed from the sensitivity information of the objective function and the constraints which are in the form of the static and dynamic compliance. The proposed methodology is demonstrated on a 2D clamped-clamped beam and compared with published results for a 2D cantilever beam. The optimization starts from the full design domain and solutions with low mass that fulfill the constraints for a range of different bounds are found. The results also indicate that the mass is much more sensitive to changes in the static compliance constraint than in the dynamic compliance constraint. The effect of mass and upper bound of the constraints on the dynamic compliance at the fundamental resonance frequency is also studied, though no clear conclusions can be drawn. Finally the sensitivity information at the converged topology is studied and it is shown that the algorithm converges because the structural regions that are non-critical for the different constraints do not overlap.

The effect of using thin plies to increase the bearing strength of composite laminates has been investigated. A series of 5 laminates of theoretically identical stiffness with varying proportions of thin plies were manufactured using a single material system. Four specimens from each plate were tested for bearing strength and damage was subsequently characterized using an optical microscope. The results show that performance in terms of bearing stiffness, strength at onset of damage, and ultimate bearing stress increase proportionally with the increasing amount of thin plies within the stack. Shifting from a 100% conventional ply laminate to a 100% thin-ply laminate gave an increase of 47% in the strength at onset of damage. Placement of the thin plies within the stack was also shown to be important for strength at initial onset of damage. Microscopic examination of the failure modes for all samples showed fiber kinking, localized to the center of the hole, to be the dominant failure mode regardless of the stacking sequence.

Topology optimization is used to design multifunctional sandwich panels that fulfill multiple functional constraints. The purpose is to expand the methodology for multifunctional design in earlystages of the vehicle design process, to allow for design of multifunctional vehicle systems thatcan replace multiple subsystems and reduce the total mass of the vehicle. The focus of the research is the inclusion of dynamic behaviour into the topology optimization framework. The casestudy for this research is a train cabin sandwich structure, with the functional requirements beingthe structural and acoustic properties of the structure. The core of the sandwich panel is the designdomain of the optimization . The problem is modelled and solved as a mass minimization topology optimization problem with the structural requirements being translated into constraints onthe static response of the structure and the acoustic requirements being translated into constraintson the response when subjected to time-harmonic loads. The topology optimization problem issolved using the Topology Optimization of Binary Structures (TOBS) method.

A static-dynamic topology-sizing optimisation method is presented. Thesolution is based on a sequential Mixed-Integer Linear Programming solutionand aims to minimise the mass of a structure subjected to concurrentconstraints on static and dynamic response. It is shown that the classicalproblem of the dynamics of lightweight sandwich structures may be mitigatedthrough core topology and face sheet thickness combinations, retaining thestatic load carrying capacity while presenting stringent dynamic propertiesat a low mass penalty.A numerical example, in the form of a load carrying sandwich beam whichis excited at different frequencies, is used to demonstrate the method.

The design of lightweight sandwich structures with constraints the response to static and dynamic loads is investigated. A concurrent optimization of the face sheet thickness and core topology is used to minimize the structural mass of a sandwich beam with constraints on both the static load bearing properties and the average response to a time-harmonic load over a frequency band. The results show that the mass of the resulting structure is very dependent on how tight the dynamic constrain is if the frequency band covers the fundamental resonance frequency of the structure. If the frequency band of excitation covers the second resonance frequency or is between two resonance frequencies, lowering the dynamic response is much cheaper in terms of mass.