Multiscale optimisation of dynamic properties for additively manufactured lattice structures

A framework for tailoring the dynamic properties of functionally graded lattice structures through the use of multiscale optimisation is presented in this thesis. The multiscale optimisation utilises a two scale approach to allow for complex lattice structures to be simulated in real time at a similar computational expense to traditional finite element problems. The micro and macro scales are linked by a surrogate model that predicts the homogenised material properties of the underlying lattice geometry based on the lattice design parameters. Optimisation constraints on the resonant frequencies and the Modal Assurance Criteria are implemented that can induce the structure to resonate at specific frequencies whilst simultaneously tracking and ensuring the correct mode shapes are maintained. This is where the novelty of the work lies, as dynamic properties have not previously been optimised for in a multiscale, functionally graded lattice structure. Multiscale methods offer numerous benefits and increased design freedom when generating optimal structures for dynamic environments. These benefits are showcased in a series of optimised cantilever structures. The results show a significant improvement in dynamic behavior when compared to the unoptimised case as well as when compared to a single scale topology optimised structure. The validation of the resonant properties for the lattice structures is performed through a series of mechanical tests on additive manufactured lattices. These tests address both the micro and the macro scale of the multiscale method. The homogeneous and surrogate model assumptions of the micro scale are investigated through both compression and tensile tests of uniform lattice samples. The resonant frequency predictions of the macro scale optimisation are verified through mechanical shaker testing and computed tomography scans of the lattice structure. Sources of discrepancy between the predicted and observed behavior are also investigated and explained.Open Acces

Topology Optimization via Machine Learning and Deep Learning: A Review

Topology optimization (TO) is a method of deriving an optimal design that satisfies a given load and boundary conditions within a design domain. This method enables effective design without initial design, but has been limited in use due to high computational costs. At the same time, machine learning (ML) methodology including deep learning has made great progress in the 21st century, and accordingly, many studies have been conducted to enable effective and rapid optimization by applying ML to TO. Therefore, this study reviews and analyzes previous research on ML-based TO (MLTO). Two different perspectives of MLTO are used to review studies: (1) TO and (2) ML perspectives. The TO perspective addresses "why" to use ML for TO, while the ML perspective addresses "how" to apply ML to TO. In addition, the limitations of current MLTO research and future research directions are examined

A small perturbation based optimization approach for the frequency placement of high aspect ratio wings

Design denotes the transformation of an identified need to its physical embodiment in a traditionally iterative approach of trial and error. Conceptual design plays a prominent role but an almost infinite number of possible solutions at the outset of design necessitates fast evaluations. The traditional practice of empirical databases loses adequacy for novel concepts and an ever increasing system complexity and resource scarsity mandate new approaches to adequately capture system characteristics. Contemporary concerns in atmospheric science and homeland security created an operational need for unconventional configurations. Unmanned long endurance flight at high altitudes offers a unique showcase for the exploration of new design spaces and the incidental deficit of conceptual modeling and simulation capabilities. The present research effort evolves around the development of an efficient and accurate optimization algorithm for high aspect ratio wings subject to natural frequency constraints. Foundational corner stones are beam dimensional reduction and modal perturbation redesign. Local and global analyses inherent to the former suggest corresponding levels of local and global optimization. The present approach departs from this suggestion. It introduces local level surrogate models to capacitate a methodology that consists of multi level analyses feeding into a single level optimization. The innovative heart of the new algorithm originates in small perturbation theory. A sequence of small perturbation solutions allows the optimizer to make incremental movements within the design space. It enables a directed search that is free of costly gradients. System matrices are decomposed based on a Timoshenko stiffness effect separation. The formulation of respective linear changes falls back on surrogate models that approximate cross sectional properties. Corresponding functional responses are readily available. Their direct use by the small perturbation based optimizer ensures constitutive laws and eliminates a previously necessary optimization at the local level. The great economy of the developed algorithm makes it suitable for the conceptual phase of aircraft design.Ph.D.Committee Chair: Mavris, Dimitri; Committee Member: Bauchau, Olivier; Committee Member: Schrage, Daniel; Committee Member: Volovoi, Vitali; Committee Member: Yu, Wenbi

Design for Crashworthiness of Categorical Multimaterial Structures Using Cluster Analysis and Bayesian Optimization

This work introduces a cluster-based structural optimization (CBSO) method for the design of categorical multimaterial structures subjected to crushing, dynamic loading. The proposed method consists of three steps: conceptual design generation, design clustering, and Bayesian optimization. In the first step, a conceptual design is generated using the hybrid cellular automaton (HCA) algorithm. In the second step, threshold-based cluster analysis yields a lower-dimensional design. Here, a cluster validity index for structural optimization is introduced in order to qualitatively evaluate the clustered design. In the third step, the optimal design is obtained through Bayesian optimization, minimizing a constrained expected improvement function. This function allows to impose soft constraints by properly redefining the expected improvement based on the maximum constraint violation. The Bayesian optimization algorithm implemented in this work has the ability to search over (i) a real design space for sizing optimization, (ii) a categorical design space for material selection, or (iii) a mixed design space for concurrent sizing optimization and material selection. With the proposed method, materials are optimally selected based on multiple attributes and multiple objectives without the need for material ranking. The effectiveness of this approach is demonstrated with the design for crashworthiness of multimaterial plates and thin-walled structures

Application of Surrogate Based Optimisation in the Design of Automotive Body Structures

The rapid development of automotive industry requires manufacturers to continuously reduce the development cost and time and to enhance the product quality. Thus, modern automotive design pays more attention to using CAE analysis based optimisation techniques to drive the entire design flow. This thesis focuses on the optimisation design to improve the automotive crashworthiness and fatigue performances, aiming to enhance the optimisation efficiency, accuracy, reliability, and robustness etc. The detailed contents are as follows: (1) To excavate the potential of crash energy absorbers, the concept of functionally graded structure was introduced and multiobjective designs were implemented to this novel type of structures. First, note that the severe deformation takes place in the tubal corners, multi-cell tubes with a lateral thickness gradient were proposed to better enhance the crashworthiness. The results of crashworthiness analyses and optimisation showed that these functionally graded multi-cell tubes are preferable to a uniform multi-cell tube. Then, functionally graded foam filled tubes with different gradient patterns were analyzed and optimized subject to lateral impact and the results demonstrated that these structures can still behave better than uniform foam filled structures under lateral loading, which will broaden the application scope of functionally graded structures. Finally, dual functionally graded structures, i.e. functionally graded foam filled tubes with functionally graded thickness walls, were proposed and different combinations of gradients were compared. The results indicated that placing more material to tubal corners and the maximum density to the outmost layer are beneficial to achieve the best performance. (2) To make full use of training data, multiple ensembles of surrogate models were proposed to maximize the fatigue life of a truck cab, while the panel thicknesses were taken as design variables and the structural mass the constraint. Meanwhile, particle swarm optimisation was integrated with sequential quadratic programming to avoid the premature convergence. The results illustrated that the hybrid particle swarm optimisation and ensembles of surrogates enable to attain a more competent solution for fatigue optimisation. (3) As the conventional surrogate based optimisation largely depends on the number of initial sample data, sequential surrogate modeling was proposed to practical applications in automotive industry. (a) To maximize the fatigue life of spot-welded joints, an expected improvement based sequential surrogate modeling method was utilized. The results showed that by using this method the performance can be significantly improved with only a relatively small number of finite element analyses. (c) A multiojective sequential surrogate modeling method was proposed to address a multiobjective optimisation of a foam-filled double cylindrical structure. By adding the sequential points and updating the Kriging model adaptively, more accurate Pareto solutions are generated. (4) While various uncertainties are inevitably present in real-life optimisations, conventional deterministic optimisations could probably lead to the violation of constraints and the instability of performances. Therefore, nondeterministic optimisation methods were introduced to solve the automotive design problems. (a) A multiobjective reliability-based optimisation for design of a door was investigated. Based on analysis and design responses surface models, the structural mass was minimized and the vertical sag stiffness was maximized subjected to the probabilistic constraint. The results revealed that the Pareto frontier is divided into the sensitive region and insensitive region with respect to uncertainties, and the decision maker is recommended to select a solution from the insensitive region. Furthermore, the reduction of uncertainties can help improve the reliability but will increase the manufacturing cost, and the tradeoff between the reliability target and performance should be made. (b) A multiobjective uncertain optimisation of the foam-filled double cylindrical structure was conducted by considering randomness in the foam density and wall thicknesses. Multiobjective particle swarm optimisation and Monte Carlo simulation were integrated into the optimisation. The results proved that while the performances of the objectives are sacrificed slightly, the nondeterministic optimisation can enhance the robustness of the objectives and maintain the reliability of the constraint. (c) A multiobjective robust optimisation of the truck cab was performed by considering the uncertainty in material properties. The general version of dual response surface model, namely dual surrogate model, was proposed to approximate the means and standard deviations of the performances. Then, the multiobjective particle optimisation was used to generate the well-distributed Pareto frontier. Finally, a hybrid multi-criteria decision making model was proposed to select the best compromise solution considering both the fatigue performance and its robustness. During this PhD study, the following ideas are considered innovative: (1) Surrogate modeling and multiobjective optimisation were integrated to address the design problems of novel functionally graded structures, aiming to develop more advanced automotive energy absorbers. (2) The ensembles of surrogates and hybrid particle swarm optimisation were proposed for the design of a truck cab, which could make full use of training points and has a strong searching capacity. (3) Sequential surrogate modeling methods were introduced to several optimisation problems in the automotive industry so that the optimisations are less dependent on the number of initial training points and both the efficiency and accuracy are improved. (4) The surrogate based optimisation method was implemented to address various uncertainties in real life applications. Furthermore, a hybrid multi-criteria decision making model was proposed to make the best compromise between the performance and robustness

SOLID-SHELL FINITE ELEMENT MODELS FOR EXPLICIT SIMULATIONS OF CRACK PROPAGATION IN THIN STRUCTURES

Crack propagation in thin shell structures due to cutting is conveniently simulated using explicit finite element approaches, in view of the high nonlinearity of the problem. Solidshell elements are usually preferred for the discretization in the presence of complex material behavior and degradation phenomena such as delamination, since they allow for a correct representation of the thickness geometry. However, in solid-shell elements the small thickness leads to a very high maximum eigenfrequency, which imply very small stable time-steps. A new selective mass scaling technique is proposed to increase the time-step size without affecting accuracy. New ”directional” cohesive interface elements are used in conjunction with selective mass scaling to account for the interaction with a sharp blade in cutting processes of thin ductile shells

Dynamic tailoring of beam-like structures. Application to High Aspect Ratio unitized box-beam and internal resonant structures

This work is a journey into the dynamic tailoring of beam-like structures which aims to exploit unconventional couplings and nonlinearities to enlarge the design space and improving the performances of engineering systems. Particularly, two examples pertaining dynamic tailoring of aerospace and mechanical systems are investigated in depth. In the first case, the work aims to attain a desired structural performance exploiting typical nonlinear structural phenomena and unconventional couplings offered by the unitized structures. As for the unitized structures, the present work, derives two equivalent plate models of curvilinear stiffened panels namely, constant (or homogenized) stiffness model and variable stiffness model. The models are assessed through finite element analysis. In the spirit of CAS (Circumferentially Asymmetric Stiffness), the equivalent plate stiffness’s are used to determine the cross- sectional beam stiffness’s. The governing equations for the Euler-Bernoulli, anisotropic beam with variable stiffness are derived and then used to address the optimization problem. The objective of the optimization is to attain a desired static or dynamic performance of the unitized beam exploiting the enlarged design space which arises from the stiffness variability and the unconventional couplings. In the second type of system analyzed, the aim is synthesize meaningful topologies for planar resonators. The topology optimization is addressed using as initial guess a ground structure. Motivated by the results of the optimization, a generalized reduced order model is derived for multi-members beam structures. The generalized model have been then specialized for three cases namely, V- Y- and Z-shaped resonators. The analytical solution for the V-shaped resonator is also derived along with the electro-mechanical equations of motion. Different solutions are studied aiming at investigating the effect of the folding angle on to the performances of a V-shaped harvester. Beside the study of the static and dynamic behavior of the systems, the thesis presents two novel optimization algorithms namely, the Stud^P GA and the GERM. The Stud^P GA, is a population based algorithm conceived to enhance the exploration capabilities, and hence the convergence rate, of classical GA. The Stud^P GA has been preliminary assessed through benchmark problems for composite layered structure and then used for the optimization of the stiffeners' path aiming at attaining a desired static or dynamic performances. The GERM (Graph-based Element Removal Method), is a double filtering technique conceived for the topology synthesis of planar ground structures. The GERM has been used, in combination with a standard GA, to address the topology optimization problem of the two types of system namely, planar resonator and compliant structures. The work introduces also the concept of trace-based scaling for predicting the behavior of anisotropic structures. The effectiveness of the trace-based scaling is assessed through comparison between scaled and analytical performances of anisotropic structures