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.

In the transportation sector, any small changes in structural mass have a significant impact on the overall fuel and energy consumption of a vehicle over its lifetime. Thus, the pursuit of mass optimization has gained popularity to cut costs and lower energy usage. Notably, the railway bogie, a crucial component of a railway coach, accounts for more than a third of the coach's mass. Consequently, reducing the weight of the bogie can yield substantial reductions in the overall mass of the railway coach. Therefore, the utilization of materials with relatively higher performance-to-weight ratios, such as Carbon and Glass Fiber Reinforced Polymers (CFRPs/GFRPs), holds immense potential for mass reduction. However, it's crucial to adopt a holistic perspective when evaluating the energy consumption and environmental footprint of a structure due to the energy intensive nature of CFRP materials. In this research, we assess the environmental impact of a light-weight composite bogie frame using a Predictive Life-Cycle Assessment (PLCA) methodology. The impact category chosen for this cradle-to-grave assessment is the Cumulative Energy Demand (CED), with a special emphasis on evaluating the energy consumption during the EOL phase. The CED of the frame is evaluated over its service life with a comparison being made with a conventional metallic frame. The results show that using GFRPs in the composite side beam reduces the CED by approximately 25%. The break-even analysis performed showed that the steel structure has a lower energy consumption below a service life of 1,794,000 kms as compared to the GFRP side-beam manufactured by manual processes.

A probabilistic framework is developed utilizing a two-scale modeling approach to efficiently consider the material variability that is typical for composite materials. The modeling integrates a macro-scale model with effective elastic properties extracted from micro-mechanical simulations. Using a weakest link modeling approach for fatigue assessment the combined effects of defects on fatigue strength in a Carbon Fiber Reinforced Polymer (CFRP) material can be investigated. A full fatigue test program is presented and is used to calibrate the probabilistic fatigue model. By including material variability in the numerical model, the calibrated probabilistic model improves the fatigue life prediction.

The study presents a two-scale modeling approach allowing for an efficient fatigue strength evaluation on a macro scale considering a micro-mechanical defect characterization of a Carbon Fiber Reinforced Polymer (CFRP) material. The modeling approach integrates a macro model with the effective elastic properties from micro-mechanical simulations considering voids. This enables the analysis of defects’ influence on material fatigue strength using a probabilistic weakest link approach. A CFRP laminate with a cross-ply layup was investigated. Two simulation case studies demonstrate the effect of void content and size on the characteristic fatigue strength. An experimental investigation was conducted testing the laminates in tension–tension fatigue verifying the predicted numerical behavior. The numerical models identify a difference in the characteristic fatigue strength consistent with the fatigue test results. It is numerically concluded that the investigated CFRP material's fatigue strength is affected by the presence of voids and even with only a slight difference in the global void volume fraction a scatter in fatigue strength is identified.

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.

Global Sensitivity Analysis (GSA) is a well-established approach to support simulation-driven design decisions where the dependency between the simulation's output and the model's input is quantifed. However, classical GSA approaches, such as Sobol' indices based on Monte Carlo Simulations (MCS), are not convenient when computationally expensive simulation models such as Representative Volume Elements (RVE) are used as the model to analyze. A simulation framework is developed with a metamodeling-based GSA to overcome the aforementioned cost of the MCS approaches. The developed framework has been applied in a Multi-Scale Modeling (MSM) framework replacing a micromechanical RVE simulation with three different metamodels for performing GSA. The micromechanical model predicts the stiffness of a Carbon Fiber Reinforced Polymer (CFRP) material and the GSA can quantify how the experimental material parameters affect the material properties. The obtained sensitivity analysis demonstrates that void size is the most influential parameter on the outputs of interest, and the metamodel-based GSA is a computationally convenient approach.

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.

The intensified pursuit for lightweight solutions in the commercial vehicle industry increases the demand for method development of more advanced lightweight materials such as Carbon-Fiber-Reinforced Composites (CFRP). The behavior of these anisotropic materials is challenging to understand and manufacturing defects could dramatically change the mechanical properties. Voids are one of the most common manufacturing defects; they can affect mechanical properties and work as initiation sites for damage. It is essential to know the micromechanical composition of the material to understand the material behavior. Void characterization is commonly conducted using optical microscopy, which is a reliable technique. In the current study, an approach based on optical microscopy, statistically characterizing a CFRP laminate with regard to porosity, is proposed. A neural network is implemented to efficiently segment micrographs and label the constituents: void, matrix, and fiber. A neural network minimizes the manual labor automating the process and shows great potential to be implemented in repetitive tasks in a design process to save time. The constituent fractions are determined and they show that constituent characterization can be performed with high accuracy for a very low number of training images. The extracted data are statistically analyzed. If significant differences are found, they can reveal and explain differences in the material behavior. The global and local void fraction show significant differences for the material used in this study and are good candidates to explain differences in material behavior.

A micromechanical simulation approach in a Multi-Scale Modeling (MSM) framework with the ability to consider manufacturing defects is proposed. The study includes a case study where the framework is implemented exploring a cross-ply laminate. The proposed framework highlights the importance of correct input regarding micromechanical geometry and void characteristics. A Representative Volume Element (RVE) model is developed utilizing true micromechanical geometry extracted from micrographs. Voids, based on statistical experimental data, are implemented in the RVE model, and the effects on the fiber distribution and effective macromechanical properties are evaluated. The RVE algorithm is robust and maintains a good surrounding fiber distribution around the implemented void. The local void fraction, void size, and void shape affect the effective micromechanical properties, and it is important to consider the phenomena of the effective mechanical properties with regard to the overall void fraction of an RVE and the actual laminate. The proposed framework has a good prediction of the macromechanical properties and shows great potential to be used in an industrial implementation. For an industrial implementation, weak spots and critical areas for a laminate on a macro-level are found through combining local RVEs.

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.