Curvilinearly T-Stiffened Panel Optimization Framework under Multiple Load Cases Using Parallel Processing

With the advances being made in additive manufacturing, it is becoming increasingly possible to fabricate a broad class of complex-shaped designs for practical applications. This manufacturing capability has allowed structural designers to implement the use of bio-inspired curvilinear stiffeners for achieving better designs of stiffened plate and shell structures. Curvilinear stiffeners have proven to be useful over straight stiffeners in some applications for achieving better structural efficiency. A framework has been developed that employs a hybrid optimization technique of using particle swarm optimization for stiffener shape optimization and gradient-based optimization as implemented in MSC.NASTRAN SOL 200 for optimization of stiffener cross section and shell thickness. Parallel processing has been used to save extensive wall-clock time. The framework has been employed for optimally designing cylindrical shells/panels stiffened by arbitrarily placed stiffeners, the motivation being lighter-weight fuselage and space launch vehicle designs. Structural optimization results have been presented for the optimal design of stiffened shells with the objective of weight minimization for shells subjected to both buckling and stress constraints. Optimization studies show that both the stiffener placement and the stiffener geometric curvature influence the shell buckling load, which can help to decrease the structural weight by optimizing the cross-sectional dimensions for stiffeners and panel thickness. In this paper, cylindrical shells, stiffened by four stiffeners, placed arbitrarily, are studied under compression and shear load cases. It is seen that arbitrarily placed curvilinear stiffeners lead to a potential 13% weight saving as compared to the use of equally spaced straight stiffeners when designed for the compression load case.

This paper discusses current work on STRUCTURAL ASPECTS OF the design optimization of a Truss Braced Wing (TBW) configuration. These wings offer significat potential for performance improvements in terms of fuel efficiency, but also offer challenges for a structural designer. The details of the structural analysis and design methodology are presented. Two different design methodologies are discussed: structural sizing based on beam idealization considering only bending stiffness and static analysis, and a finite element based sizing optimization approach including aeroelastic effects. The paper reports all aspects of the two approaches: design parameterization, model geometry and mesh generation, analysis and optimization. The first approach has been used in the past at Virginia Tech for Multidisciplinary Design Optimization (MDO) studies of a Strut-Braced Wing (SBW), and extensions to sizing of a more general TBW configuration are discussed. The second approach is used to perform some parametric studies presented here. Comparative studies are performed for wings designed for rigid and flexible trim subject to static stress constraints. The aeroelastic performance of some TBW configurations is investigated. Only structural sizing parameters are treated as design variables. Conclusions are drawn from these results for guidance to the ongoing MDO studies of the TBW, to be reported in future papers.

Developments in rapid manufacturing techniques such as electron beam freeform fabrication have made it easier to manufacture objects with complex shapes (like panel with curvilinear stiffeners). In this paper, design optimization of stiffened panels is carried out using different types of response surfaces. Placement and sizing variables are optimized using integrated high-performance, commercially available software. The proposed approach has two optimization loops. The sizing optimization is carried out in the first loop through finite element analysis using gradient-based optimization method for different placement variables. In the second loop, optimal placement of stiffeners is carried out using response surfaces. Because of response surface construction using whole design space, the proposed approach does not suffer from getting trapped in a local minima. The proposed approach is applied to square panels subjected to in-plane biaxial and uniform surface pressure loadings. Panel weight is minimized with buckling, displacements, and stress constraints. An approach to perform both placement and sizing optimization of panels with curvilinear stiffeners is also discussed and a surrogate model is developed for placement and shape optimization of stiffeners.

This paper presents a study of aircraft featuring truss-braced wing configurations that have been optimized for minimum fuel consumption using multidisciplinary design optimization. The investigation proceeds following an earlier Boeing Subsonic Ultra Green Aircraft Research study, which selected the truss-braced wing concept as the most promising of several concept vehicles. This comes from the fact that a significantly higher-aspect-ratio wing could achieve substantial reductions in induced drag but requires major structural changes to support such a large span. This problem was explored through the use of a multidisciplinary design and analysis environment implemented in ModelCenter®. Optimization was performed using ModelCenter’s Design Explorer and Darwin genetic algorithm optimizers. Using the multidisciplinary environment, a large multidimensional design space, featuring design variables spread across the major aircraft design disciplines, was explored. Configurations featuring a strut-braced wing and truss-braced wings with one and two juries were evaluated for different span limits. Subsequently, different laminar wing design options were investigated in conjunction with lift augmentation system options. The multidisciplinary optimization used for this investigation was able to produce candidate designs with the desired attributes and performance improvements while satisfying all relevant geometric and performance constraints.

Traditional monoplane aircraft have been used for many decades. A promising improvement is represented by truss-braced wing configurations because studies have shown potential advantages in terms of fuel savings and overall efficiency. These investigations have been carried out in relatively complex multidisciplinary design and optimization computational frameworks, and thus some theoretical questions regarding the optimal conditions under which the induced drag is minimized need to be specifically addressed. This is achieved in this paper by extending the variationally derived theoretical model that the authors developed for nonplanar wings, closed systems, and multiwings to handle multiple closed paths (typical situation in the case of truss-braced wings) within the wing system. A regularization procedure, based on splines and preserving the continuity of the function and its first and second derivative, is introduced to address the geometrical corners. It is verified that, under optimal conditions, the actual value of the induced drag is a global minimum and that there is an infinite number of possible aerodynamic loads achieving the optimum. In some of them, the central part of the upper wing is more loaded, whereas in other cases, the lower wing and outer portions of the upper wing carry more aerodynamic forces. Finally, it is shown that a jury should be unloaded or at most have constant circulation to avoid penalty on the induced drag.

The development of high-fidelity multidisciplinary analysis and optimization (MDAO) capabilities is essential for advancing modern aerospace vehicle design. Traditional workflows often suffer from limited interoperability between structural solvers, aerodynamic tools, and optimization frameworks. To address these limitations, this project focuses on integrating NASTRAN, a structural solver, into the OpenMDAO framework. This effort was conducted under NASA Contract 80GRC023CA047 by M4 Engineering, Inc., as part of the broader initiative to enhance Model-Based Systems Analysis and Engineering (MBSA&E) capabilities. The primary objective of the project was to develop a robust, reusable, and modular Python-based interface that allows NASTRAN to interface within OpenMDAO workflows and improve structural optimization capabilities. This enables engineers to leverage NASTRAN's structural analysis and sensitivity capabilities while benefiting from OpenMDAO's flexibility and advanced optimization drivers. In support of this objective, multiple demonstration models were created across various NASTRAN solution sequences (SOLs), including static, aeroelastic, flutter, and buckling analyses. These models were used to evaluate the accuracy, robustness, and computational performance of the integration. Additionally, capabilities were developed to extract sensitivity data, aggregate constraint outputs, and streamline the generation of OpenMDAO components from existing NASTRAN input decks. The work described herein also included integration of third-party aerodynamic tools (e.g., transonic CFD solvers and GROM) with OpenMDAO, development of representative aircraft configurations such as the truss-braced wing (TTBW) and blended-wing body (BWB), and final deployment into NASA's Aviary conceptual design framework. The outcomes of this project provide a foundation for future multidisciplinary optimizations using high-fidelity structural models and demonstrates some of the challenges.

The algorithms for multi-material topology optimization were developed to solve compliance-minimization problems and applied to engineering problems in automotive concepts and lightweight design. Two small-scale problems of a long cantilever and a control arm were studied initially to verify the effectiveness of the developed algorithms and in-house program. Optimal solutions achieved by the multi-material topology optimization method developed were compared to their counterparts obtained by standard single-material topology optimization. To efficiently solve real-world engineering problems, the algorithms were further advanced to incorporate extrusion constraints and to handle multiple load cases. The effectiveness and the efficiency of the proposed method were demonstrated by the study of two real-world engineering problems: (a) the conceptual design of a cross-member for a chassis frame; and (b) the conceptual design of an automotive engine cradle. The two optimization design problems both involved complex geometries, design and non-design domains, prescribed regions with specific material allocations, multiple load cases, and manufacturing extrusion constraints. It was explicitly demonstrated that, for the same weight, the optimum designs achieved by the multi-material topology optimization method were stiffer than those achieved by standard single-material topology optimization.

State-of-the-art wind turbines blades are large and complex structures, consequently making design challenging. The complexity is largely a result of using laminated composites which are high-performing and versatile materials, but also inhomogeneous hence exhibiting anisotropic behavior as well as challenging failure mechanisms. Structural optimization has been shown to be an invaluable tool for solving such challenging design problems, however a framework for treating all relevant parameters, i.e., material choice, fiber orientation, stacking sequence, and layer thickness, on the current scale is not available. Thus, the motivation of the present work is to present an overall gradient-based approach, where the key structural criteria are considered for multiple design load cases. The optimization framework is based on a variation of the Discrete Material and Thickness Optimization approach, where the thickness is directly parametrized, allowing for appropriately treating the sandwich parts of the blade. Application of the developed framework leads to an optimized design consisting of complex variable-thickness laminates, a good overall distribution of the structural criteria in the model, and a 23% reduction in mass compared to the initial design.

Purpose: To develop an artificial intelligence based generative design framework to optimize radiation shielding for satellites and spacecraft using a genetic algorithm combined with a generative adversarial network and compare the performance to using only a genetic algorithm. Methods: The optimization framework is developed and tested on three different models, a simple cube, the SpaceX Dragon vehicle, and the STPSat-4 satellite. Each model's geometry is created in our Monte Carlo particle transport code with an added allowed shielding volume. Each model is exposed to a simulated radiation source using the Monte Carlo code. We use a genetic algorithm, GA, where the material distribution is represented by individuals in the algorithm. GAs are evolutionary algorithms primarily used to perform optimizations. The goal of the optimization is to minimize the dose to a specified volume inside the vehicle. Halfway through the optimization, the results are used to train a generative adversarial network, GAN, which is a type of generative model based on adversarial training. The GAN then produces new shielding solutions that are fed into the optimization process. The shielding solutions produced by the GAN-assisted-GA are compared to those produced by the GA only, and both are compared to the reference baseline of aluminum shielding. Results: Our optimization framework was able to reduce the internal dose by up to 20% for the generic satellite, 14% for the Dragon vehicle, and up to 45% for the STPSat-4 for equal weights of uniform aluminum. We found the GAN-assisted-GA was able to improve the overall optimization performance by 6% for the simple cube and 8% for the Dragon vehicle. Conclusions: Our genetic algorithm based optimization framework was able to produce radiation shielding profiles with reduced dose compared to aluminum references of the same weight. We also showed increased performance by incorporating a generative adversarial network into the genetic algorithm optimization process. This work demonstrates the ability of our approach to be used to design radiation shielding for spacecraft and satellites.

The Finite Element (FE) Analysis is an essential tool to study the biomechanical behaviour of the spine, and particularly of the intervertebral disc (IVD). The 3D reconstruction of a patient-oriented IVD has numerous obstacles. Difficulties arise mainly due to the complexity and dimensions of the IVD's constituent structures. The lack of detailed data in conventional imaging techniques causes further problems in the IVD finite element mesh generation and analysis. The accuracy of the FE computation increases if the geometry of model resembles, for instance, the natural smoothness of real anatomical structure. Accounting to this, the main idea of this work is to evaluate the impact of the reconstruction parameters by comparing the final 3D geometrical reconstruction by finite elements with an initial well-defined geometry of a given anatomical structure, and to develop the procedures for the 3D mesh generation from 2D medical imaging.

A case is made that introducing CAD-based geometry prematurely in the aircraft design process actually hinders multidisciplinary design. Consequently, a design process which allows a designer to quickly build and analyze aerospace configurations without CAD or computational meshing specialists is proposed. This allows higher fidelity analyses to be applied at conceptual design and decreases the turnaround time for trade studies and optimizations. The basic premise of conceptual geometry modeling is presented and discussed. Key features and capabilities which are essential for a successful geometry modeler are identified. Desktop Aeronautics' conceptual geometry modeler, RAGE, is described, with emphasis on recent progress and advances in the tool. A preliminary graphical-user-interface is presented along with an application programming interface. Extensibility of the RAGE modeler is discussed along with the importance of this feature. The applicability of RAGE to simple trade studies is demonstrated in an example problem. The precision of the RAGE modeler is also demonstrated on a complex aircraft design. Future plans for the geometry modeler are also discussed. I. Background In the conceptual phase of aircraft design, there is often a wide range of geometric configurations that the designer wishes to consider, analyze, and assess. A designer’s intuition and creativity are crucial to a successful conceptual design, yet are easily inhibited by the modeling and analysis process itself, particularly if high-fidelity analysis is warranted. If the time between inception and assessment of a candidate design is relatively long, a designer may be forced to limit the number of concepts considered. New data revealed in a design iteration may suggest or require significant changes to the geometry configuration. Since the majority of considered design configurations will eventually be discarded, an ideal conceptual design process should involve a highly efficient and easy to use geometry modeler. Significant changes should be allowed without tedious re-work of the geometry model. Exporting the model for analysis should require little effort and have the capability to be automated. Therefore, any modeling application used in this process should be flexible and not restrict the designer’s choice of user interface, analysis method, and design optimization environment. Most current design processes in the aerospace industry rely heavily on computer-aided-design (CAD) applications. As a general design tool, CAD is a powerful geometry modeler capable of precisely representing practically any shape. Unfortunately, this generality is realized at the cost of requiring specialized training to efficiently and effectively use the software. Also, a CAD model is often not easily modified, especially if significant re-work of the geometry is necessary. This can lead to the premature freeze of an aircraft design due to employing excessively high-fidelity geometry modeling too early in the design process. Parametric CAD modeling could address this issue, but creating a well-designed parametric CAD model is difficult. Not only does it require an extremely skilled operator, but also the designer must have some insight into what parameterization may ultimately be desired. Modifying a parametric CAD model is often more difficult than modifying a conventional CAD model. Significant changes, such as adding or removing cross-sections, may invalidate the parameterization in some cases. In most organizations, CAD modeling (whether it be parametric or conventional) is often assigned to a dedicated CAD specialist. Since the conceptual designer is usually not a CAD specialist, the latter must communicate his design intent to the former, often using sketches, dimensions, and word of mouth. When the CAD specialist interprets the sketches, any part or detail not precisely defined usually requires judgment and artistic license. This interpretation may result in loss of design intent and indeterminate iteration between the CAD specialist and designer to obtain a satisfactory result. Because this process is iterative, CAD operators often must recreate similar geometry

A fuzzy logic knowledge-based approach, FUZZYMESH, for finite element mesh generation and analysis is presented. The proposed approach initiates the adaptive process with a high quality initial mesh that is more refined around the critical points/regions in the problem domain. In order to create high quality initial meshes, the heuristic knowledge, past experience, common sense, and ad hoc methods of finite element specialists are incorporated into the knowledge base of the fuzzy system. Using the linguistic variable concept and approximate reasoning techniques, the fuzzy system makes expert decisions about the initial mesh design by considering the geometric information, as well as the boundary and loading conditions. The decision process includes the determination of priority of critical points/regions and the prediction of mesh sizes for them. According to the mesh size information, a near-optimal initial mesh is created with an automatic mesh generator that is based on the advancing front mesh generation technique. The performance of the proposed approach was measured and evaluated in terms of efficiency and accuracy. The evaluation included comparison between the results of a code based on the proposed fuzzy logic knowledge-based approach, FUZZYMESH, and the conventional approach, which starts the finite element analysis with different meshes, by solving various problems. The global as well as local errors of different solutions were examined and compared. The CPU times for different approaches to achieve a particular accuracy were also measured and compared. The results showed that due to better quality of initial meshes, FUZZYMESH results in lower levels and more accurate error estimates. In turn, the proposed approach is able to solve the problem with a more accurate solution at less cost.

Axial flux magnetic-geared double-rotor machines (AMGDRMs) are characterized as a potential core component of the power splitting system in hybrid electric vehicles (HEVs). Conventional AMGDRMs suffer from low mechanical strength due to high axial magnetic force. In this paper, an interior-modulating-rotor axial flux magnetic-geared double-rotor machine (IMR-AMGDRM) is proposed to solve this problem. An analytical model of the IMR-AMGDRM is proposed to predict the magnetic field distribution and electromagnetic performances. Since analytical model is based on 2-D geometry, a 2-D approximation of IMR-AMGDRM which has similar output performance to 3-D finite element analysis (FEA) is presented based on the permanent magnet (PM) magnetic energy equivalent principle. Utilizing subdomain method, the magnetic field distribution and electromagnetic performances are calculated. Finally, the accuracy of the proposed analytical model is validated by 3-D FEA.Index Terms—Analytical model, axial flux, magnetic-geared machine, double-rotor machine.I. IntroductionAxial flux magnetic-geared double-rotor machines (AMGDRMs), which enable high torque density, have been considered a promising candidate for power splitting in hybrid electric vehicles (HEVs) [1]. However, conventional AMGDRMs suffer from low mechanical strength due to high axial magnetic force. To enhance mechanical strength, an interior-modulating-rotor axial flux magnetic-geared double-rotor machine (IMR-AMGDRM) which can reduce axial magnetic force dramatically is proposed in this paper. Fig. 1 (a) and (b) illustrate the configuration of the proposed IMR-AMGDRM.As axial flux type machine, IMR-AMGDRMs have complex 3-D magnetic circuits. 3-D finite element analysis (FEA) can offer accurate results by taking into account the nonlinear factors such as magnetic saturation and flux leakage. But the major drawback of 3-D FEA is serious time cost. Analytical model which is much lower time-consuming provides an alternative for electromagnetic performance prediction in the initial design procedure.In this paper, an analytical model of the IMR-AMGDRM is proposed. The geometry of analytical model is derived based on PM magnetic energy equivalent principle to guarantee similar output performance to 3-D FEA. The solution to analytical model is calculated by subdomain method. To evaluate the accuracy of the proposed analytical model, the results computed by analytical model and that of 3-D FEA are compared.II. Configuration of IMR-AMGDRMIn conventional configuration, the inner and outer rotors are the permanent magnet (PM) rotor and the modulating rotor, respectively. Since the modulating rotor is closer to the PM rotor than stator, the modulating rotor suffers from high axial magnetic force. Furthermore, the modulating rotor is hollow and thus the low mechanical strength of modulating rotor becomes the major drawback of conventional configuration [1]. To solve this problem, the IMR-AMGDRM which switches positions of the PM rotor and the modulating rotor is proposed. In interior-modulating-rotor configuration, as shown in Fig. 1 (a) and (b), the PM rotor is between the modulating rotor and stator, i.e. the inner and outer rotors are the modulating rotor and the PM rotor, respectively. Owing to that the PM rotor suffers from reverse axial magnetic forces from both sides simultaneously, the total axial magnetic force is dramatically reduced. Hence, although the outer rotor is hollow in both configurations, the axial magnetic force of interior-modulating-rotor configuration is significantly decreased, leading to higher mechanical strength and reliability.III.Geometry of 2-D ApproximationGenerally, the unrolled section of axial flux machine at mean radius is used as 2-D approximation. However, few references are found to evaluate the electromagnetic performance equivalence of such approximation. To make the electromagnetic performance of 3-D model and 2-D approximation equal, the amount of magnetic energy of the PM should remain unchanged after approximation, i.e. PM magnetic energy equivalent principle [2]. A 2-D approximation of IMR-AMGDRM which has identical output performance is presented by using PM magnetic energy equivalent principle.IV. Analytical Calculation of IMR-AMGDRMThe proposed analytical model is illustrated in Fig. 1 (c). It can be seen that the model consists of four subdomains. Region i, I, II and III represent the ith slot of the modulating rotor, the inner air gap, the PM rotor and the outer air gap, respectively. Utilizing subdomain method, the magnetic field distributions in the inner and outer air gaps are obtained by the solution of Laplace’s and Poisson’s equations. Then, the electromagnetic performances such as no-load back EMF, torque and axial force can be derived from the calculated magnetic field distributions.Comparisons of computation accuracy between analytical model and 3-D FEA is shown in Fig. 2. As can be observed, the results of analytical model are well consistent with that of 3-D FEA, validating the proposed method. **

Computational cardiac models are progressively being used to understand, predict, and improve the treatment of cardiac diseases. These models commonly rely on the traditional finite element analysis (FEA), where the geometry description and consequent mesh generation are separate preprocessing steps that are required before conducting numerical analyses. The recent isogeometric analysis (IGA) paradigm eliminates the separate meshing step and integrates geometry construction and solution approximation using higher-order splines. In this study, we first investigate whether IGA can be efficiently used to model post-infarction left ventricular mechanics. Mechanics results from an established FEA model with a fine homogeneous mesh are used to investigate to what extent similar results could be obtained using hierarchical mesh refinement in IGA. The IGA-mechanics results show a good agreement while providing a mesh-independent geometry, but deviations are noticed close to the base, apex, and partially the endocardium. Second, both the FEA- and IGA-model results are used as input for an FEA-mechanics-driven electrophysiology model which is used for a ventricular tachycardia (VT)-inducibility study, as abnormal mechanics is believed to be a potential driving factor for the development of VT. The resulting VT propagation patterns agree visually for both mechanical inputs and differences in VT-exit points are within 1–7 mm for simulations where VT occurred. Furthermore, an agreement of 85% in the binary VT results is observed, where the 15% difference displays the electrophysiology-model sensitivity to deviations in mechanical input.

Hybrid IGA-FEA of fiber reinforced thermoplastic composites for forward design of AI-enabled 4D printing