Optimal Design of Unitized Structures Using Response Surface Approaches

Future aerospace vehicles like hybrid wing/body, truss-braced wing, and “double bubble” would have pressurized noncircular fuselage structures and complex wing geometry. Traditional aircraft designs have led to the confidence and experience of designing such structures using the knowledge base built over the years and the resulting rules of thumb. However, there is a lack of experience of load calculations and design of complex, multifunctional, aircraft structural concepts for future aerospace vehicles. Designing such structures will require a physics-based optimization framework. Therefore, a new optimization framework, EBF3PanelOpt, is being developed. Commercial software MD-PATRAN (geometry modeling and mesh generation) and MD-NASTRAN (finite-element analysis) are integrated in EBF3PanelOpt framework using the Python programming environment to design stiffened panels with curvilinear stiffeners. Currently, EBF3PanelOpt optimizes the stiffened panel with curvilinear blade stiffeners, where the loads ar...

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 summarizes some numerical results of optimal design study of curvilinear stiffened panels where the reference axes of the stiffeners can be curvilinear. An integrated approach to use different capabilities in relevant fields, such as NURBS, DistMesh, and MSC.NASTRAN, etc., are adopted in the MATLAB environment. Numerical studies on optimal stiffened panel designs of buckling dominant problems are made to look into the effects of certain factors, such as, orientation, spacing, location, and curvature, etc., on the optimal designs. It is observed that curvilinear placement of stiffeners plays the role of orientation, spacing, location and intersection placement of infinitesimal straight stiffeners, and provides an enhanced design space. This enhanced design space may lead to better designs than using straight stiffeners though it is not always so. This work reveals the necessity to use global optimization techniques to perform topology/placement/shape optimization of curvilinear stiffened panels along with size optimization.

This contribution investigates the application of surrogate modeling, specifically Kriging and Response Surface Methodology (RSM), in optimizing injection molding simulation processes. Injection molding simulations are computationally intensive due to the multi-physical interactions involved, making surrogate models an attractive alternative to reduce computational effort. The authors employ Kriging and RSM models to simulate the injection molding of three different geometrical configurations, assessing their performance in predicting parameters for process quality/efficiency like deformation, shrinkage, and cycle time. The study makes use of MATLABs fmincon optimization algorithm with the models, emphasizing cycle time minimization while maintaining deformation and shrinkage within acceptable limits. In addition to the prediction accuracy, this contribution demonstrates that both surrogate models reduce the computational cost per evaluation by several orders of magnitude compared to full injection molding simulations and provide fast, iterative optimization. Findings indicate that Kriging outperforms RSM, especially in complex geometries, by providing more accurate predictions with lower error rates. The validation against digital twin simulations supports the effectiveness of Kriging, making it preferable for applications requiring high precision in process optimization.

Coupling Response Surface and Differential Evolution for Parameter Identification Problems

Optimum design of structures with stress and displacement constraints using the force method

This research work deals with aspects concerned with delamination detection in composite structures as revealed by an approach based on vibration measurements. Variations in vibration characteristics generated in composite laminates indicate the existence of delaminations because degradation due to delamination causes reduction in flexural stiffness and strength of the material and as a result vibration parameters like natural frequency responses are changed. Hence, it is possible to monitor the variation in natural frequencies to identify the presence of delamination, and assess its size and location for online structural health monitoring (SHM). The approach to this paper, therefore, typically depends on undertaking the analysis of structural models implemented by finite element analysis (FEA). The numerical solutions using FE models known as the simulator computes the natural frequencies for the delaminated and undelaminated specimens of composite laminates. However, these FE models are computationally expensive, and surrogate (approximation) models are introduced to curtail the computational expense. The simulator is employed to solve the inverse problem using algorithms based on computational intelligence concepts. An artificial neural network (ANN) model is developed to also solve the inverse problem for delamination detection directly and to provide surrogate models integrated with optimization algorithms (the gradient-based local search and non-dominated sorting genetic algorithm-II) to contain the computationally expensive simulations by FEA. This approach is termed as surrogate assisted optimization and it is seen that the engagement of surrogate models in lieu of the FE models in the optimization loop greatly enhances the accuracy of delamination detection results within an affordable computational cost and provides control over handling different variables. Meanwhile, to aid with the building of effective surrogate models using substantial number of training datasets, K-means clustering algorithm is harnessed and this effectively reduces the large training datasets usually required for ANN training. This paper demonstrated that ANN and optimization algorithms with surrogates show immense potentialities for use in delamination damage detection scenarios. Prediction errors of the algorithms were quantified and they were shown to be satisfactory when applied to previously experimental data. The algorithms in their inverse formulations are capable of predicting accurately delamination parameters. Hence, these algorithms should be employed for application in the domain of SHM where their small computational requirements could be exploited for online damage detection.

PurposeThe present work aims to reveal the effect of deposition paths on transient temperature, transient stress, residual stress and residual warping in the electron beam freeform fabrication (EBF) process.Design/methodology/approachSix typical deposition paths were involved in the finite element (FE) simulations of EBF process by implementing a specially written program.FindingsThe results showed that the deposition path had a remarkable influence on heat transfer and transient temperature distribution in the scanning process, resulting in different residual stress and residual warping after cooling to room temperature. The largest and smallest temperature gradients were obtained from the zigzag and alternate-line paths, respectively. Meanwhile, the temperature gradient decreased with the increase of deposited layers. The optimum deposition path, namely, the alternate-line pattern, was determined with respect to the residual stress and residual warping.Originality/valueAlthough some researcher revealed the importance of deposition path through FE analysis and experimental observation, their studies were usually confined within one type of deposition pattern. A complete investigation of typical deposition paths and comparison among them are still lacking in literature. To address the aforementioned gap, the present work started by extensive FE simulations of EBF process involving six representative deposition paths, namely, the alternate-line, zigzag, raster, inside-out spiral, outside-in spiral and Hilbert. For each deposition path, the transient temperature field, residual stress and residual deformation were obtained to optimize the deposition path.

Background: This study focuses on the application of photoelectro-Fenton (PEF) with Mn 2+ as catalyst combined with a photocatalytic process using supported TiO2 nanoparticles for the removal of phenol from aqueous solutions. TiO2 nanoparticles (Degussa P-25) immobilized on glass plates were used as photocatalyst, and carbon nanotube-polytetrafluoroethylene electrode was employed as cathode. Response surface methodology (RSM) was performed to evaluate the effects of the four key factors (initial amount of Mn 2+ , initial concentration of phenol, reaction time, and applied current) on the PEF/TiO2 process. Results: The application of RSM after analysis of variance showed a high coefficient of determination value (R 2 = 0.918) and thus indicated a high correlation between the observed and predicted values. The optimum operation conditions were located by graphical response surface and contour plots. The optimum initial amount of Mn 2+ , initial phenol concentration, applied current, and reaction time were found to be 0.3 mM, 15 mg/L, 300 mA, and 150 min, respectively. The observed experimental response for removal efficiency was 69.36 in optimum conditions of variables. The total organic carbon measurements showed 95% mineralization of 20 mg/L phenol at 15 h using the PEF/TiO2 process. The degradation product evolution was verified by gas chromatography analysis. Conclusions: An empirical relationship between the response and independent variables was attained and expressed by the second-order polynomial equation. Effect of experimental parameters on the removal efficiency of phenol was established by the response surface and contour plots of the model-predicted responses.

The purpose of this paper is to explore some interesting aspects of optimization for crashworthiness occupant safety applications and to propose optimization strategies for highly nonlinear problems. In the first part of the paper different optimization strategies are discussed and pros and cons are compared. In addition, a methodology to get a reliable surrogate model using neural networks is introduced. The surrogate model (Meta-Model or Response Surface Model) approximates the relationship between design parameters and a physical response and can be used to visualize and explore the design space. In the second part the application of the Successive Response Surface Scheme (SRSM) for the optimization of an adaptive restraint system is conducted. For this, several front crash load cases are considered. This is performed using LS-OPT (Stander et al. [11]) as optimization software and PAM-Crash as solver for the finite element occupant safety simulations. The procedure of generating an advanced meta-model to get an approximation of the global design space using neural networks is demonstrated for this example. Furthermore, the visualization of multi-dimensional meta-models in two- and three-dimensional design space is illustrated

Electrical energy storage devices are crucial for energy storage and distribution purposes. MXene (MX), a 2D material, and conductive organic polymers, such as polypyrrole (PPy), have been widely used as electrode material in electronic energy storage devices. This work calculated the elastic modulus and the electrical conductivity of a MX/PPy nanocomposite electrode using a finite element model. Response Surface Methodology (RSM) was used to optimize the electrical conductivity and elastic modulus response variables based on the finite element (FE) simulation findings. By assigning appropriate weights to these response factors in the optimization technique, the impacts of mass fraction and aspect ratio (AR) of MX inclusion on the electrical conductivity values and elastic modulus of the electrode were analyzed. When compared to the experimental findings, the results demonstrated that the suggested finite element model could provide a satisfactory estimate of the electrical conductivity and elastic modulus of the electrodes made of MX and PPy. However, these response variables might be optimized by using the response surface approach. Therefore, when RSM was employed, both electrical conductivity and Youngs modulus could be adjusted to close to their respective maximum optimal values, with a predicted electrical conductivity of 474.33 S/m and an elastic modulus of 3.24 GPa, at 50% mass fraction of the MX and the AR of 0.2. Based on these results, if a MX/PPy nanocomposite electrode could be built to achieve this modulus and electrical conductivity, such electrode would be a viable material for metal‐ion batteries.

This study comprehensively investigates the impact of various parameters on aluminum matrix composites (AMCs) fabricated using the powder metallurgy (PM) technique. An Al-Cu matrix composite (2xxx series) was employed in the current study, and Al2O3 was used as a reinforcement. The performance evaluation of the Al-4Cu/Al2O3 composite involved analyzing the influence of the Al2O3 weight percent (wt. %), the height-to-diameter ratio (H/D) of the compacted samples, and the compaction pressure. Different concentrations of the Al2O3 reinforcement, namely 0%, 2.5%, 5.0%, 7.5%, and 10% by weight, were utilized, while the compaction process was conducted for one hour under varying pressures of 500, 600, 700, 800, and 900 MPa. The compacted Al-4Cu/Al2O3 composites were in the form of cylindrical discs with a fixed diameter of 20 mm and varying H/D ratios of 0.75, 1.0, 1.25, 1.5, and 2.0. Moreover, the machine learning (ML), design of experiment (DOE), response surface methodology (RSM), genetic algorithm (GA), and hybrid DOE-GA methodologies were utilized to thoroughly investigate the physical properties, such as the relative density (RD), as well as the mechanical properties, including the hardness distribution, fracture strain, yield strength, and compression strength. Subsequently, different statistical analysis approaches, including analysis of variance (ANOVA), 3D response surface plots, and ML approaches, were employed to predict the output responses and optimize the input variables. The optimal combination of variables that demonstrated significant improvements in the RD, fracture strain, hardness distribution, yield strength, and compression strength of the Al-4Cu/Al2O3 composite was determined using the RSM, GA, and hybrid DOE-GA approaches. Furthermore, the ML and RSM models were validated, and their accuracy was evaluated and compared, revealing close agreement with the experimental results.

This study aims to determine the viscosity characteristics of TiO2-Polyolester (POE) nanolubricant and optimize it for heat transfer applications in compressor air conditioning systems. A magnetic stirrer was used to mix TiO2 and POE lubricant for 30 min. The nanolubricant was then ultrasonicated with a probe for 120 min to stabilize the TiO2-POE nanolubricant. There were seven different types of samples examined in this study, with concentrations of 0, 0.05, 0.15, 0.25, 0.35, 0.45, and 0.85 vol%. Rotational Rheolab QC was used to quantify viscosity from 30 to 90 °C. The viscosity of nanolubricant augmented as the proportion of nanolubricant increased. In contrast, when the test temperature rises, the viscosity drops. The greatest viscosity rise was 56.657% at 0.85 vol% at 80 °C, while the lowest viscosity increase was 0.029% at 0.05% at 30 °C. Based on the Response Surface Approach, optimization using the Multivariable Functions Optimization (MBFO) method with the Central Composite Design (CCD) type. The uncertainty analysis was also performed in this study. The most optimum dynamic viscosity is 34.8098 mPa s. At a temperature of 60 °C, this condition was achieved in samples with a concentration of 0.45 vol%.KeywordsCentral composite design (CCD)Response surface methodology (RSM)NewtonianViscosityTiO2-polyolester (POE) nanolubricant

This article presents a systematic approach for modeling and analysis of machining characteristics of Micro-Wire Electric Discharge Machining (Micro-WEDM) process using the Response Surface Methodology (RSM). The effect of various input parameters, such as voltage, capacitance, and feed rate on machining, performance of material removal rate (MRR), kerf width (KW), and surface roughness (SR) was investigated. Experimental work was carried out on Aluminum Matrix Composite (A413-9% B4C) with zinc coated copper wire using RSM with central composite design (CCD). The second order mathematical modeling and analysis of variance (ANOVA) were performed to optimize the machining parameters. It has been found out that main and interaction effects are significant on the machining performance. The optimized values of MMR, KW, and SR parameters were found to be 0.259943 mm3/min, 87 µm, and 0.97 µm, respectively.

Tailored transition metal-doped TiO2@Fe3O4 nanohybrids for efficient photocatalytic dye removal: Optimization via neural networks and response surface approaches