Optimum structural design with static aeroelastic constraints

The static aeroelastic performance characteristics, divergence velocity, control effectiveness and lift effectiveness are considered in obtaining an optimum weight structure. A typical swept wing structure is used with upper and lower skins, spar and rib thicknesses, and spar cap and vertical post cross-sectional areas as the design parameters. Incompressible aerodynamic strip theory is used to derive the constraint formulations, and aerodynamic load matrices. A Sequential Unconstrained Minimization Technique (SUMT) algorithm is used to optimize the wing structure to meet the desired performance constraints

Epistemic Modeling Uncertainty of Rapid Neural Network Ensembles for Adaptive Learning

Emulator embedded neural networks, which are a type of physics informed neural network, leverage multi-fidelity data sources for efficient design exploration of aerospace engineering systems. Multiple realizations of the neural network models are trained with different random initializations. The ensemble of model realizations is used to assess epistemic modeling uncertainty caused due to lack of training samples. This uncertainty estimation is crucial information for successful goal-oriented adaptive learning in an aerospace system design exploration. However, the costs of training the ensemble models often become prohibitive and pose a computational challenge, especially when the models are not trained in parallel during adaptive learning. In this work, a new type of emulator embedded neural network is presented using the rapid neural network paradigm. Unlike the conventional neural network training that optimizes the weights and biases of all the network layers by using gradient-based backpropagation, rapid neural network training adjusts only the last layer connection weights by applying a linear regression technique. It is found that the proposed emulator embedded neural network trains near-instantaneously, typically without loss of prediction accuracy. The proposed method is demonstrated on multiple analytical examples, as well as an aerospace flight parameter study of a generic hypersonic vehicle

Fatigue Life Predictions of Additively Manufactured Components for Satelite Structures

The fatigue life properties of Additive Manufactured (AM) components are limited due to the defects naturally generated from the AM Process. For limited design life problems the finite fatigue life El-Haddad model linked defect size, applied stress, and design life. This paper developed a method to predict the smallest defect of interest for a given load case and the lowest failure generating stress for a given defect size. Experimental testing validated the method steps. The model was adjusted to demonstrate the space utility based on a 12U CubeSat chassis. Applying the design life and expected load, the finite fatigue life El-Haddad model predicted the minimum defect size for two configurations of the 12U CubeSat. The minimum defect size defined the Non-Destructive Evaluation (NDE) criteria for component certification. Combining the worst case potential defect size with the design life, the finite fatigue life El-Haddad model defined a minimum stress to generate failure. Linking the minimum stress value to the CubeSat Finite Element Model (FEM) predicted every location on the structure that could potentially fail due to the formation of AM defects. This second aspect defined the required inspection region to certify the structure for the given load case and design life

Concurrent Engineering Tools for Forging Die and Process Design

This paper discusses the development of engineering tools for die shape design in the forging process and the utilization of this information for determining optimal operating conditions. The tools discussed here are based on computer graphics, finite element modeling, design optimization and optimal control strategies, and can be run on personal computers, work stations and main frame computers, to meet a variety of customer needs and to provide user friendly tools for conducting “what if” studies. The methods developed here are applicable to several unit processes like extrusion, shape rolling, etc., besides forging. Details about the design variables, design constraints, objectives, analytical sensitivity calculations, condensed states, satisfaction of behavior constraints, and the optimal tracking algorithm are presented here with engineering case studies

Concurrent Engineering Tools for Forging Die and Process Design

This paper discusses the development of engineering tools for die shape design in the forging process and the utilization of this information for determining optimal operating conditions. The tools discussed here are based on computer graphics, finite element modeling, design optimization and optimal control strategies, and can be run on personal computers, work stations and main frame computers, to meet a variety of customer needs and to provide user friendly tools for conducting “what if” studies. The methods developed here are applicable to several unit processes like extrusion, shape rolling, etc., besides forging. Details about the design variables, design constraints, objectives, analytical sensitivity calculations, condensed states, satisfaction of behavior constraints, and the optimal tracking algorithm are presented here with engineering case studies

Structural Reliability Analysis and Optimization: Use of Approximations

This report is intended for the demonstration of function approximation concepts and their applicability in reliability analysis and design. Particularly, approximations in the calculation of the safety index, failure probability and structural optimization (modification of design variables) are developed. With this scope in mind, extensive details on probability theory are avoided. Definitions relevant to the stated objectives have been taken from standard text books. The idea of function approximations is to minimize the repetitive use of computationally intensive calculations by replacing them with simpler closed-form equations, which could be nonlinear. Typically, the approximations provide good accuracy around the points where they are constructed, and they need to be periodically updated to extend their utility. There are approximations in calculating the failure probability of a limit state function. The first one, which is most commonly discussed, is how the limit state is approximated at the design point. Most of the time this could be a first-order Taylor series expansion, also known as the First Order Reliability Method (FORM), or a second-order Taylor series expansion (paraboloid), also known as the Second Order Reliability Method (SORM). From the computational procedure point of view, this step comes after the design point identification; however, the order of approximation for the probability of failure calculation is discussed first, and it is denoted by either FORM or SORM. The other approximation of interest is how the design point, or the most probable failure point (MPP), is identified. For iteratively finding this point, again the limit state is approximated. The accuracy and efficiency of the approximations make the search process quite practical for analysis intensive approaches such as the finite element methods; therefore, the crux of this research is to develop excellent approximations for MPP identification and also different approximations including the higher-order reliability methods (HORM) for representing the failure surface. This report is divided into several parts to emphasize different segments of the structural reliability analysis and design. Broadly, it consists of mathematical foundations, methods and applications. Chapter I discusses the fundamental definitions of the probability theory, which are mostly available in standard text books. Probability density function descriptions relevant to this work are addressed. In Chapter 2, the concept and utility of function approximation are discussed for a general application in engineering analysis. Various forms of function representations and the latest developments in nonlinear adaptive approximations are presented with comparison studies. Research work accomplished in reliability analysis is presented in Chapter 3. First, the definition of safety index and most probable point of failure are introduced. Efficient ways of computing the safety index with a fewer number of iterations is emphasized. In chapter 4, the probability of failure prediction is presented using first-order, second-order and higher-order methods. System reliability methods are discussed in chapter 5. Chapter 6 presents optimization techniques for the modification and redistribution of structural sizes for improving the structural reliability. The report also contains several appendices on probability parameters

Reduced-Order Model Development for Airfoil Forced Response

Two new reduced-order models are developed to accurately and rapidly predict geometry deviation effects on airfoil forced response. Both models have significant application to improved mistuning analysis. The first developed model integrates a principal component analysis approach to reduce the number of defining geometric parameters, semianalytic eigensensitivity analysis, and first-order Taylor series approximation to allow rapid as-measured airfoil response analysis. A second developed model extends this approach and quantifies both random and bias errors between the reduced and full models. Adjusting for the bias significantly improves reduced-order model accuracy. The error model is developed from a regression analysis of the relationship between airfoil geometry parameters and reduced-order model error, leading to physics-based error quantification. Both models are demonstrated on an advanced fan airfoil's frequency, modal force, and forced response

Distortion Minimization During Gas Quenching Process

During gas quenching, independent process parameters include the preheat temperature of the component and the temperature of the circulated gas. One of the most important dependent process parameters is the heat transfer coefficient between the component and the circulated gas. The heat transfer coefficient has significant influence on the quenching results, such as distortion, residual stresses, and hardness distribution. Large distortions after quenching will increase the cost due to the post-quenching processes, such as the grinding and hot rectification. The objective in this research is to minimize the distortion caused by quenching. In this paper, the surface of a component is divided into several regions, and different values of the heat transfer coefficient are imposed on each region. Constraints on the residual stresses and surface hardness distribution are imposed to improve the service properties. The heat transfer coefficients are ideal design variables to optimize the gas quenching process. The commercial finite element software, DEFORM-HT, is used to predict the material response during the quenching process. The response surface method is used to obtain the analytical models of the objective function and constraints in terms of the design variables. Once the closed-form response surface models are obtained, a commercially available design optimization tool, design optimization tool (DOT), is used to search for the optimum design point. This paper summarizes the methodology used to optimize the gas quenching process together with an application of a steel disk example