Robust design and optimization of composite stiffened panels in post-buckling

<div class="section abstract"><div class="htmlview paragraph">Existing multi-axle steering system designs generally use the deterministic optimization method without considering the uncertainties during the design process; therefore an actual steering movement may deviate from the ideal movement calculated by some mathematical models. In order to make design results have less sensitive to the uncertainties in the design process, some uncertainties need be taken into account at the early design stage. This paper proposes a robust optimization design method for a double front axle steering system (DFASS) of heavy trucks based on Monte Carlo method. The DFASS consists of two trapezoidal steering mechanisms (TSM) and one rocker system, and the optimization objectives of DFASS include the minimum mean value and variance of the maximum turning angle error of the TSM and rocker system. In addition, the robust optimization model includes 13 design variables which are all geometry parameters of DFASS and represented by normal distribution. Through the orthogonal experiment, we obtain the important factors affecting optimization objectives and build the response surface models of optimization objective. Based on the response surfaces, robustness design of DFASS is performed. By simulating analysis, the improved robustness of DFASS based on robust design method is approved.</div></div>

The design process of new air- and rotorcraft is commonly separated into three different consecutive phases. In the conceptual design phase, the viability of different designs is investigated with respect to customer requirements and/or the market situation. It usually ends with the identification of a basic aircraft lay-out. In the subsequent preliminary design stage the various disciplines are introduced, thus redefining the design process as a multidisciplinary optimization (MDO) task. The objective of this design stage is to enhance the initial aircraft configuration by establishing an advanced design comprising a loft provided with primary structure. This updated aircraft configuration represents a global optimum solution for the specified requirements which will then be optimized on a local level in the concluding detailed design phase with particular regard to manufacturing aspects. The investigations in the preliminary design phase comprise the generation of numerous similar but still different analytical and finite element (FE) models. Even though computational power is constantly increasing the model generation process is still a time-consuming task. Moreover, it is also a potential source of errors which — in the worst case — may lead to time- and cost-intensive redesign activities during the detailed design. As the preliminary design stage, therefore, is of particular importance during the overall design process the model generation process benefits from parametric models and automated process chains. The presented paper overviews the tools used for the automated generation of FE models developed and used at the Institute of Structures and Design (BT) of the German Aerospace Center (DLR) for the subsequent use in numerical simulations. Furthermore, basic requirements for the effective use of parametrization and automation like a common data format and infrastructure will be introduced. Exemplary models and applications will be presented to illustrate the positive impact on efficiency in aircraft design. Concluding, future development steps and possible applications will be discussed.

The purpose of robust design optimization is to minimize variations in design performances and therefore to make the design insensitive to uncertainties. Current robust design methods fall into two types — probabilistic robust design and worst-case (interval) robust design. The former method is used when random variables are involved. In this method, robustness is measure by standard deviations of design performances. The later method is used when uncertainties are represented by intervals. The widths of design performances are then used to measure robustness. In many engineering application, both random variables and interval variables may exist simultaneously. In this paper, a general approach to robust design optimization is proposed. The generality comes from the ability to handle both random and interval variables. To alleviate the computational burden, we employ a previously developed general robustness assessment method — semi-second-order Taylor expansion method, to evaluate the maximum and minimum standard deviations of a design performance. An efficient integration strategy of the general robustness assessment and optimization is proposed. With the integration strategy, the number of function calls can be reduced while good accuracy is maintained. A robust shaft design problem is given for demonstration.

The importance of designing airfoils to be robust with respect to uncertainties in operating conditions is well recognized. However, often, the probability distribution of such uncertainties does not exist or is unknown, and a designer looking to perform a robust optimization is tasked with deciding how to represent these uncertainties within the optimization framework. This paper asks the following: “How important is the choice of how to represent input uncertainties mathematically in robust airfoil optimization?” It specifically compares probabilistically based aleatory uncertainties and interval-based epistemic uncertainties. This is first investigated by considering optimizations on several algebraic test problems, which illustrate the mechanisms by which the representation of uncertainty becomes significant in a robust optimization. This insight is then used to predict and subsequently demonstrate that, for two airfoil design problems, the advantage of doing a robust optimization over a deterministic optimization is similar, regardless of how the input uncertainties are represented mathematically. The benefit of this is potentially eliminating the time required to establish an accurate representation of the uncertainties from the preliminary stage of design, where time is a valuable resource.

This paper focuses on Deterministic and Reliability Based Design Optimization (DO and RBDO) of composite stiffened panels considering post-buckling regime and progressive failure analysis. The ultimate load that a post-buckled panel can hold is to be maximised by changing the stacking sequence of both skin and stringers composite layups. The RBDO problem looks for a design that collapses beyond the shortening of failure obtained in the DO phase with a target reliability while considering uncertainty in the elastic properties of the composite material. The RBDO algorithm proposed is decoupled and hence separates the Reliability Analysis (RA) from the deterministic optimization. The main code to drive both the DO and RBDO approaches is written in MATLAB and employs Genetic Algorithms (GA) to solve the DO loops because discrete design variables and highly nonlinear response functions are expected. The code is linked with Abaqus to perform parallel explicit nonlinear finite element analyses in order to obtain the structural responses at each generation. The RA is solved through an inverse Most Probable failure Point (MPP) search algorithm that benefits from a Polynomial Chaos Expansion with Latin Hypercube Sampling (PCE-LHS) metamodel when the structural responses are required. The results led to small reductions in the maximum load that the panels can bear but otherwise assure that they will collapse beyond the shortening of failure imposed with a high reliability.

Robust design optimization of fixed-fixed beam piezoelectric energy harvester considering manufacturing uncertainties

:A robust multi-objective wing design optimization procedure using CFD is presented in this work. Instead of directly applying CFD to wing design optimization, a Kriging aerodynamic model that approximates CFD result is proposed to save computational cost. By introducing 6σ robust approach as a sub-objective function, multi-objective wing design problems can be solved with aerodynamic robustness. Non-Uniform Rational B-Spline curves (NURBS) are introduced to depict the wing geometry in design optimization process. The most important parameters of the wing geometry can then be screened by design of experiment and treated as design variables due to the local variation property of NURBS. Under this formulation, a multi-objective genetic algorithm based on non-dominated sorting is employed to handle multiple flight conditions in wing design. The optimum wing geometry is selected according to trade-off among design objects on the non-dominated front. To validate the proposed approach, two robust design optimization cases are studied for ONERA-M6-Wing. It turns out that the drag coefficient is insensitive to Mach number between Ma0.8–Ma0.9 after robust optimization. The result also verifies the effectiveness of our method in boosting performance and robustness of multiple flight conditions: the lift curve slope (Ma0.3) of optimum wing and the 6σ objective function of transonic drag (Ma0.8–Ma0.9) increase by 11.9% and 25.4%, respectively. Observations in the optimization cases are concluded as follows: 1) For wing aerodynamic design problems, the multi-objective robust optimization can both improve the performance at different flight conditions and provide robustness. 2) The Kriging aerodynamic model derived from CFD result can satisfy the precision requirement of wing design. 3) Even though the optimization result is subject to the weights of the 6σ function in sub-object, the influence is not comparable to the trade-off among design objects. 4) The optimum solution obtained by proposed approach is superior to gradient based optimization method, while the computational cost is acceptable.

Robust multi-objective optimization for sustainable design of distributed energy supply systems

Once a design concept has been chosen and parameterised, the embodiment design stage consists of choosing materials and dimensions to ensure a 'good matching' with the expected performances. In this context of preliminary design stages, several approaches exist, which correspond to slightly different complexities and issues and must consequently be used at different moments. We consider in this paper three families of approaches: 1) exploring design (parametric) dimensioning under uncertainty (through constraint programming techniques, representations of feasible design points or Pareto frontiers); 2) robust design and multidisciplinary optimisation; 3) design for reliability. We advocate and state in this paper that these approaches must be used in that order of increasing complexity. Indeed, applying an approach allows one to quickly figure out inadequacies with performance specifications or initial allowable bounds of design parameters and then to backtrack or to refine the design issue before proceeding to the next stage or approach. We illustrate that phenomenon by successively applying the three approaches on a dimensioning issue of a two-member truss structure. We clearly show that the successive optimal designs obtained are notably different, but that the optimal point obtained in a given approach is used to explore its surroundings within the next approach.

The process and plant design stages, in particular the preliminary process design (PPD) stage, are performed repeatedly to cope with environmental changes at a plant during its lifecycle. The stages after the original design are called revamp design stages. As the PPD is repeated, operational flexibility is decreased. As a result, slight deviations from the intended critical process conditions during operation can lead to problems. However, in many cases, the causes of an operational problem are not identified, leading to safety issues. To overcome this, a framework including two Business Process Models (BPMs) is developed and modeled using IDEF0 with a hierarchical nature and ability to describe the PDCA engineering cycle. One BPM is developed to acquire the information on critical process conditions generated in the PPD stage. The other BPM is developed to systematize the acquired generated information into technology for the PPD by associating the information with design variables. The former BPM must first be developed as a reference model for the latter as a requirement. Furthermore, the framework is clearly divided into the above-mentioned two BPMs to manage the technology throughout the plant lifecycle while keeping consistent linkage to each other. Finally, it is confirmed that the developed framework has the necessary structure to systematize the technology of the PPD throughout the plant lifecycle by tracing a practical example problem of a distillation column in the framework.

With the development of modern technology, the degree of integration between design business and information technology is increasing. The digital design with three-dimensional digital design as the core will become the main axis throughout the whole process and the entire life cycle management. Through the gradual exploration and application in the power industry, certain results have been achieved in three-dimensional digital design, but the main problems remain in the local scope of individual units, and the overall lack of technical standards and development plans. Based on the full understanding and research of transformer substation design status and three-dimensional digital design, this paper draws the design depth of each professional three-dimensional digital design at each design stage by analyzing the application of three-dimensional digital design in the feasibility study, preliminary design and construction drawing stage. This paper provides a reference for comprehensive promotion of applications.

The multiple quality aspects of robust design have brought more and more attention in the advancement of robust design methods. Neither the Taguchi’s signal-to-noise ratio nor the weighted-sum method is adequate in addressing designer’s preference in making tradeoffs between the mean and variance attributes. An interactive multiobjective robust design procedure that follows upon the developments on relating utility function optimization to a multiobjective programming method has been proposed by the authors. This paper is an extension of our previous work on this topic. It presents a formal procedure for deriving a quadratic utility function at a candidate solution as an approximation of the efficient frontier to explore alternative robust design solutions. The proposed procedure is investigated at different locations of candidate solutions, with different ranges of interest, and for efficient frontiers with both convex and nonconvex behaviors. This quadratic utility function provides a decision maker with new information regarding how to choose a most preferred Pareto solution. As an integral part of the interactive robust design procedure, the proposed method assists designers in adjusting the preference structure and exploring alternative efficient robust design solutions. It eliminates the needs of solving the original bi-objective optimization problem repeatedly using new preference structures, which is often a computationally expensive task for problems in a complex domain. Though demonstrated for robust design problems, the principle is also applicable to any bi-objective optimization problems.

Rapid turn-around time for investigating new design concepts is a primary force driving design productivity initiatives across the industry. An integration framework focusing on the collaborative nature of rapid design automation at the preliminary and detailed design stage would ensure higher quality designs from the beginning of the product design cycle. As a result, producing reliable, robust optimum designs from the preliminary design phase would enable companies to reduce the overal design cycle time.

A procedure for evaluation of multiple attributes in the preliminary design stage is necessary to the development of a more formal theory and methodology of design. In this paper we prescribe, demonstrate, and compare two such techniques: fuzzy set analysis and multiattribute utility analysis. We analyze the problem of preliminary material selection for an automotive bumper beam to illustrate the application of both analytical procedures. Preliminary assessment of incommensurate performance measures of weight, cost, shape restriction, stiffness, and corrosion are made for steel and polymer composite alternatives. Fuzzy analysis readily accommodates design evaluation based on semantic assessment of relative attribute levels, although it can also employ information which is entirely numerical. In contrast, utility analysis requires considerable numerical quantification. For the example studied, the ordinal ranking of alternatives was the same for both methods. Recommendations include using fuzzy analysis in the earliest stages of preliminary design evaluation or in situations limited to semantic input from design decision makers. Utility analysis may be used in later stages of preliminary design, where numerical quantification of attribute levels is possible and when decision makers are able to assess the individual attribute utility functions in the standard way. The results of utility analysis can be used to quantify acceptable design tradeoffs between attribute levels and can be used in later stages of the iterative design process.

The paper aims to explore how organizations in the transition phase of co-location to multi-locations production environment applied Robust Design approach to accommodate the complexity of manufacturing and assembly operation in multi-location production environment. By using a single case study method on a home appliances Research and Development (R&D) Company, this paper examines the detail of design and operational transformations within the organization at pre and post implementation stage of Robust Design. The paper starts with enlightenment of issues faced by the company that drove the move to explore the application of Robust Design, follows by illustrations on how Robust Design concept is re-configured and executed across the product design process within the company. The paper subsequently reviews operational impact driven by the implementation of Robust Design, this is followed by discussion and recommendation for improvement. Result from the case study suggested that top management commitment is the key success factor for the implementation of Robust Design in Research and Development firm. In addition, the case study offers an alternative and effective approach to develop a robust system within design and development environment.