Elastic behavior of corrugated cardboard: experiments and modeling

Three-dimensional analysis of shear wave propagation observed by in vivo magnetic resonance elastography of the brain

Summary Based on molecular mechanics, a new structural mechanics model, a 2-D frame composed of equivalent anisotropic beams and flexible connections, is proposed for the simulation of the static and dynamic flexural behavior of monolayer graphene. The equivalent beam representing the C-C bond in the new molecular structural mechanics (MSM) model has two salient features compared with other MSM models proposed for the analysis of carbon nanotubes: one is that the flexible connections at the beam ends are used to account for the bond-angle variations between the C-C bonds; and the other is that there are two principal bending rigidities used, respectively, for the in-plane bending energy associated with bond angle variations and the inversion energy to characterize the different behaviors of the i?3-bond and i??-bond in the graphene lattice. The mechanical properties of the equivalent beam representing the C-C bond in the graphene lattice are evaluated from the molecular mechanics. The in-plane mechanical properties as well static and vibrational flexural behaviors of monolayer graphene are analyzed using the proposed new MSM model coupled with ANSYS. The simulation results show that the 2-D flexibly connected frame model of the new MSM model proposed in this paper gives improved predictions of the in-plane Young’s moduli, Poisson ratios and flexural rigidities of monolayer graphene than other MSM models. The present study also indicates that the modeling of bond angle variation is very important in the mechanical behavior simulations of graphene lattice. For example, the present new MSM model in which a monolayer graphene is modeled as flexibly connected planar lattice predicts very good results of Poisson ratios of graphene, but on the other hand the original MSM model in which a monolayer graphene is modeled as rigidly connected planar lattice yields much smaller Poisson ratios although this structural mechanics model is able to predict a quite good longitudinal deformation, The present study also shows that monolayer graphene sheet is kind of an anisotropic material since both the in-plane elastic properties and the flexural rigidities of monolayer graphene are chirality dependent.

Modelling of the dynamic behaviour of profiled composite floors

In the preliminary design phase of aircraft design, estimating the production cost accurately is a challenging task. At this stage, many design parameters that affect the overall cost are still undefined. This paper establishes cost-estimation models for civil, commercial aircraft using a parametric cost analysis (PCA) approach. Aircraft are characterised based on their size, ranging from a wide body to executive jets, into four categories. Key design parameters, such as maximum take-off weight, number of passengers, range, wing area, span, fuselage length, to name a few, are likely to be available in the preliminary design stage and significantly impact the aircraft design. These variables either directly or indirectly affect the overall production cost or performance. The PCA approach includes both correlation and multiple linear regression techniques. The empirical models thus developed were able to predict the aircraft cost with an error of less than ±4% for all aircraft categories considered. Two aircraft in each defined category were not part of the PCA models and were used to verify the models. The proposed models provide the ability to estimate the aircraft cost quickly in the early stages of the preliminary design phase and provide the possibility of performing parametric studies involving the key variables to determine the cost sensitivity to the main design parameters.

Preliminary design on high-end workstation cooling system using loop heat pipes

To reduce development cost and to avoid late design fixes in aircraft design, methods that are fast and economic in estimating the aerodynamic characteristics of complex flight vehicles at the preliminary design stage are desired. This work and thesis focus on the adaptive-fidelity CFD approach, with emphasis on the high end of the CFD tools available today. The core idea of the method is to use computationally cheap modeling in the part of the flight envelope where it is applicable. When the complexity in the flow field increases more details and realism is included in the mathematical model, at a computationally higher cost. A typical case where this would be required could be at the border of the flight envelope, where flow phenomena such as shocks, flow separation, and interacting vortex systems could occur. Since the number of cases needed to resolve the flight envelope could be in the order of ten thousands automation is required. The bottlenecks are the discretization of the fluid volume and evaluation of raw CFD data and post processing of the data. These issues are also discussed in this work. The method has been tested on two real flying aircraft, the X-31 delta-winged aircraft with vector thrust, and the Ranger 2000 Jet trainer, as well as on the SACCON preliminary wing-body UCAV design. The results provide improved understanding of the usefulness of this method as an analysis tool during the preliminary design phase all the way into the flight test diagnostic phase of a new aircraft.

Simple closed form results for the size-dependent elastic properties of macro-, micro- and nano-sized regular honeycombs with hexagonal, square and equilateral triangular cells are presented in this paper. The results indicate that at the micrometer scale, strain gradient has a dominant effect on the in-plane elastic properties; and that at the nanometer scale, surface elasticity dominates the effects on all the elastic constants of honeycombs.

Free vibration analysis of super-elliptical composite thin plates was investigated. Plate is formed by symmetrical quasi-isotropic laminates. Rayleigh-Ritz method was used for parametric analysis based on the governing differential equations of Classical Laminated Plate Theory (CLPT). Simply supported and clamped boundary conditions at the periphery of plates were considered. Parametric study was performed for the effect of different lamination type, aspect ratio, thickness and super-elliptical power on natural frequencies. Convergence study and validation of isotropic case were achieved. A number of design parameters like different dimensions, structure systems, panel sizes, panel thicknesses, lamination sequences, boundary conditions and loading conditions must be considered in the production of composite ships. The number of possible combinations practically may be so high that a parametric study should be carried out in order to determine the optimum design parameters rapidly during the preliminary design stage. The use of Rayleigh-Ritz method could make this parametric study possible. Thereby it might be decreasing the consumption of time, material and labor. Certain results for some different super-elliptical powers presented in tabulated form in Appendix for designers as well.

The finite formulation of the 4-node thin shell element based on Co-rotational (CR) and Timoshenko`s theory was presented for the analysis of laminated composite structures. Based on the Timoshenko`s theory the present thin shell element avoids shear locking behavior, and a bilinear in-plane displacement field is introduced for the coupling of in-plane and bending actions, and such element performs simple formulation and highly efficienct. A highly efficient CR formulation was also established to define the motion of the element with large displacement. The characteristics of the element are more pronounced when shells get thin, each node of the 4-node element has five degrees of freedom. An incremental iterative method based on the Newton Raphson method was used to solve the nonlinear equilibrium equations. A number of numerical examples were given to verify that the formula is computationally efficient and the results showed good agreement.

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.

Inherent safety index module (ISIM) to assess inherent safety level during preliminary design stage

In this article, a topology optimization method is proposed to obtain a new preliminary shape design of the twin-web turbine disc considering the burst speed constraint. The burst speed constraint is converted to the constraints on the averaged hoop stress and the maximum averaged radial stress. The linear density filter and Heaviside projection are employed to prevent the mesh dependency and chequerboard pattern and ensure distinct solid/void interfaces in the optimization result. The geometric extraction is easily implemented using the least square fitting with B-spline method. Through illustrative examples, the importance of considering the burst speed constraint in the design of turbine disc is verified, which contributes towards obtaining a safer design at the preliminary design stage. The effectiveness of the proposed method in obtaining a lighter preliminary twin-web turbine disc design is also demonstrated compared with the parametric optimization method.

How can multi-robot self-organizing systems be designed so that they show the desired behaviors and are able to perform tasks specified by designers? Multi-robot self-organizing systems, e.g., swarm robots, have great potential for adapting when performing complex tasks in a changing environment. However, such systems are difficult to design due to the stochasticity of the system performance and the non-linearity between the local actions/interaction and the desired global behavior. In order to address this, in this paper we propose a framework for designing self-organizing systems using Multi-Agent Reinforcement Learning (MARL) and the compromise Decision-Support Problem (cDSP) construct. The design framework consists of two stages — preliminary design and design improvement. In the preliminary design stage, MARL is used to help designers train the robots so that they show stable group behavior for performing the task. In the design improvement stage, the cDSP construct is used to enable designers to explore the design space and identify satisfactory solutions considering several performance indicators based on the trained system established in the previous stage. Between the two stages, surrogate models are used to map the relationship between local parameters and global performance indicators utilizing the data generated in preliminary design. The surrogate models represent the goal functions in the cDSP. A multi-robot box-pushing problem is used as an example to test the efficacy of the proposed framework. The framework is general and can be extended to design other multi-robot self-organizing systems. Our focus in this paper is in describing the framework.

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.

Correct evaluation of rudder performance is a key issue in assessing ship maneuverability. This paper presents a simplified approach based on a viscous flow solver to address propeller and rudder interactions. Viscous flow solvers have been applied to this type of problems, but the large computational requests limit (or even prevent) their application at a preliminary ship design stage. Based on this idea, a simplified approach to include the propeller effect in front of the rudder is considered to speed up the solution. Based on the concept of body forces, this approach enables sufficiently fast computation for a preliminary ship design stage, thereby maintaining its reliability. To define the limitations of the proposed procedure, an extensive analysis of the simplified method is performed and the results are compared with experimental data presented in the literature. Initially, the reported results show the capability of the body-force approach to represent the inflow field to the rudder without the full description of the propeller, also with regard to the complex bollard pull condition. Consequently, the rudder forces are satisfactorily predicted at least with regard to the lift force. However, the drag force evaluation is more problematic and causes higher discrepancies. Nevertheless, these discrepancies may be accepted due to their lower influence on the overall ship maneuverability performance.