Shape Optimization of the Conventional Simple Shear Specimen

Various optimization problems have been studied for the purpose of structural morphogenesis by many researchers. Structural optimization problems can be classified into three different sub-problems, namely size, shape and topology optimization problem. Size optimization problem is consisted of small sets of design variables. The shape and topology of a structure are defined by a set of design variables, and these design variables are adjusted to achieve given objectives, such as minimum volume. Such optimization problems can be solved iteratively, using gradient-based techniques. Introducing more design variables increases the complexity of the optimization problem. Therefore, it becomes difficult to solve the optimization problem by using MP techniques with large sets of design variables. Heuristics can be improved the difficulty. There are many studies using heuristics like genetic algorithm and simulated annealing. An effective method for structural morphogenesis inspired by self-organization phenomena is presented in this paper. Self-organization is a phenomenon that an entire structure gradually emerges by interaction between elements of the structure, and the elements are affected by the entire structure. Since the self-organization algorithm consists of simple calculation iteration, it can be applied to problems with large number of design variables. Proposed method is applied to problems of uniform member length, minimization of strain energy and cross-section design for frame structures, and the effectiveness is demonstrated through some examples. On the other hand, the number of projects incorporating computational design has increased in recent year, and designs with complicated forms composed of free surfaces are also increasing. In order to design such a shape, the designer needs to consider the rationality of the structure from the initial stage. So, it seems necessary to develop simple software for the structural morphogenesis. Therefore, we developed components of Grasshopper that works within Rhinoceros, so that it will be possible to reassemble algorithms in an intuitive way for designers who have never experienced programming. Grasshopper is one of Graphical Algorithm Editor (GAE), and can be visually constructed an algorithm by connecting components that is a function of modeling. Analysis by gradient-based MP techniques often involves jumping of solutions and analytical instability peculiar to non-linear problems, and it is difficult to apply to the computer aided systems as described above. Analysis algorithms based on self-organizing algorithms are considered to be suitable for the above system due to their high robustness.

Traditionally, computational design optimization of commercial aircraft is performed by considering a small number of representative operating conditions. These conditions are based on the design Mach number, altitude, payload, and range for which the aircraft will be flown. However, the design also influences which routes and mission parameters are optimal, and so there is coupling that is ignored when using the traditional approach. Here, the aircraft design, mission profiles, and the allocation of aircraft to routes in an airline network are simultaneously optimized. This is a mixed-integer nonlinear programming problem that is reformulated as a nonlinear programming problem because of the large number of design variables. The reformulated problem is solved using a gradient-based optimization approach with a parallel computational framework that facilitates the multidisciplinary analysis and the derivative computation. A surrogate model is used for the computational fluid dynamics analysis that is retrained in each optimization iteration given the new set of shape design variables. The resulting optimization problem contains over 4,000 design variables and close to 14,000 constraints. The optimization results show a 2% increase in airline profit compared with the traditional multipoint optimization approach. The wing area increases to the upper bound, enabling a higher cruise altitude that improves propulsive efficiency. This study finds that simultaneously optimizing the allocation, mission, and design to maximize airline profit results in a different optimized wing design from that resulting from the multipoint optimization approach.

The Segmentation Parameter Tuner (SPT) is a tool designed for automatic tuning of segmentation parameters. In SPT, the goodness of a set of parameter values is given by the level of agreement between the segmentation result and a given reference (representing the desired outcome) quantified by a metric selected by the user (empirical discrepancy methods). This metric is used as the fitness function of an optimization algorithm that searches the parameter space for the minimum value, which is expected to correspond to the segmentation outcome most similar to the reference. SPT 3.1 offers many interesting features such as: five segmentation algorithms (for Optical, Hyperspectral and SAR images), four optimization algorithms (stochastic and direct search optimization methods) and seven discrepancy metrics (pixel and object-based). This paper describes the optimization procedure underlying SPT 3.1, the features added to this version as well as an experiment that illustrates the operation of the tool.

Direct search optimization method: Lai, Y.S. and Achenbach, J.D.Amer. Soc. Civ. Eng., Proc. J. Struct. Div., Vol 99 (1973) No ST-1 pp 19–31

The Effects of Stress Triaxiality on the Neck Initiation and Fracture of High-density Polyethylene (HDPE)

With increasing awareness of sustainability, demands on optimized design of building shapes with a view to maximize its thermal performance have become stronger. Current research focuses more on building envelopes than shapes, and thermal comfort of building occupants has not been considered in maximizing thermal performance in building shape optimization. This paper attempts to develop an innovative ANN (artificial neural network)-exhaustive-listing method to optimize the building shapes and envelope physical properties in achieving maximum thermal performance as measured by both thermal load and comfort hour. After verified, the developed method is applied to four different building shapes in five different climate zones in China. It is found that the building shape needs to be treated separately to achieve sufficient accuracy of prediction of thermal performance and that the ANN is an accurate technique to develop models of discomfort hour with errors of less than 1.5%. It is also found that the optimal solutions favor the smallest window-to-external surface area with triplelayer low-E windows and insulation thickness of greater than 90 mm. The merit of the developed method is that it can rapidly reach the optimal solutions for most types of building shapes with more than two objective functions and large number of design variables.

The shear gage: For reliable shear modulus measurements of composite materials

In this paper, the study on aerodynamic shape optimization of contra rotating open rotor is presented. Computational fluid dynamics simulations combined with Neural networks (radial basis function) surrogate model is applied to solve the problem. The difficulty is associated with both time-consuming computational fluid dynamics simulations and the large number of design variables involved. The contra rotating open rotor optimization problem is to find the variables that produces the maximum propulsive efficiency for a limited range of thrust requirement. The DOE (deign of experiment) process is completed by uniform design and computational fluid dynamics simulations. The non-linear programming by quadratic lagrangian (NLPQL) is used to tackle the optimization problem. Infill sampling criteria is used in this process to reduce demand on the number of initial samples while keep the accuracy of surrogate model. After building the initial surrogate from DOE sampling, the update point is selected according to the infill sampling criteria. It shows that the infill sampling criteria is helpful in surrogate model building process and surrogate-based optimization method is valid for aerodynamic shape optimization of contra rotating open rotor.

Aerodynamic shape optimization of aircraft configurations often ignores stability considerations. To address this, a method for the computation of static, dynamic, and transient aircraft stability derivatives and their sensitivities for use in gradient-based optimization is introduced and evaluated. Computational fluid dynamics in the form of a three-dimensional structured-grid multiblock flow solver with both Euler and Reynolds-averaged Navier–Stokes equations is used. To compute the stability derivatives, a time-spectral formulation is used to compute an oscillating solution for the configuration of interest. From this oscillating solution, a series of linear regressions is performed to calculate the various stability derivatives. Because the solution is time dependent, it contains the information required to compute the transient, or “dot,” derivatives for the configuration. An adjoint method is used to compute the gradients of the stability derivatives of interest, enabling gradient-based stability-constrained aerodynamic shape optimization with respect to a large number of design variables. The computed stability derivatives are verified for an airfoil and validated for a generic unmanned combat aerial vehicle. The stability-constrained optimization of a wing demonstrates the viability and usefulness of the method for aircraft design optimization.

Effective adjoint approaches for computational fluid dynamics

Computational fluid dynamics (CFD) is increasingly used to analyze wind turbines, and the next logical step is to develop CFD-based optimization to enable further gains in performance and reduce model uncertainties. We present an aerodynamic shape optimization framework consisting of a Reynolds-averaged Navier Stokes solver coupled to a numerical optimization algorithm, a geometry modeler, and a mesh perturbation algorithm. To efficiently handle the large number of design variables, we use a gradient-based optimization technique together with an adjoint method for computing the gradients of the torque coefficient with respect to the design variables. To demonstrate the effectiveness of the proposed approach, we maximize the torque of the NREL VI wind turbine blade with respect to pitch, twist, and airfoil shape design variables while constraining the blade thickness. We present a series of optimization cases with increasing number of variables, both for a single wind speed and for multiple wind speeds. For the optimization at a single wind speed performed with respect to all the design variables (1 pitch, 11 twist, and 240 airfoil shape variables), the torque coefficient increased by 22.4% relative to the NREL VI design. For the multiple-speed optimization, the torque increased by an average of 22.1%. Depending on the CFD mesh size and number of design variables, the optimization time ranges from 2 to 24h when using 256 cores, which means that wind turbine designers can use this process routinely. Copyright © 2016 John Wiley & Sons, Ltd.

Development of an S-specimen geometry for shear testing of woven thermoplastic composites

This paper is devoted to the application of local micromechanisms of failure to the prediction of the macroscopic fracture toughness properties of metallic materials — a field pioneered by F. McClintock. The global approach of fracture assumes that failure can be described in terms of a single parameter, such as K IC or J IC . This approach may yet prove to be questionable in complex situations. This is the reason why local approaches of fracture have also to be developed. An attempt is made here to review the application of these local approaches, especially those which are micro-mechanistically based and to indicate a number of research fields which necessitate further studies. The paper is divided into two main parts. In the first part, the three basic fracture modes encountered in metallic materials, i.e. cleavage, intergranular fracture, and ductile rupture are reviewed. For cleavage fracture, a statistical model based on the Weibull weakest link concept is introduced and applied to a number of low-alloy ferritic steels. Some questions relating to intergranular fracture are also discussed. For ductile rupture, the emphasis is laid on the discontinuous or continuous character of the nucleation of cavities from second phase particles, on cavity growth and coalescence. The mechanics of plastic porous materials is briefly introduced to model this mode of failure and the statistical aspects of ductile rupture. It is shown that, in spite of the large research effort devoted to ductile rupture over the past few decades, it is still necessary to use an empirical fracture criterion based on the concept of critical void growth, that was originally introduced by McClintock. The second part of the paper is devoted to the application of these local fracture criteria to predict the fracture toughness of specimens or the fracture load of components. The concept of characteristic distances related to the microstructure of materials and that of the “process zone” are briefly discussed. Then theoretical expressions between the fracture toughness (K IC or J IC ) for 2D cracks, tested under small-scale yielding conditions, and local criteria are introduced. The local criterion for brittle cleavage fracture is based on Weibull statistics, which gives rise to a size effect, while the criterion for ductile rupture is based on critical void growth. Finite element method (FEM) numerical simulations of compact tension (CT) and center-cracked panel (CCP) specimens under large-scale yielding conditions were used in conjunction with these local fracture criteria to show that the ligament size requirements for “valid” J IC measurements are not only dependent on the specimen geometry (crack length, tension versus bending), but also on material work-hardening exponent and, more importantly, on the microscopic modes of failure. Further applications of the local approach of fracture are also presented, including fracture toughness testing of 3D cracks, the ductile-to-brittle transition behavior for ferritic steels, and fracture tests of specimens and components under non-isothermal conditions. Finally, further developments are briefly discussed.

The dispersion behavior of different carbon black grades was investigated in a common elastomer matrix under shear using a transparent plate‐and‐plate counter‐rotating shear cell coupled with an optical microscope. The objective was to investigate the effect of carbon black intrinsic characteristics (specific area and structure) on dispersion mechanisms. Shear conditions were selected to study independently erosion and rupture mechanisms. The independent study of rupture and erosion mechanisms brings new findings on the respective effect of the filler intrinsic characteristics on each mechanism: (a) Rupture is a sudden mechanism occurring above a critical shear stress, which depends on the pellet size. The rupture criterion appears not to depend on the carbon black specific area or the structure. (b) Erosion proceeds via the detachment of a fixed eroded volume per strain unit and is driven by the applied shear stress and strain. Erosion is a local mechanism. The erosion rate depends on the carbon black characteristics. Faster erosion was measured for a carbon black with a higher structure at equivalent specific area or with a lower specific area at equivalent structure. This in situ characterization of dispersion mechanisms highlights that the effect of the carbon black characteristics on the two main dispersion mechanisms (rupture and erosion) is completely different. © 2012 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2013

Problems of shape optimization for thin‐walled beam cross‐sections are investigated. In particular, shape optimization under torsional loading is treated. The shape of the beam cross‐section is described by non‐uniform rational B‐splines (NURBs). Biquadratic and p‐version finite elements are used to calculate the warping function. The definition of the element geometry is carried out by isoparametric and B‐spline mappings. Both methods are discussed and compared. For structural shape optimization the B‐spline mapping in connection with the p‐version finite elements is very efficient. The optimization is implemented using convex linearisation and a dual method of mathematical programming. Sensitivity analysis is performed analytically. Sample calculations are included.