Optimized design of multi-material cellular structures by level-set method with Guyan reduction

2021 ◽  
pp. 1-15
Author(s):  
Hayoung Chung ◽  
Zongliang Du
Keyword(s):  
Level Set ◽  
Design Method ◽  
Numerical Models ◽  
Computational Cost ◽  
Cellular Structures ◽  
Optimized Design ◽  
Optimization Framework ◽  
Unit Cells ◽  
Guyan Reduction ◽  
And Storage

Abstract Owing to their tailorable physical properties, periodic cellular structures are considered promising materials for use in various engineering applications. To fully leverage the potential of such structures, it will be necessary to develop an optimized design method capable of producing intricate material layouts without sacrificing manufacturability. This paper presents a topology optimization framework for designing manufacturable, multi-material cellular structures that are to be subjected to temperature change. Under this framework, multi-material layouts within designable unit cells are represented using level-set functions and corresponding Boolean operations; by assuming a common length scale between these unit cells and the macrostructure, the manufacturability of optimized designs is guaranteed. Increases in computational cost and storage requirement are minimized by applying the Guyan reduction method, in which the secondary degree of freedom is condensed out to reduce the size of the discretized model. The design capabilities of the proposed method were investigated using several numerical models, with the results demonstrating that the method achieves overall improvements in performance as a result of its expanded design space.

scholarly journals Multi-Fidelity Optimization of a Composite Airliner Wing Subject to Structural and Aeroelastic Constraints

Aerospace ◽  
2021 ◽  
Vol 8 (12) ◽  
pp. 398
Author(s):  
Angelos Kafkas ◽  
Spyridon Kilimtzidis ◽  
Athanasios Kotzakolios ◽  
Vassilis Kostopoulos ◽  
George Lampeas
Keyword(s):  
Low Cost ◽  
Computational Cost ◽  
Design Stage ◽  
Computational Time ◽  
High Fidelity ◽  
Full Potential ◽  
Optimized Design ◽  
Structural Representation ◽  
Optimization Framework ◽  
Variable Fidelity

Efficient optimization is a prerequisite to realize the full potential of an aeronautical structure. The success of an optimization framework is predominately influenced by the ability to capture all relevant physics. Furthermore, high computational efficiency allows a greater number of runs during the design optimization process to support decision-making. The efficiency can be improved by the selection of highly optimized algorithms and by reducing the dimensionality of the optimization problem by formulating it using a finite number of significant parameters. A plethora of variable-fidelity tools, dictated by each design stage, are commonly used, ranging from costly high-fidelity to low-cost, low-fidelity methods. Unfortunately, despite rapid solution times, an optimization framework utilizing low-fidelity tools does not necessarily capture the physical problem accurately. At the same time, high-fidelity solution methods incur a very high computational cost. Aiming to bridge the gap and combine the best of both worlds, a multi-fidelity optimization framework was constructed in this research paper. In our approach, the low-fidelity modules and especially the equivalent-plate methodology structural representation, capable of drastically reducing the associated computational time, form the backbone of the optimization framework and a MIDACO optimizer is tasked with providing an initial optimized design. The higher fidelity modules are then employed to explore possible further gains in performance. The developed framework was applied to a benchmark airliner wing. As demonstrated, reasonable mass reduction was obtained for a current state of the art configuration.

Testing Some Alpha-Models of Turbulence on Wing Profiles

2013 ◽  
Vol 198 ◽  
pp. 243-247
Author(s):  
Miguel A. Moreno ◽  
Begoña González ◽  
Vicente Enríquez ◽  
Fabián A. Déniz ◽  
Ricardo Aguasca ◽  
...  
Keyword(s):  
Stokes Equations ◽  
Design Method ◽  
Computational Cost ◽  
Turbulence Models ◽  
Navier Stokes ◽  
Optimized Design ◽  
Navier Stokes Equations ◽  
Practical Applications ◽  
Mutation Operators ◽  
Maximum Angle

In this paper some numerical simulations of the Navier-Stokes Equations (NSE) to test the novel NS-α and NS-ω turbulence models [1, , which conserve energy, enstrophy, and helicity, are presented. These algorithms verify more conservation properties than other implementations of the NSE, however their rotational form [ makes the scaling study of the coupling between the velocity and pressure errors with respect to the Reynolds number, a very interesting research line. Nowadays we are designing a wing profile in the context of Unmanned Aerial Vehicle (UAV) on incompressible flow conditions [. First a genetic algorithm (GA) is used to obtain the optimized design geometry and then the NS-α and NS-ω turbulence models are run to study its performance for different attack angles. The GA objective function evaluates the general potential theory of each wing section considered, because that requires less computational cost than the alternative of solving the NSE, and a wing design method proposed in [ is applied. Thus the optimized design geometry was found by evaluating the potential flow of all candidate solutions generated from the selection, crossover and mutation operators in each GA iteration. It takes the order of hundreds of simulations per iteration to evaluate all candidate solutions. Summarizing, two practical applications for a UAV are presented: the optimized design of an airfoil for environmental purposes, named CEANI airfoil, and the application of relevant turbulence models as NS-α and NS-ω in order to evaluate with accuracy the lift, drag and maximum angle of attack.

Development and Applications of a Wellhead Protection Area Delineation Computer Program

1991 ◽  
Vol 24 (11) ◽  
pp. 51-62 ◽  
Author(s):  
N. Guiguer ◽  
T. Franz
Keyword(s):  
Case History ◽  
Numerical Models ◽  
Groundwater Resources ◽  
Theoretical Background ◽  
Human Interaction ◽  
Wellhead Protection ◽  
First Case ◽  
Protection Area ◽  
And Storage ◽  
The Town

In the last few years, groundwater management has concentrated on the protection of groundwater quality. An increasing number of countries has adopted policies to protect vital groundwater resources from deterioration by regulating human interaction with the subsurface, the use of potential contaminants, land use restrictions, and waste transport and storage. One of the more common regulatory approaches to the protection of groundwater focuses on public water supplies to reduce the potential of human exposure to hazardous contaminants. Under the framework of the Safe Drinking Water Act amended by U.S. Congress in 1986, The U.S.EPA (1987) issued guidelines for the delineation of wellhead protection areas, recommending the use of analytical and numerical models for the identification of such areas. In this study, the theoretical background for the development of one such numerical model is presented. Two real-world applications are discussed: in the first case history, the model is applied to a Superfund Site in Puerto Rico as a tool for assessment of the effectiveness of a proposed pump-and-treat scheme for aquifer remediation. Based on simulation results for the evolution of the existing contaminant plume it was verified that such a scheme would not work with the proposed purging wells. The second case history is the delineation of a wellhead protection area in the Town of Littleton, Massachusetts, and subsequent design of a monitoring well network.

A two-stage design optimization framework for multifield origami-inspired structures

2021 ◽  
pp. 1045389X2110116
Author(s):  
Wei Zhang ◽  
Saad Ahmed ◽  
Jonathan Hong ◽  
Zoubeida Ounaies ◽  
Mary Frecker
Keyword(s):  
Case Studies ◽  
Computing Time ◽  
Computational Cost ◽  
High Fidelity ◽  
Fe Model ◽  
Two Stage ◽  
Baseline Design ◽  
Optimization Framework ◽  
Highly Nonlinear ◽  
Stage 1

Different types of active materials have been used to actuate origami-inspired self-folding structures. To model the highly nonlinear deformation and material responses, as well as the coupled field equations and boundary conditions of such structures, high-fidelity models such as finite element (FE) models are needed but usually computationally expensive, which makes optimization intractable. In this paper, a computationally efficient two-stage optimization framework is developed as a systematic method for the multi-objective designs of such multifield self-folding structures where the deformations are concentrated in crease-like areas, active and passive materials are assumed to behave linearly, and low- and high-fidelity models of the structures can be developed. In Stage 1, low-fidelity models are used to determine the topology of the structure. At the end of Stage 1, a distance measure [Formula: see text] is applied as the metric to determine the best design, which then serves as the baseline design in Stage 2. In Stage 2, designs are further optimized from the baseline design with greatly reduced computing time compared to a full FEA-based topology optimization. The design framework is first described in a general formulation. To demonstrate its efficacy, this framework is implemented in two case studies, namely, a three-finger soft gripper actuated using a PVDF-based terpolymer, and a 3D multifield example actuated using both the terpolymer and a magneto-active elastomer, where the key steps are elaborated in detail, including the variable filter, metrics to select the best design, determination of design domains, and material conversion methods from low- to high-fidelity models. In this paper, analytical models and rigid body dynamic models are developed as the low-fidelity models for the terpolymer- and MAE-based actuations, respectively, and the FE model of the MAE-based actuation is generalized from previous work. Additional generalizable techniques to further reduce the computational cost are elaborated. As a result, designs with better overall performance than the baseline design were achieved at the end of Stage 2 with computing times of 15 days for the gripper and 9 days for the multifield example, which would rather be over 3 and 2 months for full FEA-based optimizations, respectively. Tradeoffs between the competing design objectives were achieved. In both case studies, the efficacy and computational efficiency of the two-stage optimization framework are successfully demonstrated.

Optimization Research on Dynamic Balance of Spatial Engine under Limiting Shaking Moment

2009 ◽  
Vol 626-627 ◽  
pp. 693-698
Author(s):  
Yong Yong Zhu ◽  
S.Y. Gao
Keyword(s):  
Mathematical Model ◽  
Objective Function ◽  
Kinetic Analysis ◽  
Optimization Design ◽  
Design Method ◽  
Dynamic Balance ◽  
Optimized Design ◽  
Design Variables ◽  
The Mathematical Model ◽  
Shaking Moment

Dynamic balance of the spatial engine is researched. By considering the special wobble-plate engine as the model of spatial RRSSC linkages, design variables on the engine structure are confirmed based on the configuration characters and kinetic analysis of wobble-plate engine. In order to control the vibration of the engine frame and to decrease noise caused by the spatial engine, objective function is choosed as the dimensionless combinations of the various shaking forces and moments, the restriction condition of which presents limiting the percent of shaking moment. Then the optimization design is investigated by the mathematical model for dynamic balance. By use of the optimization design method to a type of wobble-plate engine, the optimization process as an example is demonstrated, it shows that the optimized design method benefits to control vibration and noise on the engines and improve the performance practically and theoretically.

scholarly journals Buckling of regular, chiral and hierarchical honeycombs under a general macroscopic stress state

2014 ◽  
Vol 470 (2167) ◽  
pp. 20130856 ◽  
Author(s):  
Babak Haghpanah ◽  
Jim Papadopoulos ◽  
Davood Mousanezhad ◽  
Hamid Nayeb-Hashemi ◽  
Ashkan Vaziri
Keyword(s):  
Finite Element ◽  
Stress State ◽  
Closed Form ◽  
Plane Stress ◽  
Plane Stress State ◽  
Cellular Structures ◽  
Two Dimensional ◽  
Buckling Strength ◽  
Macroscopic Stress ◽  
Unit Cells

An approach to obtain analytical closed-form expressions for the macroscopic ‘buckling strength’ of various two-dimensional cellular structures is presented. The method is based on classical beam-column end-moment behaviour expressed in a matrix form. It is applied to sample honeycombs with square, triangular and hexagonal unit cells to determine their buckling strength under a general macroscopic in-plane stress state. The results were verified using finite-element Eigenvalue analysis.

Multiscale Topology Optimization With Gaussian Process Regression Models

2021 ◽  
Author(s):  
Joel C. Najmon ◽  
Homero Valladares ◽  
Andres Tovar
Keyword(s):  
Topology Optimization ◽  
Gaussian Process ◽  
Regression Models ◽  
Computational Cost ◽  
Gaussian Process Regression ◽  
Analytical Sensitivity ◽  
Inverse Homogenization ◽  
Discrete Location ◽  
Unit Cells ◽  
Periodic Microstructures

Abstract Multiscale topology optimization (MSTO) is a numerical design approach to optimally distribute material within coupled design domains at multiple length scales. Due to the substantial computational cost of performing topology optimization at multiple scales, MSTO methods often feature subroutines such as homogenization of parameterized unit cells and inverse homogenization of periodic microstructures. Parameterized unit cells are of great practical use, but limit the design to a pre-selected cell shape. On the other hand, inverse homogenization provide a physical representation of an optimal periodic microstructure at every discrete location, but do not necessarily embody a manufacturable structure. To address these limitations, this paper introduces a Gaussian process regression model-assisted MSTO method that features the optimal distribution of material at the macroscale and topology optimization of a manufacturable microscale structure. In the proposed approach, a macroscale optimization problem is solved using a gradient-based optimizer The design variables are defined as the homogenized stiffness tensors of the microscale topologies. As such, analytical sensitivity is not possible so the sensitivity coefficients are approximated using finite differences after each microscale topology is optimized. The computational cost of optimizing each microstructure is dramatically reduced by using Gaussian process regression models to approximate the homogenized stiffness tensor. The capability of the proposed MSTO method is demonstrated with two three-dimensional numerical examples. The correlation of the Gaussian process regression models are presented along with the final multiscale topologies for the two examples: a cantilever beam and a 3-point bending beam.

A Study of the Behaviour of a Single-Bladed Waste-Water Pump

2006 ◽  
Vol 220 (2) ◽  
pp. 79-87 ◽  
Author(s):  
J Keays ◽  
C Meskell
Keyword(s):  
Waste Water ◽  
Power Consumption ◽  
Turbulence Model ◽  
Numerical Models ◽  
Sewage Treatment ◽  
Computational Cost ◽  
Primary Source ◽  
Pressure Head ◽  
Primary Objective ◽  
Pump Efficiency

A single-vaned centrifugal pump, typical of the kind employed in waste-water applications (e.g. sewage treatment), has been investigated numerically. The primary objective was to identify a modelling approach that was accurate, but at an acceptable computational cost. A test program has been executed to provide data to validate the numerical models. The global performance of the pump was assessed in terms of the pressure head, the mass flowrate, the power consumption, and the pump efficiency. In addition, time-resolved surface-pressure measurements were made at the volute wall. Five combinations of three modelling approximations (two or 3D; k-ε or Reynolds stress model turbulence model; unsteady or quasi-steady) were investigated and compared with the experimental results. It was found that the choice of turbulence model did not have a significant effect on the predictions. In all cases, the head-discharge curve was well predicted. However, it was found that only the quasi-steady models could capture the trend of the power consumption curve, and hence that of the efficiency. Discrepancies in the magnitude of the power consumption can be accounted for by the lack of losses such as leakage in the numerical models. Qualitative analysis of the numerical results identifies the trailing edge of the impeller as the primary source of power loss, with the flow in the region of the cut water also contributing significantly to the poor overall efficiency of the design.

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