Topological optimization of ballistic protective structures through genetic algorithms in a vulnerability-driven environment

Reducing the vulnerability of a platform,i.e.,the risk of being affected by hostile objects,is of paramount importance in the design process of vehicles,especially aircraft.A simple and effective way to decrease vulnerability is to introduce protective structures to intercept and possibly stop threats.However,this type of solution can lead to a significant increase in weight,affecting the performance of the aircraft.For this reason,it is crucial to study possible solutions that allow reducing the vulnerability of the aircraft while containing the increase in structural weight.One possible strategy is to optimize the topology of protective solutions to find the optimal balance between vulnerability and the weight of the added structures.Among the many optimization techniques available in the literature for this purpose,multiobjective genetic algorithms stand out as promising tools.In this context,this work proposes the use of a in-house software for vulnerability calculation to guide the process of topology optimization through multi-objective genetic algorithms,aiming to simultaneously minimize the weight of protective structures and vulnerability.In addition to the use of the in-house software,which itself represents a novelty in the field of topology optimization of structures,the method incorporates a custom mutation function within the genetic algorithm,specifically developed using a graph-based approach to ensure the continuity of the generated structures.The tool developed for this work is capable of generating protections with optimized layouts considering two different types of impacting objects,namely bullets and fragments from detonating objects.The software outputs a set of non-dominated solutions describing different topologies that the user can choose from.

Web Layout Design of Large Cavity Structures Based on Topology Optimization

Large cavity structures are widely employed in aerospace engineering, such as thin-walled cylinders, blades andwings. Enhancing performance of aerial vehicles while reducing manufacturing costs and fuel consumptionhas become a focal point for contemporary researchers. Therefore, this paper aims to investigate the topologyoptimization of large cavity structures as a means to enhance their performance, safety, and efficiency. By usingthe variable density method, lightweight design is achieved without compromising structural strength. Theoptimization model considers both concentrated and distributed loads, and utilizes techniques like sensitivityfiltering and projection to obtain a robust optimized configuration. The mechanical properties are checked bycomparing the stress distribution and displacement of the unoptimized and optimized structures under the sameload. The results confirm that the optimized structures exhibit improved mechanical properties, thus offering keyinsights for engineering lightweight, high-strength large cavity structures.

Multi-Material Topology Optimization for Spatial-Varying Porous Structures

This paper aims to propose a topology optimization method on generating porous structures comprising multiple materials.The mathematical optimization formulation is established under the constraints of individual volume fraction of constituent phase or total mass,as well as the local volume fraction of all phases.The original optimization problem with numerous constraints is converted into a box-constrained optimization problem by incorporating all constraints to the augmented Lagrangian function,avoiding the parameter dependence in the conventional aggregation process.Furthermore,the local volume percentage can be precisely satisfied.The effects including the globalmass bound,the influence radius and local volume percentage on final designs are exploited through numerical examples.The numerical results also reveal that porous structures keep a balance between the bulk design and periodic design in terms of the resulting compliance.All results,including those for irregular structures andmultiple volume fraction constraints,demonstrate that the proposedmethod can provide an efficient solution for multiple material infill structures.

Concurrent Two-Scale Topology Optimization of Thermoelastic Structures Using a M-VCUT Level Set Based Model of Microstructures

By analyzing the results of compliance minimization of thermoelastic structures,we observed that microstructures play an important role in this optimization problem.Then,we propose to use a multiple variable cutting(M-VCUT)level set-based model of microstructures to solve the concurrent two-scale topology optimization of thermoelastic structures.A microstructure is obtained by combining multiple virtual microstructures that are derived respectively from multiple microstructure prototypes,thus giving more diversity of microstructure and more flexibility in design optimization.The effective mechanical properties of microstructures are computed in an off-line phase by using the homogenization method,and then a mapping relationship between the design variables and the effective properties is established,which gives a data-driven model of microstructure.In the online phase,the data-driven model is used in the finite element analysis to improve the computational efficiency.The compliance minimization problem is considered,and the results of numerical examples prove that the proposed method is effective.

Full-Scale Isogeometric Topology Optimization of Cellular Structures Based on Kirchhoff-Love Shells

Cellular thin-shell structures are widely applied in ultralightweight designs due to their high bearing capacity and strength-to-weight ratio.In this paper,a full-scale isogeometric topology optimization(ITO)method based on Kirchhoff-Love shells for designing cellular tshin-shell structures with excellent damage tolerance ability is proposed.This method utilizes high-order continuous nonuniform rational B-splines(NURBS)as basis functions for Kirchhoff-Love shell elements.The geometric and analysis models of thin shells are unified by isogeometric analysis(IGA)to avoid geometric approximation error and improve computational accuracy.The topological configurations of thin-shell structures are described by constructing the effective density field on the controlmesh.Local volume constraints are imposed in the proximity of each control point to obtain bone-like cellular structures.To facilitate numerical implementation,the p-norm function is used to aggregate local volume constraints into an equivalent global constraint.Several numerical examples are provided to demonstrate the effectiveness of the proposed method.After simulation and comparative analysis,the results indicate that the cellular thin-shell structures optimized by the proposed method exhibit great load-carrying behavior and high damage robustness.

Topological Structure-Modulated Collagen Carbon as Two-in-One Energy Storage Configuration toward Ultrahigh Power and Energy Density

Efficient energy storage devices with suitable electrode materials,that integrate high power and high energy,are the crucial requisites of the renewable power source,which have unwrapped new possibilities in the sustainable development of energy and the environment.Herein,a facile collagen microstructure modulation strategy is proposed to construct a nitrogen/oxygen dual-doped hierarchically porous carbon fiber with ultrahigh specific surface area(2788 m^(2)g^(-1))and large pore volume(4.56 cm^(3)g^(-1))via local microfibrous breakage/disassembly of natural structured proteins.Combining operando spectroscopy and density functional theory unveil that the dual-heteroatom doping could effectively regulate the electronic structure of carbon atom framework with enhanced electric conductivity and electronegativity as well as decreased diffusion resistance in favor of rapid pseudocapacitive-dominated Li^(+)-storage(353 mAh g^(-1)at 10 A g^(-1)).Theoretical calculations reveal that the tailored micro-/mesoporous structures favor the rapid charge transfer and ion storage,synergistically realizing high capacity and superior rate performance for NPCF-H cathode(75.0 mAh g^(-1)at 30 A g^(-1)).The assembled device with NPCF-H as both anode and cathode achieves extremely high energy density(200 Wh kg^(-1))with maximum power density(42600 W kg^(-1))and ultralong lifespan(80%capacity retention over 10000 cycles).

Delineating homogeneous domains of fractured rocks using topological manifolds and deep learning

Determining homogeneous domains statistically is helpful for engineering geological modeling and rock mass stability evaluation.In this text,a technique that can integrate lithology,geotechnical and structural information is proposed to delineate homogeneous domains.This technique is then applied to a high and steep slope along a road.First,geological and geotechnical domains were described based on lithology,faults,and shear zones.Next,topological manifolds were used to eliminate the incompatibility between orientations and other parameters(i.e.trace length and roughness)so that the data concerning various properties of each discontinuity can be matched and characterized in the same Euclidean space.Thus,the influence of implicit combined effect in between parameter sequences on the homogeneous domains could be considered.Deep learning technique was employed to quantify abstract features of the characterization images of discontinuity properties,and to assess the similarity of rock mass structures.The results show that the technique can effectively distinguish structural variations and outperform conventional methods.It can handle multisource engineering geological information and multiple discontinuity parameters.This technique can also minimize the interference of human factors and delineate homogeneous domains based on orientations or multi-parameter with arbitrary distributions to satisfy different engineering requirements.

Optical manipulation of the topological phase in ZrTe_(5) revealed by time-and angle-resolved photoemission

High-resolution time-and angle-resolved photoemission measurements were conducted on the topological insulator ZrTe_(5).With strong femtosecond photoexcitation,a possible ultrafast phase transition from a weak to a strong topological insulating phase was experimentally realized by recovering the energy gap inversion in a time scale that was shorter than 0.15 ps.This photoinduced transient strong topological phase can last longer than 2 ps at the highest excitation fluence studied,and it cannot be attributed to the photoinduced heating of electrons or modification of the conduction band filling.Additionally,the measured unoccupied electronic states are consistent with the first-principles calculation based on experimental crystal lattice constants,which favor a strong topological insulating phase.These findings provide new insights into the longstanding controversy about the strong and weak topological properties in ZrTe_(5),and they suggest that many-body effects including electron–electron interactions must be taken into account to understand the equilibrium weak topological insulating phase in ZrTe_(5).

Elimination of cracks in stainless steel casings via 3D printed sand molds with an internal topology structure

The important supporting component in a gas turbine is the casing,which has the characteristics of large size,complex structure,and thin wall.In the context of existing 3DP sand casting processes,casting crack defects are prone to occur.This leads to an increase in the scrap rate of casings,causing significant resource wastage.Additionally,the presence of cracks poses a significant safety hazard after the casings are put into service.The generation of different types of crack defects in stainless steel casings is closely related to casting stress and the high-temperature concession of the sand mold.Therefore,the types and causes of cracks in stainless steel casing products,based on their structural characteristics,were systematically analyzed.Various sand molds with different internal topology designs were printed using the 3DP technology to investigate the impact of sand mold structures on high-temperature concession.The optimal sand mold structure was used to cast casings,and the crack suppression effect was verified by analyzing its eddy current testing results.The experimental results indicate that the skeleton structure has an excellent effect on suppressing cracks in the casing.This research holds important theoretical and engineering significance in improving the quality of casing castings and reducing production costs.

Identification of time-varying system and energy-based optimization of adaptive control in seismically excited structure

The combination of structural health monitoring and vibration control is of great importance to provide components of smart structures.While synthetic algorithms have been proposed,adaptive control that is compatible with changing conditions still needs to be used,and time-varying systems are required to be simultaneously estimated with the application of adaptive control.In this research,the identification of structural time-varying dynamic characteristics and optimized simple adaptive control are integrated.First,reduced variations of physical parameters are estimated online using the multiple forgetting factor recursive least squares(MFRLS)method.Then,the energy from the structural vibration is simultaneously specified to optimize the control force with the identified parameters to be operational.Optimization is also performed based on the probability density function of the energy under the seismic excitation at any time.Finally,the optimal control force is obtained by the simple adaptive control(SAC)algorithm and energy coefficient.A numerical example and benchmark structure are employed to investigate the efficiency of the proposed approach.The simulation results revealed the effectiveness of the integrated online identification and optimal adaptive control in systems.

Structural phase transition and transport properties in topological material candidate NaZn_(4)As_(3)

We report a comprehensive study on a layered-structure compound of NaZn_(4)As_(3),which has been predicted to be an ideal topological semimetal(TSM) candidate.It is found that NaZn_(4)As_(3) undergoes a structural transformation from high temperature rhombohedral to a low temperature monoclinic phase.The electric resistivity exhibits a metal-to-insulatorlike transition at around 100 K,and then develops a plateau at low temperature,which might be related to the protected topologically conducting surface states.Our first-principles calculation confirms further that NaZn_(4)As_(3) is a topological insulator(TI) for both different phases rather than a previously proposed TSM.The Hall resistivity reveals that the hole carriers dominate the transport properties for the whole temperature range investigated.Furthermore,an obvious kink possibly associated to the structure transition has been detected in thermopower around ~ 170 K.The large thermopower and moderate κ indicate that NaZn_(4)As_(3) and/or its derivatives can provide a good platform for optimizing and studying the thermoelectric performance.

Explicit Topology Optimization Design of Stiffened Plate Structures Based on the Moving Morphable Component(MMC)Method

This paper proposes an explicit method for topology optimization of stiffened plate structures.The present work is devoted to simultaneously optimizing stiffeners’shape,size and layout by seeking the optimal geometry parameters of a series of moving morphable components(MMC).The stiffeners with straight skeletons and the stiffeners with curved skeletons are considered to enhance the modeling and optimization capability of the current approach.All the stiffeners are represented under the Lagrangian-description framework in a fully explicit way,and the adaptive ground structure method,as well as dynamically updated plate/shell elements,is used to obtain optimized designs with more accurate analysis results.Compared with existing works,the proposed approach provides an explicit description of the structure.Thus,a stiffened plate structure with clear stiffener distribution and smooth geometric boundary can be obtained.Several numerical examples provided,including straight and curved stiffeners,hierarchical stiffeners,and a stiffened plate with a cutout,validate the effectiveness and applicability of the proposed approach.

Independent continuous mapping for topological optimization of frame structures

Based on the Independent Continuous Mapping method （ICM）, a topological optimization model with continuous topological variables is built by introducing three filter functions for element weight, element allowable stress and element stiffness, which transform the 0-1 type discrete topological variables into continuous topological variables between 0 and 1. Two methods for the filter functions are adopted to avoid the structural singularity and recover falsely deleted elements： the weak material element method and the tiny section element method. Three criteria （no structural singularity, no violated constraints and no change of structural weight） are introduced to judge iteration convergence. These criteria allow finding an appropriate threshold by adjusting a discount factor in the iteration procedure. To improve the efficiency, the original optimization model is transformed into a dual problem according to the dual theory and solved in its dual space. By using MSC/Nastran as the structural solver and MSC/Patran as the developing platform, a topological optimization software of frame structures is accomplished. Numerical examples show that the ICM method is very efficient for the topological optimization of frame structures.

Topological edge states and electronic structures of a 2D topological insulator: Single-bilayer Bi (111)

Providing the strong spin-orbital interaction, Bismuth is the key element in the family of three-dimensional topological insulators. At the same time, Bismuth itself also has very unusual behavior, existing from the thinnest unit to bulk crystals. Ultrathin Bi （111） bilayers have been theoretically proposed as a two-dimensional topological insulator. The related experimental realization achieved only recently, by growing Bi （111） ultrathin bilayers on topological insulator Bi2Te3 or Bi2Se3 substrates. In this review, we started from the growth mode of Bi （111） bilayers and reviewed our recent progress in the studies of the electronic structures and the one-dimensional topological edge states using scanning tunneling microscopy/spectroscopy （STM/STS）, angle-resolved photoemission spectroscopy （ARPES）, and first principles calculations.

M-P INVERSE TOPOLOGICAL VARIATION METHODOF FINITE ELEMENT STRUCTURES

Using Moore-Penrose inverse theory, a set of formulations for calculating the static responses of a changed finite element structure are given in this paper. Using these formulations by structural analysis may eliminate the need of assembling the stiffness matrix and solving a set of simultaneous equations.

TOPOLOGY AND VORTEX STRUCTURES OF A CURVING TURBINE CASCADE WITH TIP CLEARANCE (Ⅰ)- EXPERIMENTAL MODEL AND TOPOLOGICAL FLOW PATTERNS ON BOTH ENDWALLS AND BLADE SURFACES

By means of ink trace visualization of the flows in conventional straight, positively curved and negatively curved cascades with tip clearance, and measurement of the aerodynamic parameters in the transverse section, and by appling topology theory, the structures on both endwalls and blade surfaces were analyzed. Compared with conventional straight cascade, blade positive curving eliminates the separation line of the upper passage vortex and leads the secondary vortex to change from close separation to open separation, while blade negative curving effects merely the positions of singular points and the intensities and scales of vortex.

A METHOD FOR TOPOLOGICAL OPTIMIZATION OF STRUCTURES WITH DISCRETE VARIABLES UNDER DYNAMIC STRESS AND DISPLACEMENT CONSTRAINTS

A method for topological optimization of structures with discrete variables subjected to dynamic stress and displacement constraints is presented. By using the quasistatic method, the structure optimization problem under dynamic stress and displacement constraints is converted into one subjected to static stress and displacement constraints. The comprehensive algorithm for topological optimization of structures with discrete variables is used to find the optimum solution.

STATIC REANALYSIS FOR TOPOLOGICAL MODIFICATIONS OF STRUCTURES

A procedure for reanalysis of various structures subjected tovarious topologic modifi- cations is presented. The procedure isbased on the results of a single exact analysis and the factoriza-tion of the stiffness matrix of initial structures. It is suitablefor the addition of joints, where the number of the degrees offreedom is increased. The method deals with the stiffness matrix ofstruc- tures directly, so it can be used with a general finiteelement system. It is shown that the proposed ap- proximation methodis most effective in terms of accuracy, efficiency, and ease ofimplementation.

TOPOLOGY AND VORTEX STRUCTURES OF A CURVING TURBINE CASCADE WITH TIP CLEARANCE (Ⅱ)- TOPOLOGICAL FLOW PATTERN AND VORTEX STRUCTURE IN THE TRANSVERSE SECTION OF A BLADE CASCADE

By means of ink trace visualization of the flows in conventional straight, positively curved and negatively curved cascades with tip clearance, and measurement of the aerodynamic parameters in transverse section, and by appling topology theory, the topological structures and vortex structure in the transverse section of a blade cascade were analyzed. Compared with conventional straight cascade, blade positive curving eliminates the separation line of the upper passage vortex, and leads the secondary vortex to change from close separation to open separation, while blade negative curving effects merely the positions of singular points and the intensities and scales of vortex.

THE TOPOLOGICAL OPTIMIZATION FOR TRUSS STRUCTURES WITH STRESS CONSTRAINTS BASED ON THE EXIST-NULL COMBINED MODEL

A new exist-null combined model is proposed for the structural topology optimization. The model is applied to the topology optimization of the truss with stress constraints. Satisfactory computational result can be obtained with more rapid and more stable convergence as compared with the cross-sectional optimization. This work also shows that the presence of independent and continuous topological variable motivates the research of structural topology optimization.