Inverse design of mechanical metamaterial achieving a prescribedconstitutive curve

Besides exhibiting excellent capabilities such as energy absorption,phase-transforming metamaterials offer a vast design space for achieving nonlinear constitutive relations.This is facilitated by switching between different patterns under deformation.However,the related inverse design problem is quite challenging,due to the lack of appropriate mathematical formulation and the convergence issue in the post-buckling analysis of intermediate designs.In this work,periodic unit cells are explicitly described by the moving morphable voids method and effectively analyzed by eliminating the degrees of freedom in void regions.Furthermore,by exploring the Pareto frontiers between error and cost,an inverse design formulation is proposed for unit cells.This formulation aims to achieve a prescribed constitutive curve and is validated through numerical examples and experimental results.The design approach presented here can be extended to the inverse design of other types of mechanical metamaterials with prescribed nonlinear effective properties.

A Review of the Key Points in the Design of Small-Radius Curved Ramp Bridges

This article explores the fundamentals of small-radius curved ramp bridges.It covers the selection of box girder spans,support methods,and forms,along with design optimization techniques for this type of bridge structure.The purpose of this paper is to provide robust support for enhancing the design quality of these bridges and ensuring their efficacy in real-world applications.

3D image system improves the learning curve and contributes to medical education of rhinoplasty

Background: Rhinoplasty is a complex surgical procedure that requires critical analysis and precise design before surgery, making it a challenging operation for both the surgical team and medical educators. This study aimed to evaluate the impact of 3D design involvement on learning curves and to establish a more effective method for rhinoplasty education.Methods: Surgeons who participated in an educational program were divided into two groups. The experimental group was involved in the 3D design before the operation, and the control group was asked to review the rhinoplasty atlas. A self-assessment questionnaire was used to evaluate the learning curve of the eight rhinoplasty procedures for each surgeon, and the overall satisfaction rate data were also collected.Results: The self-assessment scores in both groups showed an increasing trend from the first to the eighth operation. The mean scores of the experimental group were significantly higher than those of the control group at the fifth operation(P=0.01). The satisfaction rate of the experimental group(91.7%) was higher than that of the control group(54.5%).Conclusion: The 3D imaging system can improve the learning curve and satisfaction rate of rhinoplasty education,proving that it is an easy and effective tool for medical education.

A new slope optimization design based on limit curve method

A new method is proposed for slope optimization design based on the limit curve method, where the slope is in the limit equilibrium state when the limit slope curve determined by the slip-line field theory and the slope intersect at the toe of the slope. Compared with the strength reduction (SR) method, finite element limit analysis method, and the SR method based on Davis algorithm, the new method is suitable for determining the slope stability and limit slope angle (LSA). The optimal slope shape is determined based on a series of slope heights and LSA values, which increases the LSA by 2.45°-11.14° and reduces an invalid overburden amount of rocks by 9.15%, compared with the space mechanics theory. The proposed method gives the objective quantification index of instability criterion, and results in a significant engineering economy.

Design Curves for Mooring Lines of Turret Mooring Systems

This paper presents a series of design curves to aid in the selection of turret mooring systems for tankers based Floating Production Storage and Offloading (FPSO) systems. These curves are appropriate to water depths ranging from 100 m to 600 m. The curves can be used as a preliminary design tool, allowing the designer to quickly evaluate alternative mooring system configurations, including the number of mooring lines, the characteristics of chain and wire rope to be deployed and the. initial tension. With a knowledge of the total environmental force and vessel motion characteristics, the designer can determine the appropriate system for closer evaluation.

Comparative Analysis of Equal and Unequal Grounding Grid Configurations by Compression Ratio and Least Square Curve Fitting Techniques

The primary aim of the power system grounding is to safeguard the person and satisfying the performance of the power systemtomaintain reliable operation.With equal conductor spacing grounding grid design,the distribution of the current in the grid is not uniform.Hence,unequal grid conductor span in which grid conductors are concentrated more at the periphery is safer to practice than equal spacing.This paper presents the comparative analysis of two novel techniques that create unequal spacing among the grid conductors:the least-square curve fitting technique and the compression ratio techniquewith equal grid configuration for both square and rectangular grids.Particle Swarm Optimization(PSO)is adopted for finding out one optimal feasible solution among many feasible solutions of equal grid configuration for both square and rectangular grids.Comparative analysis is also carried out between square and rectangular grids using the least square curve fitting technique as it results in only one unequal grid configuration.Simulation results are obtained by theMATLAB software developed.Percentage of improvement in ground potential rise,step voltage,touch voltage,and grid resistancewith variation in compression ratios are plotted.

Design Method of Curved-bar Refining Plates for Disc Refiner

Straight-and curved-bar refining plates are two important types of plates commonly used in disc refiners in the papermaking industry.Theoretically,the curved-bar refining plate has a relatively uniform bar interaction angle,which indicates uniform refining effects.The bar angle of the curved bar was proposed and two typical curved-bar plates,the three-stage radial curved-bar plate and isometric curved-bar plate,were designed in this paper.The arc equations of the curved-bar center line and curved-bar edges were established and finally,the specific edge load(SEL)of the curved-bar plate was derived.The determination of bar parameters was discussed,which provides a theoretical basis for the design of curved-bar plates.

FAIRING TECHNIQUE OF THE CURVES AND SURFACES IN INDUSTRIAL STYLING DESIGN

To many industrial products such as cell phone, family appliance, vehicle, a pretty shape of nice visual effect is indispensable. To fulfill this target, designers are endeavoring to make the curve and surface of the products smooth and continuous during the shape design. Through the analysis and generalization of the present smoothing methods, the energy optimization method which combines the merits of energy method and least squares method together is studied, the target function of energy optimization method is derived, the solution to the target function and steps of curve fairing is introduced, the skills and methods building A-class surface which are based on cloud data measured from 3D scanning are studied, the validity of energy optimization method is verified with the example of the shape design ofa mini-EV as well.

ON CURVED SURFACE APPROXIMATION AND HIDDEN SURFACE ELIMINATION IN 3-D COMPUTER AIDED GARMENT DESIGN

An approximation method for curved surface mannequin and hidden surface eliminationin 3-D computer aided garment design system is described. The mannequin is the basis of the3-D modeling for clothes. In terms of the requirements of computer aided garment design,the authors put forward a method for curved surface approximation in the meaning of leastsquares. Using. this method the computation of geometric modeling is simple andefficient. It is also convenient for curved surface modification and shading.

Force Analysis and Curve Design for Laying Pipe in Loop Laying Head of Wire Rod Mills

Laying head is a high-precision engineering device in hot-rolled high speed wire rod production line. Previously research works are focused on the laying pipe wear-resisting. Laying pipe curve design method based on wire rod kinematics and dynamics analyses are not reported before. In order to design and manufacture the laying pipe, the motion and force process of the wire rod in the laying pipe should be studied. In this paper, a novel approach is proposed to investigate the force modeling for hot-rolled wire rod in laying pipe. An idea of limited element method is used to analysis and calculates the forces between laying pipe inner surface and wire rod. The design requirements of laying pipe curve for manufacturing are discussed. The kinematics and dynamics modeling for numerical calculation are built. A laying pipe curve equation is proposed by discussing design boundary conditions. Numerical results with di erent laying pipe curves design parameters are plotted and compared. The proposed approach performs good result which can be applied for laying pipe curve design and analysis for engineering application.

Development of Cubic Bezier Curve and Curve-Plane Intersection Method for Parametric Submarine Hull Form Design to Optimize Hull Resistance Using CFD

Optimization analysis and computational fluid dynamics （CFDs） have been applied simultaneously, in which a parametric model plays an important role in finding the optimal solution. However, it is difficult to create a parametric model for a complex shape with irregular curves, such as a submarine hull form. In this study, the cubic Bezier curve and curve-plane intersection method are used to generate a solid model of a parametric submarine hull form taking three input parameters into account： nose radius, tail radius, and length-height hull ratio （L/H）. Application program interface （API） scripting is also used to write code in the ANSYS DesignModeler. The results show that the submarine shape can be generated with some variation of the input parameters. An example is given that shows how the proposed method can be applied successfully to a hull resistance optimization case. The parametric design of the middle submarine type was chosen to be modified. First, the original submarine model was analyzed, in advance, using CFD. Then, using the response surface graph, some candidate optimal designs with a minimum hull resistance coefficient were obtained. Further, the optimization method in goal-driven optimization （GDO） was implemented to find the submarine hull form with the minimum hull resistance coefficient （Ct）. The minimum C, was obtained. The calculated difference in （7, values between the initial submarine and the optimum submarine is around 0.26%, with the C, of the initial submarine and the optimum submarine being 0.001 508 26 and 0.001 504 29, respectively. The results show that the optimum submarine hull form shows a higher nose radius （rn） and higher L/H than those of the initial submarine shape, while the radius of the tail （r1） is smaller than that of the initial shape.

Ideal Drift Response Curve for Robust Optimal Damper Design for Elastic-Plastic MDOF Structures under Multi-Level Earthquakes Dedicated to Professor Karl S.Pister for his 95th birthday

A new method of robust damper design is presented for elastic-plastic multi-degree-of-freedom(MDOF)building structures under multi-level ground motions(GMs).This method realizes a design that is effective for various levels of GMs.The robustness of a design is measured by an incremental dynamic analysis(IDA)curve and an ideal drift response curve(IDRC).The IDRC is a plot of the optimized maximum deformation under a constraint on the total damper quantity vs.the design level of the GMs.The total damper quantity corresponds to the total cost of the added dampers.First,a problem of generation of IDRCs is stated.Then,its solution algorithm,which consists of the sensitivity-based algorithm(SBA)and a local search method,is proposed.In the application of the SBA,the passive added dampers are removed sequentially under the specified-level GMs.On the other hand,the proposed local search method can search the optimal solutions for a constant total damper quantity under GMs’increased levels.In this way,combining these two algorithms enables the comprehensive search of the optimal solutions for various conditions of the status of the GMs and the total damper quantity.The influence of selecting the type of added dampers(oil,hysteretic,and so on)and the selection of the input GMs on the IDRCs are investigated.Finally,a robust optimal design problem is formulated,and a simple local search-based algorithm is proposed.A simple index using the IDRC and the IDA curve of the model is used as the objective function.It is demonstrated that the proposed algorithm works well in spite of its simplicity.

Discussion on Reverse Design of Components with Complex Curved Surface and Computer Numerical Control Machining

With the continuous development and advancement of science and technology,the work of tool path planning has received extensive attention.Among them,curved surface generation and data processing are the focus of management and design,which necessitate the full application of reverse design of complex curved surface components to complete numerical control processing,effective optimization and upgrading,integration the tasks of point cloud data collection,and point cloud data processing to ensure that the corresponding computer numerical control machining model can exert its actual value.This paper briefly analyzes the basic principles of curved surface reconstruction as well as discusses the reverse design of complex curved components and the experimental processes and results that involved computer numerical control machining,which serves the purpose as reference only.

6-26 Conceptual Design of a 3.6 T Curved Tilted Solenoid Superconducting Magnet

The type of tilted solenoid is a novel approach to be used in superconducting dipole magnet design. The dipolefield is obtained by using concentric pairs of helically-wound coils that are tilted at opposite angles; this effectivelycancels the solenoid component of the field and adds the dipole content of each layer. Fig. 1 shows a dipole magnetcomposed of a pair of coils.According to the principle of modulating the tilted solenoid, we proposed a conceptual design of curved superconductingmagnet. The magnet with 150 mm bore diameter is curved 60 ? at a radius of 833 mm. The magnetconsists of 10 layers and the thickness of each layer is 5 mm. It could be cooled by a GM refrigerator. The detailedparameters of magnet are showed in Table 1.

An optimization method for rational Bézier curve design

Adjusting weights as a shape control tool in rational B6zier curve design is not easy because the weights have a global in- fluence. The curve could not approximate control polygon satisfactorily by an interactive manner. In order to produce a curve close enough to control polygon at every control vertex, an optimization model is established to minimize the distance between rational B6zier curve and its control points. This optimization problem is converted to a quadratic programming problem by separating and recombining the objective function. The new combined multi-objective optimization problem is reasonable and easy to solve. With an optimal parameter, the computing process is discussed. Comparative examples show that the designed curve is closer to control polygon and preserves the shape of the control polygon well.

Many-Knot Spline Interpolating Curves and Their Applications in Font Design

Many-knot spline interpolating is a class of curves and surfaces fitting method presentedin 1974. Many-knot spline interpolating curves are suitable to computer aided geometric design anddata points interpolation. In this paped, the properties of many-knot spline interpolating curves arediscussed and their applications in font design are considered. The differences between many-knotspline interpolating curves and the curves genoaed by exceeding-lacking adjuStment algorithm aregiven.

Weight-based shape modification of NURBS curves by constrained optimization

A new method for shape modification of non-uniform rational B-splines (NURBS) curves was presented, which was based on constrained optimization by means of altering the corresponding weights of their control points. Using this method, the original NURBS curve was modified to satisfy the specified geometric constraints, including single point and multi-point constraints. With the introduction of free parameters, the shapes of modified NURBS curves could be further controlled by users without destroying geometric constraints and seem more naturally. Since explicit formulae were derived to compute new weights of the modified curve, the method was simple and easy to program. Practical examples showed that the method was applicable for computer aided design (CAD) system.

Approximate merging of B-spline curves and surfaces

Applying the distance function between two B-spline curves with respect to the L2 norm as the approximate error, we investigate the problem of approximate merging of two adjacent B-spline curves into one B-spline curve. Then this method can be easily extended to the approximate merging problem of multiple B-spline curves and of two adjacent surfaces. After minimizing the approximate error between curves or surfaces, the approximate merging problem can be transformed into equations solving. We express both the new control points and the precise error of approximation explicitly in matrix form. Based on homogeneous coordinates and quadratic programming, we also introduce a new framework for approximate merging of two adjacent NURBS curves. Finally, several numerical examples demonstrate the effectiveness and validity of the algorithm.

Regionalization of Rainfall Intensity-Duration-Frequency (IDF) Curves in Botswana

A regional analysis of design storms, defined as the expected rainfall intensity for given storm duration and return period, is conducted to determine storm Rainfall Intensity-Duration-Frequency (IDF) relationships. The ultimate purpose was to determine IDF curves for homogeneous regions identified in Botswana. Three homogeneous regions were identified based on topographic and rainfall characteristics which were constructed with the K-Means Clustering algorithm. Using the mean annual rainfall and the 24 hr annual maximum rainfall as an indicator of rainfall intensity for each homogeneous region, IDF curves and maps of rainfall intensities of 1 to 24 hr and above durations were produced. The Gamma and Lognormal probability distribution functions were able to provide estimates of rainfall depths for low and medium return periods (up to 100 years) in any location in each homogeneous region of Botswana.

Calculation of Space NURBS Curve Interpolation Error

Aiming at the problem of low accuracy of interpolation error calculation of existing NURBS curves, an approximate method for the distance between a point and a NURBS interpolation curve is proposed while satisfying the accuracy of the solution. Firstly, the minimum parameter interval of the node vector corresponding to the data point under test in the original data point sequence is determined, and the parameter interval is subdivided according to the corresponding step size, and the corresponding parameter value is obtained. Secondly, the distance from the measured point to the NURBS curve is calculated, and the nearest distance is found out. The node interval is subdivided again on one side of the nearest distance. Finally, the distance between the data point to be measured and each subdivision point is calculated again, and the minimum distance is taken as the interpolation error between the point and the NURBS curve. The simulation results of actual tool position data show that this method can more accurately obtain the error of spatial NURBS interpolation curve.