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.

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.

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.

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

优化分析和计算液体动力学(CFD ) 同时被使用了，在哪个一个参量的模型在发现最佳的答案起一个重要作用。然而，与不规则的曲线为复杂形状创造一个参量的模型是困难的，例如一种海底的壳形式。在这研究，立方的 Bezier 曲线和曲线飞机交叉方法被用来产生考虑三个输入参数的一种参量的海底的壳形式的一个稳固的模型：鼻子半径，尾巴半径，和长度高度壳比率(L/H ) 。应用程序接口(API ) 脚本也被用来在 ANSYS 设计 modeler 写代码。结果证明海底的形状能与输入参数的某变化被产生。一个例子被给那显示出建议方法怎么能成功地被用于一个壳抵抗优化盒子。中间的海底的类型的参量的设计被选择被修改。首先，预先，原来的海底的模型用 CFD 被分析。然后，使用反应表面图，某候选人有一个最小的壳抵抗系数的最佳的图案被获得。进一步，在目标驱动的优化(GDO ) 的优化方法被实现与最小的壳抵抗系数发现海底的壳形式(C t ) 。最小的 C t 被获得。在在起始的潜水艇和最佳潜水艇之间的 C t 价值的计算差别在 0.26% 附近，与起始的潜水艇和是的最佳潜水艇的 C t 0.001 508 26 和 0.001 504 29 分别地。结果证明最佳潜水艇壳形式显示出更高的鼻子半径(r n ) 和更高的 L/H 起始的潜水艇比那些塑造，当时尾巴的半径(r t ) 比起始的形状的小。

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.

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.

Shape Control and Modification of Rational Bezier Curve and Surface

A Bezier interpolation approach is proposed which uses local generation of endpoint slopes and forces the curve and the surface to pass through an arbitrarily specified point to control and modify the shape of curve and surface, making the result satisfactory.

Residue curve maps of ethyl acetate synthesis reaction

The residue curve maps are considered as a powerful tool for the preliminary design of reactive distillation. The residue curve maps of ethyl acetate synthesis reaction were calculated based on the pseudo-homogeneous rate-based kinetic model and the NRTL activity coefficient model. The results show that the unstable node branch emerges from the ethyl acetate/water edge, moving toward the chemical equilibrium surface with the increase of Damk ler value (D), and the node reaches the ternary reactive azeotrope when D→∞ eventually. Conceptual design for the ethyl acetate synthesis of reactive distillation based on the residue curve maps is presented at last.

The Layout and Simulation of Logarithmic Spiral Double Curved Arch Dam Transverse Joints

Because of its good condition with mechanics, logarithmic spiral double curve arch bam has been widely used in the practical engineering. The introduction of a new method in how to divide transverse joint in arch dam will be given and the further research of its calculation has been done. The C＋＋ is used in electronic procedure and the 3D simulation has been finished with AutoCAD, which will provide the object model for computer simulation of the arch dam and the division of finite element mesh. Meanwhile, this method in dividing the transverse joint in arch dam also can be taken as the calculated basis for the design and calculation of arch dam, construction lofting and the calculation of the work amount.