参数Bezier三角曲面的GC^1设计

本文从三次Ｂｅｚｉｅｒ三角曲面片边界曲线构造入手，综合分析了计算几何中有关Ｂｅｚｉｅｒ三角曲面ＧＣ＾１拼接设计的理论和方法。针对３Ｄ离散数据曲面插值问题，全面讨论了Ｂｅｚｉｅｒ三角曲面片内部Ｂｅｚｉｅｒ顶点计算。提出了一种基于三次Ｂｅｚｉｅｒ三角曲面片内部Ｂｅｚｉｅｒ顶点ｄ１１１选取优化的整体ＧＣ＾１Ｂｅｚｉｅｒ三角曲面设计方法。     

参数Bezier三角曲面G1光滑拼接的相容性

本文对参数Ｂｅｚｉｅｒ三角曲面拼接的相容性问题进行了研究。给出拼接的相容性条件。实现了任意多片参数三角曲面片的一阶几何连续拼接，可对任意复杂形状进行造型。     

复合三角Bezier曲面/平面的过渡和裁剪

由初始交点出发,利用拓扑关系跟踪计算复合三角Bezier曲面与平面的交线,对一系列交点进行点对应修正,曲面片间边界点计算、交线两端交点的跟踪、截面线构造、截面线离散,构造出与基曲面达到G′连续、结构相似的过渡曲面,交点作为型值点值入复合曲面的型值点集中、对三角网格局域三角化,以交线为界分离,重新构造拓扑关系生成两张新的曲面,实现裁剪的目的,测试显示,上述方法简单可靠。     

应用区域变换实现三角 Bezier 曲面分割

本文根据实际应用需要采用参数域变换方法对三角Ｂｅｚｉｅｒ曲面片进行分割，可简单地确定复杂分割模型下各子曲面片的控制顶点，避免了采用Ｃ－Ｔ分割带来的冗余计算和某些情况下的复杂处理过程，并且使分割算法统一。     

组合三角Bezier曲面任意截面线GC^1构造及其优化二次表示

截面曲线构造是曲面测量分析，数控加工质量分析等应用中的基本问题之一。针对组合三角Ｂｅｚｉｅｒ曲面／平面求交交点的分布特点，本文系统研究了组合ＧＣ＾１截面曲线构造及其数据精减优化二次表示，并将其转化成ＩＧＥＳ标准格式输出，为实现两类造型系统（拓扑三角曲面和拓扑矩形曲面）之间的数据交换奠定了良好的基础。     

三角域上三次DP曲面的扩展

给出了三角域上带双参数的四次DP混合函数,它是三角域上三次DP基函数的扩展。分析了该组混合函数的性质并定义了三角域上带双形状参数的四次DP参数曲面。该组混合函数及其参数曲面分别具有与三次DP基函数及三次DP参数曲面类似的性质。当两参数为0时,可分别退化到三次DP基函数及三次DP参数曲面。研究表明,通过改变两个形状参数的取值,既可整体又可局部调整曲面的形状。     

孤子局域共振激发的一种物理模型

作为非线性领域的重要内容,孤子自从被发现以来就得到了广泛的关注。虽然目前关于孤子的传播及其相互作用性质等方面的研究已经相当成熟,但是对于孤子的产生问题仍然没有系统的认识。孤子产生问题的深入研究,不仅对于理解自然界及物理系统中的非线性现象十分重要,对孤子现象的工程应用也极为重要。基于这些原因,一些孤子激发方法的研究不断被提出。在非线性阵列带隙中的能量超透射现象激发孤子理论的基础上,局域共振孤子激发的方法被提出。该方法通过在半无限长β-FPU链中加入缺陷来引入局域共振机制,不仅有效降低了孤子激发的临界驱动振幅,还实现了孤子激发的可控操作。然而,虽然理论分析与数值模拟都证明了这一方法的可行性,但关于该方法的相关实验验证还是空白。为了进一步将该方法推向实际实验,提出了一种简易可行的实验方案,并做了深入的理论分析与大量的数值模拟。该方案给出一种物理模型,该模型以线性弹簧为基本元件,利用结构的几何非线性来构建β-FPU链,并以耦合摆阵列来实现。通过大量数值模拟证明了该方法的可行,同时研究了孤子释放周期与驱动频率、振幅的关系,结果与前述理论一致。此外,还通过数值模拟研究了孤子的激发周期与缺陷处阻尼大小的关系,以及单元质量不均匀性对孤子激发与传播的影响,为进一步实验提供依据。     

多曲面间的光滑自由过渡和数控加工

本文在分析自由过渡曲面设计方法的基础上，对多曲面间光滑自由过渡曲面的设计方法进行了研究，提出了多边域自由过渡曲面的分割拼接设计方法，由于采用了Bezier曲面模型，图形数据符合IGES标准，可和商品化CAD／CAM系统进行数据交换，因而可解决多曲面间的光滑自由过渡曲面的设计和数据加工问题。     

三角域上邻接有理Bezier曲面片的G^1和G^2光滑

由曲面的Ｇ＾１和Ｇ＾２连接的条件，得到三角域上有理Ｂｅｚｉｅｒ曲面片Ｇ＾１与Ｇ＾２光滑连接控制网点表示的条件，作为特例，给出了非有理Ｂｅｚｉｅｒ曲面片Ｇ＾１与Ｇ＾２光滑连接的条件。     

曲面形貌轮廓仪传感器的机构设计

介绍一种适于曲面形貌测量的新型触针式轮廓仪的传感机构。它采用顶尖支承作为测杆的支承形式，并以测杆自重为传感器的测力源，无导头。本文分析了其动态特性和动态测力问题。     

Efficient three-node triangular element based on a new mixed global-local higher-order theory for multilayered composite plates

Abstract

An accurate and computationally attractive global-local higher-order theory (GLHT) is developed for the linearly elastic analysis of cross-ply multilayered composite plates. The theory is derived using the kinematic assumptions of GLHT in conjunction with the Reissner mixed variational principle. For a low-order linear element, it is difficult to accurately compute the transverse shear stresses even applying the three-dimensional equilibrium equation post-processing technique. The reason for this difficulty is that the higher-order derivatives of displacement variables are included in the transverse shear stress fields after using the post-processing technique. Thus, by employing the Reissner mixed variational principle, the higher-order derivatives of displacement variables have been removed from the transverse shear stress components before the finite element procedure is implemented. Based on the mixed GLHT, a computationally efficient C⁰-type three-node triangular plate element with linear interpolation function is proposed for the analysis of multilayered composite plates. The advantage of the present formulation is that no post-processing approach is needed to calculate the transverse shear stresses while maintaining the computational accuracy of a linear plate element. Performance of the proposed element is assessed by comparing with several benchmark solutions. Numerical results show that the present elements can robustly and accurately predict the displacements and stresses of multilayered composite plates.     

Local buckling modelling of isogrid and anisogrid lattice cylindrical shells with triangular cells

The paper deals with a refined analytical model for the local buckling failure modes of composite anisogrid lattice cylindrical shells made of a regular system of triangular cells. Such structures are preliminarily designed with the aid of closed-form solutions specifying the minimum mass and the corresponding optimal design variables under a set of formulated constraint equations. These equations address the main failure mechanisms that can be typically experienced by the structure due to axial compressive loads, namely, the global buckling of the shell, the local buckling of helical ribs, and the material failure of helical ribs. However, the local buckling of helical ribs is normally based on a simplified and qualitative approach. Thus, the scope of the present work is to improve the prediction of this failure mode by means of a rather accurate modelling which accounts for the interaction of intersecting hoop and helical ribs, the influence of the number of hoop sections of the shell, and the effect of the prebuckling tensile force in hoop ribs. The proposed model - that has been verified with the aid of finite-element analysis - lastly suggests the possibility to improve the preliminary design solution with respect to the fully analytical approach.     

C1连续曲面重构与光顺的有限元算法

提出了一种基于离散的测量数据重建光顺自由曲面的有限元新方法。根据最佳逼近与能量光顺原理，建立正定的目标泛函，采用18自由度三角形板单元对泛函离散，进行极小化，求得最优解。根据有限元插值计算，重新构造出全场C^1连续的自由曲面。这种方法结合了能量光顺技术，有效地抑制了输入数据上误差噪声的影响，曲面重建的精度高、光顺性好，而且能给出合理的一阶导数。该方法计算简单、便于应用，所需的输入数据点少，并可用于处理曲线边界区域的问题。     

A method for creating a class of triangular C1 finite elements

Finite elements providing a C¹ continuous interpolation are useful in the numerical solution of problems where the underlying partial differential equation is of fourth order, such as beam and plate bending and deformation of strain‐gradient‐dependent materials. Although a few C¹ elements have been presented in the literature, their development has largely been heuristic, rather than the result of a rational design to a predetermined set of desirable element properties. Therefore, a general procedure for developing C¹ elements with particular desired properties is still lacking. This paper presents a methodology by which C¹ elements, such as the TUBA 3 element proposed by Argyris et al., can be constructed. In this method (which, to the best of our knowledge, is the first one of its kind), a class of finite elements is first constructed by requiring a polynomial interpolation and prescribing the geometry, the location of the nodes and the possible types of nodal DOFs. A set of necessary conditions is then imposed to obtain appropriate interpolations. Generic procedures are presented, which determine whether a given potential member of the element class meets the necessary conditions. The behaviour of the resulting elements is checked numerically using a benchmark problem in strain‐gradient elasticity. Copyright © 2011 John Wiley & Sons, Ltd.     

复合材料蒙皮加筋壁板结构成本-质量优化设计

介绍了复合材料整体化结构的制造成本估算方法。将成本作为主要的优化设计参,针对蒙皮加筋壁板结构采用共固化成型技术,考虑结构约束及与成型工艺相关的制造约束,提出了在压力和剪切力作用下复合材料蒙皮加筋壁板结构基于成本2质量平衡的优化设计方法。以蒙皮 T形加筋为例,分别选取最小质量和最小成本为优化目标参量验证工时估算模型的有效性。讨论了7种常见形状加筋整体化壁板结构的制造成本和质量,估算值与实验值吻合较好。研究结果表明,蒙皮T形筋制造工时最短而质量仅高于最小质量J形结构的0.5%,是基于成本2质量平衡优化的最佳选择结构。研究结果为复合材料整体化蒙皮加筋结构设计提供指导。     

Global design and analysis of deep sea FRP composite risers under combined environmental loads

The use of composite materials in offshore engineering for deep sea oil production riser systems has drawn considerable interest due to the potential weight savings and improvement in durability that can be achieved. The design of composite risers consists of two stages: (1) local design based on critical local load cases (LCs) to obtain the geometric configuration of the riser which will be analysed in the global design stage, and (2) global analysis of the full length composite riser under global loads including top tension force, platform motion, hydrostatic pressure, gravity, buoyancy, wave and current loads to determine and assess critical locations. This study describes the methodology, LCs, analysis procedure and results of the global design of the composite riser based on the geometries of the tubular optimised in the local design stage. The results show that a careful local design of the tubular using inclined reinforcements in addition to axial and hoop reinforcements can offer substantial weight savings and at the same time ensure that the structure is capable of withstanding the global loads applied on it.     

Topology design for composite components of minimum weight

This work presents a new philosophy for optimisation of composite structures in relation to lightweight design. It is based on Michell optimum lay-out theory, which uses orthogonal mesh structures disposed in the direction of principal stress trajectories, associated with an absolutely uniform distribution of stress in the fibres. The fibres in the composite component micro structure are disposed orthogonally like the minimum weight Michell structures, with voids filled with resin. This is the same mechanical principle which governs the optimisation of natural composites such as bones, horn, trees etc. Based on this natural rule, a procedure to find the optimum topology for the design of optimum composite mechanical components has been developed. A CAD-CAE software system based on finite element analysis using ABAQUS produces interactively on a screen the structure of optimum topology where the optimum fibre arrangement will be made.     

Application of rotatable central composite design in the preparation and optimization of poly(lactic-co-glycolic acid) nanoparticles for controlled delivery of paclitaxel

Context: Polymeric carrier systems of paclitaxel (PCT) offer advantages over only available formulation Taxol® in terms of enhancing therapeutic efficacy and eliminating adverse effects. Objective: The objective of the present study was to prepare poly (lactic-co-glycolic acid) nanoparticles containing PCT using emulsion solvent evaporation technique. Methods: Critical factors involved in the processing method were identified and optimized by scientific, efficient rotatable central composite design aiming at low mean particle size and high entrapment efficiency. Twenty different experiments were designed and each formulation was evaluated for mean particle size and entrapment efficiency. The optimized formulation was evaluated for in vitro drug release, and absorption characteristics were studied using in situ rat intestinal permeability study. Results: Amount of polymer and duration of ultrasonication were found to have significant effect on mean particle size and entrapment efficiency. First-order interactions of amount of miglyol with amount of polymer were significant in case of mean particle size, whereas second-order interactions of polymer were significant in mean particle size and entrapment efficiency. The developed quadratic model showed high correlation (R² > 0.85) between predicted response and studied factors. The optimized formulation had low mean particle size (231.68 nm) and high entrapment efficiency (95.18%) with 4.88% drug content. The optimized formulation showed controlled release of PCT for more than 72 hours. In situ absorption study showed faster and enhanced extent of absorption of PCT from nanoparticles compared to pure drug. Conclusion: The poly (lactic-co-glycolic acid) nanoparticles containing PCT may be of clinical importance in enhancing its oral bioavailability.