一类C2连续可调控的交错B样条曲面

提出一类C^2连续可调控的带参数ε的交错B样条曲面的生成方法,这种曲面具有普通3次B样条曲面的主要性质,在控制点固定时,改变参数ε的值能调控曲面的位置,当ε→0时曲面整体地逼近于控制多面体网。     

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.     

A Smoothed Finite Element Method for Mechanics Problems

In the finite element method (FEM), a necessary condition for a four-node isoparametric element is that no interior angle is greater than 180° and the positivity of Jacobian determinant should be ensured in numerical implementation. In this paper, we incorporate cell-wise strain smoothing operations into conventional finite elements and propose the smoothed finite element method (SFEM) for 2D elastic problems. It is found that a quadrilateral element divided into four smoothing cells can avoid spurious modes and gives stable results for integration over the element. Compared with original FEM, the SFEM achieves more accurate results and generally higher convergence rate in energy without increasing computational cost. More importantly, as no mapping or coordinate transformation is involved in the SFEM, its element is allowed to be of arbitrary shape. Hence the restriction on the shape bilinear isoparametric elements can be removed and problem domain can be discretized in more flexible ways, as demonstrated in the example problems.     

Finite element formulations of strain gradient theory for microstructures and the C0–1 patch test

Based on finite element formulations for the strain gradient theory of microstructures, a convergence criterion for the C^0–1 patch test is introduced, and a new approach to devise strain gradient finite elements that can pass the C^0–1 patch test is proposed. The displacement functions of several plane triangular elements, which satisfy the C⁰ continuity and weak C¹ continuity conditions are evaluated by the C^0–1 patch test. The difference between the proposed C^0–1 patch test and the C⁰ constant stress and C¹ constant curvature patch tests is elucidated. An 18-DOF plane strain gradient triangular element (RCT9+RT9), which passes the C^0–1 patch test and has no spurious zero energy modes, is proposed. Numerical examples are employed to examine the performance of the proposed element by carrying out the C^0–1 patch test and eigenvalue test. The proposed element is found to be without spurious zero energy modes, and it possesses higher accuracy compared with other strain gradient elements. Copyright © 2004 John Wiley & Sons, Ltd.     

Smoothing Measured Displacements and Computing Strains Utilising Finite Element Method

Abstract: A method for smoothing measured displacements and computing strains utilising finite element and least‐squares methods is proposed. Nodal displacement values of a finite element model are determined by fitting the interpolation functions of elements to measured displacement values using the method of least‐squares. The displacements in the region where the measurement values are not obtained or unreliable are determined by solving finite element equations. Then, strains are obtained using a displacement‐strain relationship. The validity is demonstrated by applying the proposed method to the displacement distributions of a plate with a hole obtained using finite element method and those around a crack tip obtained using digital image correlation. Results show that the displacements and the strains can be determined accurately by the proposed method. Furthermore, the strains near free boundaries and strain concentration region can be computed. As strains can be evaluated easily and accurately, the proposed method can be used as one of the data processing methods for optical methods.     

基于广义能量法的截面曲线光顺

对于气动流形曲面,除了满足对原始数据的逼近精度要求之外,通常还要求曲面具有较高的光顺性能。笔者在综合分析现有光顺方法不足的基础上,提出了同时考虑曲面几何及物理等多项光顺准则的基于广义能量法的曲面整体光顺思路,建立了包含曲面截线族粗光顺、曲面精光顺两个步骤的曲面光顺方法。这种方法对于提高曲面的整体光顺性能具有良好的效果。     

EPS泡沫包装箱有限元分析与优化设计

目的为了节省泡沫包装箱设计和制造时间,减少材料浪费,以提高使用性能。方法首先在UG中建立所选取的销量较好的3种EPS泡沫包装箱模型,然后导入Abaqus中进行结构静力学分析,最后根据分析结果对包装箱结构进行优化设计及结构静力学分析。结果得到了3种样品模型和优化模型的应力分布云图,3种样品模型最大应力均位于箱盖与箱体接触区域,箱盖中心区域变形最大。结论优化设计后的模型最大应力减小,应力分布更加合理。     

冲击-接触问题有限元仿真的并行计算

冲击．接触问题广泛存在于汽车碰撞等的模拟计算中。简单介绍了求解该类问题的显式有限元方法，对显式有限元方法的并行性进行了讨论。根据显式有限元和冲击一接触问题的计算特点，设计并实现了接触均衡的分区算法。算例计算结果表明：该并行算法具有较好的加速比和并行效率。     

基于特征单元的三角形蜂窝异面压缩的有限元分析

目的 研究三角形蜂窝排列方式对三角形蜂窝异面动态压缩性能的影响。方法 借助Ansys/LS-DYNA建立基于特征单元的三角形蜂窝异面动态压缩的有限元分析模型,研究三角形蜂窝排列方式对三角形蜂窝异面压缩性能的影响。结果 将三角形蜂窝胞元阵列模型的有限元分析结果与理论值进行对比,证明三角形蜂窝的有限元模型是可靠的,随后将三角形胞元阵列模型与此研究中采用的特征单元模型计算结果进行对比,结果显示2种有限元计算模型的计算结果一致,证明此研究特征单元结构的选取和模型的建立是可靠的。结论 不同排列方式对三角形蜂窝在异面方向上的动态峰应力和单位体积能量吸收没有影响。     

A Posteriori Error Estimates of Semidiscrete Mixed Finite Element Methods for Parabolic Optimal Control Problems

A posteriori error estimates of semidiscrete mixed finite element methods for quadratic optimal control problems involving linear parabolic equations are developed. The state and co-state are discretised by Raviart-Thomas mixed finite element spaces of order $k$, and the control is approximated by piecewise polynomials of order $k$ ($k≥0$). We derive our a posteriori error estimates for the state and the control approximations via a mixed elliptic reconstruction method. These estimates seem to be unavailable elsewhere in the literature, although they represent an important step towards developing reliable adaptive mixed finite element approximation schemes for the control problem.     

Analytical modelling of laminated composites

A significant number of research papers has been published on the analytical modelling of composite laminates over the past 20 years. The drive for more accurate analysis has led us to techniques which have become computationally more and more burdensome, while the engineering world continues to use simple, first-older shear deformable plate theory as its primary tool. This paper presents a unique approach to the analysis of thick laminated composites by presenting two simple finite element methods. The first uses the Predictor Corrector technique to extend the simple Mindlin type element to achieve greater accuracy, and the second develops a new Least Squares element which can approximate a C¹ continuous element. The Least Squares element has the capability to incorporate a simplified higher order basis into a piecewise continuous displacement field creating an accurate, yet computationally simple, element. These two methods have the potential to upgrade analysis methods significantly with little additional computational cost. It is hoped that this work can instigate further research into efficient modelling of composite laminates.