颗粒形状对复合材料单轴棘轮行为及其细观塑性变形特征的影响

在细观有限元模型基础上 , 利用 ABAQUS有限元程序对具有不同颗粒形状(球形、 立方体、 短棱柱和短圆柱)的 SiC P/ 6061Al 合金复合材料的单调拉伸行为和单轴棘轮行为进行数值模拟 , 讨论颗粒形状对复合材料棘轮行为的影响。 结果表明: 颗粒形状对复合材料的弹性模量、 单拉行为和单轴棘轮行为均有较大影响。 在所讨论的几种颗粒形状中 , 球形颗粒的增强效果最弱 , 抵抗棘轮变形的能力最差 ; 不同短棱柱颗粒的增强效果与其拥有的棱边数有关 , 即五棱柱颗粒的增强效果最好 , 然后随棱边数的增加逐渐下降 , 最后接近于短圆柱形颗粒。通过有限元分析结果讨论了不同颗粒形状下基体的细观塑性变形特征及其演化规律 , 这些结果有助于分析该类复合材料损伤和失效机制。      

A partial-boundary element approach to the elastic torsion problem of a prismatic beam with a cracked rectangular cross-section

Using the partial-boundary element approach, in which only a part of the boundary in problem is discretized, the elastic torsion problem of a prismatic beam of a cracked rectangular cross-section has been solved in this brief paper, together with a numerical example to show the accuracy and versatility of the approach.     

Dual finite element analysis for plasticity–friction torsion of composite bar

The quasi-static problem of torsion of an elastic–plastic, prismatic, composite bar is considered in the paper. The phenomenon of slip on the interfaces between the components of the bar is taken into account. The elastic–plastic behaviour of the material is described by the Prandtl-Reuss constitutive relation. The slip on the interface is governed by the Coulomb friction law—it is assumed that there is no cohesion between components of the bar. The stresses normal to the interfaces are considered to be caused by shrinkage of the matrix of the bar or by external forces acting perpendicularly to its longitudinal axis. The problem is set in the dual variational forms and solved with the help of the finite element method. Two approximate kinematically and statically admissible solutions are obtained. The stress function is used for calculation of the second one. The iterative algorithms solving the problem and some numerical results are presented in the paper.     

Modal analysis of plates using the dual reciprocity boundary element method

This paper presents a new method for determining the natural frequencies and mode shapes for the free vibration of thin elastic plates using the boundary element and dual reciprocity methods. The solution to the plate's equation of motion is assumed to be of separable form. The problem is further simplified by using the fundamental solution of an infinite plate in the reciprocity theorem. Except for the inertia term, all domain integrals are transformed into boundary integrals using the reciprocity theorem. However, the inertia domain integral is evaluated in terms of the boundary nodes by using the dual reciprocity method. In this method, a set of interior points is selected and the deflection at these points is assumed to be a series of approximating functions. The reciprocity theorem is applied to reduce the domain integrals to a boundary integral. To evaluate the boundary integrals, the displacements and rotations are assumed to vary linearly along the boundary. The boundary integrals are discretized and evaluated numerically. The resulting matrix equations are significantly smaller than the finite element formulation for an equivalent problem. Mode shapes for the free vibration of circular and rectangular plates are obtained and compared with analytical and finite element results.     

An exact dynamic stiffness matrix for axially loaded double-beam systems

An exact dynamic stiffness method is presented in this paper to determine the natural frequencies and mode shapes of the axially loaded double-beam systems, which consist of two homogeneous and prismatic beams with a distributed spring in parallel between them. The effects of the axial force, shear deformation and rotary inertia are considered, as shown in the theoretical formulation. The dynamic stiffness influence coefficients are formulated from the governing differential equations of the axially loaded double-beam system in free vibration by using the Laplace transform method. An example is given to demonstrate the effectiveness of this method, in which ten boundary conditions are investigated and the effect of the axial force on the natural frequencies and mode shapes of the double-beam system are further discussed.     

Hybrid‐stress six‐node prismatic elements

This paper presents three novel hybrid‐stress six‐node prismatic elements. Starting from the element displacement interpolation, the equilibrating non‐constant stress modes for the first element are identified and orthogonalized with respect to the constant stress modes for higher computational efficiency. For the second element, the non‐constant stress modes are non‐equilibrating and chosen for the sake of stabilizing the reduced‐integrated element. The first two elements are intended for three‐dimensional continuum analysis with both passing the patch test for three‐dimensional continuum elements. The third element is primarily intended for plate/shell analysis. Shear locking is alleviated by a new assumed strain scheme which preserves the element accuracy with respect to the twisting load. Furthermore, the Poisson's locking along the in‐plane and out‐of‐plane directions is overcome by using the hybrid‐stress modes of the first element. The third element passes the patch test for plate/shell elements. Unless the element assumes the right prismatic geometry, it fails the patch test for three‐dimensional continuum elements. It will be seen that all the proposed elements are markedly more accurate than the conventional fully integrated element. Copyright © 2004 John Wiley & Sons, Ltd.     

Formulation of reference surface element and its applications in dynamic analysis of delaminated composite beams

This paper presents a new finite element formulation, referred to as reference surface element (RSE) model, for numerical prediction of dynamic behaviour of delaminated composite beams and plates using the finite element method. The RSE formulation can be readily incorporated into all elements based on the Timoshenko beam theory and the Reissner–Mindlin plate theory taking into account the transverse shear deformations. The ‘free model' and ‘constrained model' for dynamic analysis of delaminated composite beams and/or plates have been unified in this RSE formulation. The RSE formulation has been applied to an existing 2-node Timoshenko beam element taking into account the transverse shear deformations and the bending–extension coupling. Frequencies and vibration mode shapes are determined through solving an eigenvalue problem. Numerical results show that the present RSE model is reliable and practical when used to predict frequencies and mode shapes of delaminated composite beams. The RSE formulation has also been used to investigate the effects of the number, size and interfacial loci of delaminations on frequencies and mode shapes of composite beams.     

Experimental preforming of highly double curved shapes with a case corner using an interlock reinforcement

This experimental work concerns the study of the preforming of a specific highly double curved geometry with a triple point (case corner) by the sheet forming process using powdered interlock reinforcement (G1151®). Three different punches (square box, prism, tetrahedron) were used in this study, each of them presenting highly double curved geometry with a case corner. A specific sheet forming device specially designed for the preforming of textile reinforcement was used. The expected shapes with the three punches have been obtained with an optimized blank-holder pressure. No classical defaults such as wrinkling or yarn damage are present in the useful zone of the preforms. However, a new default, not observed for spherical or hemispherical shape has been identified. It concerns the out of plane buckling of yarns. This phenomenon not observed on the square box is visible on some faces and edges of the prismatic and tetrahedron shapes. For the square box, it is easily possible to control the orientation of the yarn within the preform in the faces, whereas this is not possible for triangular faces of the prismatic and tetrahedron shapes. The square box punch is therefore more adapted to preform the highly doubled curved shape with the case corner.     

Recognition of interacting rotational and prismatic machining features from 3-D mill-turn parts

Current feature recognition methods generally recognize and classify machining features into two classes: rotational features and prismatic features. Based on the different characteristics of geometric shapes and machining methods, rotational features and prismatic features are recognized using different methods. Typically, rotational features are recognized using two-dimensional (2-D) edge and profile patterns. Prismatic features are recognized using 3-D geometric characteristics, for example, patterns in solid models such as 3-D face adjacency relationships. However, the current existing feature recognition methods cannot be applied directly to a class of so-called mill-turn parts where interactions between rotational and prismatic features exist. This paper extends the feature recognition domain to include this class of parts with interacting rotational and prismatic features. A new approach, called the machining volume generation method, is developed. The feature volumes are generated by sweeping boundary faces along a direction determined by the type of machining operation. Different types of machining features can be recognized by generating different forms of machining volumes using various machining operations. The generated machining volumes are then classified using face adjacency relationships of the bounding faces. The algorithms are executed in four steps, classification of faces, determining machining zones, generation of rotational machining volumes and prismatic machining volumes, and classification of features. The algorithms are implemented using the 3-D boundary representation data modelled on the ACIS solid modeller. Example parts are used to demonstrate the developed feature recognition method.     

Numerical instability in linearized planing problems

The hydrodynamics of planing ships are studied using a finite pressure element method. In this method, a boundary value problem (BVP) is formulated based on linear planing theory; the planing ship is represented by the pressure distribution acting on the wetted bottom of the ship, and the magnitude of this pressure distribution is evaluated using a boundary element method. The pressure is discretized using overlapping pressure pyramids, known as tent functions, so that the resulting distribution is piece‐wise continuous in both longitudinal and transverse directions. A set of linear algebraic equations for the determination of the pressure is then established using a collocation technique. It is found that the matrix of the linear equations is ill conditioned; this leads to oscillatory behaviour of the predicted pressure distribution if the direct solution method of LU decomposition or Gaussian elimination is used to solve the system of linear equations. In the current study, this numerical instability is analysed in detail. It is found that the problem can be addressed by adopting singular value decomposition (SVD) technique for the solution of the linear equations. Using this method, the hydrodynamic results for flat‐bottomed and prismatic planing ships are calculated and a good agreement is demonstrated with Savitsky's empirical relations. Copyright © 2006 John Wiley & Sons, Ltd.     

破片头部系数对TNT冲击起爆临界速度影响规律研究

为研究破片头部形状在炸药冲击起爆中的影响,基于破片冲击起爆炸药的临界能量判据准则,结合LS-DYNA有限元软件,分别计算了正四棱柱破片、正六棱柱破片、圆柱破片、模拟弹丸破片（fragment-simulating projectiles,FSP）和球头形破片等5种破片冲击起爆TNT装药的理论和仿真速度阈值,并拟合出FSP冲击起爆炸药的理论头部形状系数。结果表明,在相同质量和撞击横截面积下,不同头部形状的破片撞击TNT装药的起爆阈值不等;起爆时间与破片的动能大小有关,动能越大,起爆时间越短。对于多边正棱柱类型的破片（如正四棱柱破片、正六棱柱破片、正八棱柱破片等）,提出了以正棱柱的外接圆柱作为简化模型来计算多边形正棱柱破片冲击起爆TNT速度阈值,发现多边正棱柱破片横截面的边数越多,计算结果与数值模拟结果吻合越好。     

Shear stresses in prismatic beams with arbitrary cross‐sections

In this paper the approximate computation of shear stresses in prismatic beams due to Saint–Venant torsion and bending using the finite element method is investigated. The shape of the considered cross‐sections may be arbitrary. Furthermore, the basic co‐ordinate system lies arbitrarily to the centroid, and not necessarily in principal directions. For numerical reasons Dirichlet boundary conditions of the flexure problem are transformed into Neumann boundary conditions introducing a conjugate stress function. Based on the weak formulation of the boundary value problem isoparametric finite elements are formulated. The developed procedure yields the relevant warping and torsion constants. Copyright © 1999 John Wiley & Sons, Ltd.     

Passage of light through a general three dimensional model—equations linking characteristic parameters with system parameters

The determination of the secondary principal stress difference and their orientations for a discrete slice of thickness dz along a particular light path in a three dimensional photoelastic model is discussed in this paper. These quantities are determined in terms of the characteristic parameters¹ and their variations at discrete points distance z and z + dz along the light path. The variations of the characteristic parameters are obtained by deriving the equations linking the characteristic parameters for the light path and the system parameters of the discrete element. The validity of the equations so derived has also been checked by applying these equations to the solution of the problem of a uniformly twisted prismatic bar.     

Shape detection with vision: implementing shape grammars in conceptual design

Despite more than 30 years of research, shape grammar implementations have limited functionality. This is largely due to the difficult problem of subshape detection. Previous research has addressed this problem analytically and has proposed solutions that directly compare geometric representations of shapes. Typically, such work has concentrated on shapes composed of limited geometry, for example straight lines or parametric curves, and as a result, their application has been restricted. The problem of general subshape detection has not been resolved. In this paper, an alternative approach is proposed, in which subshape detection is viewed as a problem of object recognition, a sub-domain of computer vision. In particular, a general method of subshape detection is introduced based on the Hausdorff distance. The approach is not limited in terms of geometry, and any shapes that can be represented in an image can be compared according to the subshape relation. Based on this approach, a prototype shape grammar system has been built in which the geometry of two-dimensional shapes is not restricted. The system automates the discovery of subshapes in a shape, enabling the implementation of shape rules in a shape grammar. Application of the system is illustrated via consideration of shape exploration in conceptual design. The manipulations of sketched design concepts are formalised by shape rules that reflect the types of shape transformations employed by designers when sketching.     

可动节点复合单元的基本原理及在一维问题中的应用

着重于开发一种以常规线性单元为基底,附加中间移动节点而构成的新型高精度的复合有限单元方法。移动节点复合单元法作为一种高精度有限单元法,通过调节中间可动节点的位置改变其单元内部的场分布,从而只需少量单元即可达到较高的计算精度。由于此种复合单元的中间移动节点的形函数采用计算机图形学常用的Bezier函数,故可简称为‘Bezier复合单元’(BCE)。应用此Bezier单元对具有解析解的一维受分布载荷作用的等截面杆问题和受集中载荷作用的变截面杆问题进行模拟,并与解析解及采用常规有限单元法的模拟结果进行对照和分析。     

Variational generation of prismatic boundary‐layer meshes for biomedical computing

Boundary‐layer meshes are important for numerical simulations in computational fluid dynamics, including computational biofluid dynamics of air flow in lungs and blood flow in hearts. Generating boundary‐layer meshes is challenging for complex biological geometries. In this paper, we propose a novel technique for generating prismatic boundary‐layer meshes for such complex geometries. Our method computes a feature size of the geometry, adapts the surface mesh based on the feature size, and then generates the prismatic layers by propagating the triangulated surface using the face‐offsetting method. We derive a new variational method to optimize the prismatic layers to improve the triangle shapes and edge orthogonality of the prismatic elements and also introduce simple and effective measures to guarantee the validity of the mesh. Coupled with a high‐quality tetrahedral mesh generator for the interior of the domain, our method generates high‐quality hybrid meshes for accurate and efficient numerical simulations. We present comparative study to demonstrate the robustness and quality of our method for complex biomedical geometries. Copyright © 2009 John Wiley & Sons, Ltd.     

Sensitivity analysis and shape optimization in nonlinear solid mechanics

The objective of this paper is twofold. First, it presents a boundary element formulation for sensitivity analysis for solid mechanics problems involving both material and geometric nonlinearities. The second focus is on the use of such sensitivities to obtain optimal design for problems of this class. Numerical examples include sensitivity analysis for small (material nonlinearities only) and large deformation problems. These numerical results are in good agreement with direct integration results. Further, by using these sensitivities, a shape optimization problem has been solved for a plate with a cutout involving only material nonlinearities. The difference between the optimal shapes of solids, undergoing purely elastic or elasto-viscoplastic deformation is shown clearly in this example.     

Comparison of boundary element and finite element methods in the inelastic torsion of prismatic shafts

The accuracy and computational efficiency of the boundary element and the finite element methods are compared in this paper for problems of time-dependent inelastic torsion of prismatic shafts. Several cross-sections and two types of twisting history are considered in the numerical examples. The shaft material is assumed to obey an elastic-time hardening creep constitutive model.     

The effects of element shape on the critical time step in explicit time integrators for elasto‐dynamics

In this paper, the effects of element shape on the critical time step are investigated. The common rule‐of‐thumb, used in practice, is that the critical time step is set by the shortest distance within an element divided by the dilatational (compressive) wave speed, with a modest safety factor. For regularly shaped elements, many analytical solutions for the critical time step are available, but this paper focusses on distorted element shapes. The main purpose is to verify whether element distortion adversely affects the critical time step or not. Two types of element distortion will be considered, namely aspect ratio distortion and angular distortion, and two particular elements will be studied: four‐noded bilinear quadrilaterals and three‐noded linear triangles. The maximum eigenfrequencies of the distorted elements are determined and compared to those of the corresponding undistorted elements. The critical time steps obtained from single element calculations are also compared to those from calculations based on finite element patches with multiple elements. Copyright © 2014 John Wiley & Sons, Ltd.