Moving kriging interpolation and element‐free Galerkin method

A new formulation of the element‐free Galerkin (EFG) method is presented in this paper. EFG has been extensively popularized in the literature in recent years due to its flexibility and high convergence rate in solving boundary value problems. However, accurate imposition of essential boundary conditions in the EFG method often presents difficulties because the Kronecker delta property, which is satisfied by finite element shape functions, does not necessarily hold for the EFG shape function. The proposed new formulation of EFG eliminates this shortcoming through the moving kriging (MK) interpolation. Two major properties of the MK interpolation: the Kronecker delta property (?_I( s _J)=δ_IJ) and the consistency property (∑_Iⁿ?_I( x )=1 and ∑_Iⁿ?_I( x )x_Ii=x_i) are proved. Some preliminary numerical results are given. Copyright © 2002 John Wiley & Sons, Ltd.     

基于密度分布曲线法的复合材料变刚度铺层优化

基于梯度的优化方法对复合材料层合板进行了变刚度铺层优化设计。在优化过程中需确定铺层中各单元的密度以及角度。为了使优化结果具有可制造性,优化结果需满足制造工艺约束并且铺层角度需从预定角度中选取。为了避免在优化问题中引入过多的约束并减少设计变量的数目,提出密度分布曲线法(DDCM)对层合板中各单元的密度进行参数化。根据各单元的密度以及角度设计变量并基于Bi-value Coding Parameterization(BCP)方法中的插值公式确定各单元的弹性矩阵。优化过程中以结构柔顺度作为优化目标,结构体积作为约束,优化算法采用凸规划对偶算法。对碳纤维复合材料的算例结果表明:采用DDCM可得到较理想的优化结果,并且收敛速率较快。     

A new method of shear stiffness prediction of periodic Timoshenko beams

This article interprets the new implementation of an asymptotic homogenization method for effective bending stiffness of heterogeneous beam structures with periodic microstructure along its axial direction in an intuitionistic way. With this interpretation, the authors then develop a new method of evaluating effective shear stiffness for their Timoshenko beam model. This method can be easily implemented numerically in commercial software. Different kinds of elements and modeling techniques available in commercial software can be applied to model the unit cell. Several examples are given to demonstrate the effectiveness of this new method.     

泰伯式挺度与L&W挺度的相关性分析研究

本文介绍了挺度的定义、测定原理,分析了两种挺度仪的结构和工作原理,研究了两种挺度仪测试数据之间的关系,结果表明:L&W挺度可以转换为泰伯式挺度。     

A Fourier‐series‐based virtual fields method for the identification of 2‐D stiffness distributions

The virtual fields method (VFM) is a powerful technique for the calculation of spatial distributions of material properties from experimentally determined displacement fields. A Fourier‐series‐based extension to the VFM (the F‐VFM) is presented here, in which the unknown stiffness distribution is parameterised in the spatial frequency domain rather than in the spatial domain as used in the classical VFM. We present in this paper the theory of the F‐VFM for the case of elastic isotropic thin structures with known boundary conditions. An efficient numerical algorithm based on the two‐dimensional Fast Fourier Transform (FFT) is presented, which reduces the computation time by three to four orders of magnitude compared with a direct implementation of the F‐VFM for typical experimental dataset sizes. Artefacts specific to the F‐VFM (ringing at the highest spatial frequency near to modulus discontinuities) can be largely removed through the use of appropriate filtering strategies. Reconstruction of stiffness distributions with the F‐VFM has been validated on three stiffness distribution scenarios under varying levels of noise in the input displacement fields. Robust reconstructions are achieved even when the displacement noise is higher than in typical experimental fields.Copyright © 2014 John Wiley & Sons, Ltd.     

Free vibration analysis of sandwich beams using improved dynamic stiffness method

In this paper, free vibration of three-layered symmetric sandwich beam is investigated using dynamic stiffness and finite element methods. To determine the governing equations of motion by the present theory, the core density has been taken into consideration. The governing partial differential equations of motion for one element contained three layers are derived using Hamilton’s principle. This formulation leads to two partial differential equations which are coupled in axial and bending deformations. For the harmonic motion, these equations are combined to form one ordinary differential equation. Closed form analytical solution for this equation is determined. By applying the boundary conditions, the element dynamic stiffness matrix is developed. They are assembled and the boundary conditions of the beam are applied, so that the dynamic stiffness matrix of the beam is derived. Natural frequencies and mode shapes are computed by the use of numerical techniques and the known Wittrick–Williams algorithm. After validation of the present model, the effect of various parameters such as density, thickness and shear modulus of the core for various boundary conditions on the first natural frequency is studied.     

计及塑性接触层的法向接触刚度等效方法

采用典型的粗糙体——刚性面接触模型,针对完全弹性和理想弹塑性两种材料,分析了一般法向接触刚度等效方法是否准确,发现了一般方法在处理弹塑性接触时存在较大差并揭示了其中的本质原因。通过引入界面接触层,提出了接触界面等效的新方法并验证了其准确性,最终实现了对原系统的准确动力等效。通过实例采用两种等效方法对比分析了对动力系统振动特性的影响,为工程实际中含接触界面系统的动力学研究提供了参考。     

中厚椭球壳自由振动动力刚度法分析

介绍精确动力刚度法分析中厚椭球壳自由振动具体实施方法,据环向波数不同将中厚椭球壳自由振动分解为一系列确定环向波数的一维振动;利用控制方程Hamilton形式建立动力刚度关系,用常微分方程求解器COLSYS求解控制方程获得单元动力刚度,用Wittrick-Williams算法求得该环向波数下椭球壳自振频率。数值算例给出中厚圆球壳及椭球壳不同边界条件的自振频率,验证动力刚度法高效、可靠、精确。     

基于非线性刚度约束下的精密机床主轴系统优化设计

 采用“卸积木式”力学模型及以拟静力学模型建立的主轴轴承刚度矩阵对机床主轴系统的结构进行优化,通过数学变换较大地减少计算量;经过对多种机床主轴系统的分析计算,实现了体积和刚度的优化．并以M2110A型内圆磨床的磨头为例,验证了优化设计的效果．     

Stress analysis with arbitrary body force by boundary element method

Linear stress analysis without body force can be easily carried out by means of the boundary element method. Some cases of linear stress analysis with body force can also be solved without the domain integral. However domain integrals are generally necessary to solve the linear stress problems with complicated body forces. This paper shows that the linear stress problems with complicated body forces can be solved approximately without the domain integral. In order to solve these problems, the domain is divided into small areas using contour lines of body force. In these areas, the distributions of body force are assumed approximately to satisfy the Laplace equation.     

Investigation of the flexural stiffness of asymmetric multilayer beams

We present the results of investigation of flexible stiffness of multilayer beams with geometric and/or stiffness asymmetry. An algorithm is proposed for the evaluation of coordinates of the geometric and stiffness centers and the analysis of flexural stiffness in any direction and its extreme values in multilayer beams with asymmetry of any kind. We study the kinetics of coordinates of the geometric and stiffness centers and flexural stiffness depending on the behavior of the geometric parameters and the ratio of the moduli of elasticity of layers and the cross-sectional shape of a multilayer beam. __________ Translated from Problemy Prochnosti, No. 6, pp. 51–65, November–December, 2006.     

汽车排气系统吊耳动刚度优化方法的研究

基于汽车排气系统吊耳传递的动态载荷最小、吊耳耐疲劳性最好,建立了考虑动力总成在内的排气系统振动分析模型。进行了排气系统的自由模态和约束模态的测试,并和计算值进行了对比分析,证明了所建立的排气系统振动模型的正确性。以吊耳的垂向动态载荷最小和其静变形量在一定范围内为优化目标,建立了排气系统吊耳动刚度优化模型。优化后,在怠速工况和2档全负荷加速工况下对车身底板驾驶员位置进行了振动响应测试,测试结果表明,利用优化后的吊耳刚度,能够有效降低车身底板的振动加速度,表明了阐述的排气系统建模和吊耳动刚度优化方法的有效性。文中建模与优化方法,对排气系统的吊耳动刚度计算与优化具有指导意义。     

The complementary functions method for the element stiffness matrix of arbitrary spatial bars of helicoidal axes

The statical behaviour of a spatial bar of an elastic and isotropic material under arbitrary distributed loads having a non-circular helicoidal axis and cross-section supported elastically by single and/or continuous supports is studied by the stiffness matrix method based on the complementary functions approach. By considering the geometrical compatibility conditions together with the constitutive equations and equations of equilibrium, a set of 12 first-order differential equations having variable coefficients is obtained for spatial elements of helicoidal axes. The stiffness matrix and the element load vector of a helicoidal bar with a non-circular axis and arbitrary cross-section are obtained taking into consideration both the presence of an elastic support and the effects of the axial and shear deformations. For helicoidal staircases, the significance of both axial and shear deformations and eccentricities existing in wide and shallow sections are also investigated. The developed model has been coded in Fortran-77, which has been applied to various example problems available in the relevant literature, and the results have been compared.     

Linearized buckling analysis of isotropic and composite beam-columns by Carrera Unified Formulation and dynamic stiffness method

Abstract

This article introduces a one-dimensional (1D) higher-order exact formulation for linearized buckling analysis of beam-columns. The Carrera Unified Formulation (CUF) is utilized and the displacement field is expressed as a generic N-order expansion of the generalized unknown displacement field. The principle of virtual displacements is invoked along with CUF to derive the governing equations and the associated natural boundary conditions in terms of fundamental nuclei, which can be systematically expanded according to N by exploiting an extensive index notation. After the closed form solution of the N-order beam-column element is sought, an exact dynamic stiffness (DS) matrix is derived by relating the amplitudes of the loads to those of the responses. The global DS matrix is finally processed through the application of the Wittrick-Williams algorithm to extract the buckling loads of the structure. Isotropic solid and thin-walled cross-section beams as well as laminated composite structures are analyzed in this article. The validity of the formulation and its broad range of applicability are demonstrated through comparisons of results from the literature and by using commercial finite element codes.     

High-order free vibration analysis of sandwich beams with a flexible core using dynamic stiffness method

In this paper, high-order free vibration of three-layered symmetric sandwich beam is investigated using dynamic stiffness method. The governing partial differential equations of motion for one element are derived using Hamilton’s principle. This formulation leads to seven partial differential equations which are coupled in axial and bending deformations. For the harmonic motion, these equations are divided into two ordinary differential equations by considering the symmetrical sandwich beam. Closed form analytical solutions of these equations are determined. By applying the boundary conditions, the element dynamic stiffness matrix is developed. The element dynamic stiffness matrices are assembled and the boundary conditions of the beam are applied, so that the dynamic stiffness matrix of the beam is derived. Natural frequencies and mode shapes are computed by use of numerical techniques and the known Wittrick–Williams algorithm. Finally, some numerical examples are discussed using dynamic stiffness method.     

A simulated annealing method for design of laminates with required stiffness properties

Designing a laminate based on its stiffness properties requires finding the optimum lamination stacking sequence to yield the required stiffness properties. The design variables to be considered are the number of layers and orientation angle of fibers in each layer group, which are treated as discrete-variables. The optimum lamination is then obtained by minimizing a cost function composed of the relative difference between the calculated effective stiffness properties and weight of trial laminate and the desired properties. This error minimization problem was solved using a modified simulated annealing heuristic method. The new simulated annealing implementation comprises a cooling procedure in which the temperature decrease relied adaptively on the objective function evolution. It is shown that the proposed method can give rise to an improvement in convergence speed. To achieve a further improvement in the performance of the method, simulated annealing parallelization implemented using the proposed cooling process. The main features of this algorithm are described and its encouraging results are presented.     

Meshless thermo‐elastoplastic analysis by triple‐reciprocity boundary element method

In general, internal cells are required to solve thermo‐elastoplasticity problems by a conventional boundary element method (BEM). However, in this case, the merit of BEM, which is the easy preparation of data, is lost. A conventional multiple‐reciprocity boundary element method (MRBEM) cannot be used to solve elastoplasticity problems, because the distribution of initial strain or stress cannot be determined analytically. In this study, it is shown that without the use of internal cells, two‐dimensional thermo‐elastoplasticity problems can be solved by a triple‐reciprocity BEM using a thin plate spline. Initial strain and stress formulations are adopted and the initial strain or stress distribution is interpolated using boundary integral equations. A new computer program was developed and applied to solve several problems. Copyright © 2009 John Wiley & Sons, Ltd.     

汽车覆盖件刚度评价指标的研究

汽车覆盖件刚度是反映覆盖件使用性能的一项重要指标.如何评价覆盖件的刚度,目前尚没有统一的标准.为了建立覆盖件刚度的评价指标和检验标准,以扁壳类零件为模型,对不同材料、曲率半径(单曲)、弧高(双曲)及厚度的曲面扁壳类零件,利用自动测试装置得出载荷-挠度曲线.根据所得曲线对比分析了4种刚度评价指标,给出了弹性变形选取范围及K值的确定方法.研究结果表明这是一种比较准确适用的覆盖件刚度评价方法与评价指标.     

全复合材料桁架扭转刚度分析

为了解决全复合材料桁架扭转刚度缺少实验外有效表征手段的问题,首先,基于均匀化思想,依据单胞剪切刚度相等原则,将全复合材料桁架等效为闭口薄壁梁,推导其等效扭转刚度;然后提出位移转换法并测量桁架转角,对全复合材料桁架扭转刚度进行了实验研究;最后,在梁单元桁架模型中嵌入精细化接头模型,对全复合材料桁架扭转刚度进行了仿真分析。结果表明:等效及仿真结果与实验值基本吻合,等效分析方法能够有效预测全复合材料桁架的扭转刚度,桁架仿真模型具有一定的工程实用性;实验方案可靠,所提出的位移转换法能够解决小转角测量相对误差较大的问题。     

A refined dynamic stiffness element for free vibration analysis of cross-ply laminated composite cylindrical and spherical shallow shells

An exact free vibration analysis of doubly-curved laminated composite shallow shells has been carried out by combining the dynamic stiffness method (DSM) and a higher order shear deformation theory (HSDT). In essence, the HSDT has been exploited to develop first the dynamic stiffness (DS) element matrix and then the global DS matrix of composite cylindrical and spherical shallow shell structures by assembling the individual DS elements. As an essential prerequisite, Hamilton’s principle is used to derive the governing differential equations and the related natural boundary conditions. The equations are solved symbolically in an exact sense and the DS matrix is formulated by imposing the natural boundary conditions in algebraic form. The Wittrick–Williams algorithm is used as a solution technique to compute the eigenvalues of the overall DS matrix. The effect of several parameters such as boundary conditions, orthotropic ratio, length-to-thickness ratio, radius-to-length ratio and stacking sequence on the natural frequencies and mode shapes is investigated in details. Results are compared with those available in the literature. Finally some concluding remarks are drawn.