一种精确积分的四结点板弯曲单元

本文从Ｍｉｎｄｌｉｎ／Ｒｅｉｓｓｎｅｒ理论出发,采用一种新的平行四边形母单元和相应的形函数推导四结点板弯曲单元刚度矩阵的精确积分解。弯曲应变和横向剪切应变分别采用不同的插值公式构成单元刚度矩阵。理论和算例分析表明本文方法克服了“闭锁”现象并能应用于很薄的板,单元刚度矩阵计算速度比采用数值积分计算的同类单元的快四倍。     

一种考虑剪切变形的矩形板元素刚度矩阵

本文应用应变能分项插值的概念推导了一种具有12个参数的考虑剪切变形的正交各向异性矩形平板元素的刚度矩阵,在计算应变能的近似值时,对不同的项采取了不同的位移函数.基本的位移函数是根据考虑剪切变形的直梁的位移得到的,其中包含了弯曲刚度与剪切刚度的比值D/C,因此得到的刚度矩阵对各种剪切刚度值直至薄板(C→∞)都能应用.刚度矩阵以显式表示,使用方便.对典型问题的静力、动力计算表明结果是良好的.     

一类新型受任意载荷的杂交旋转壳单元

本文从弹性力学Reissner变分原理出发推导旋转壳曲线坐标系下内分，位移的二类变量广义变分原理，依据这个原理推导一类旋转壳坐标系中具有独立横向转角的受谐和外载荷下的杂交旋转壳单元，内力模式的选用使刚度矩阵的剪切部份在薄壳情况下能反映Kirchhoff假设，并使单元刚度矩阵满秩，从而保证单元无剪切自锁和零能模式，数例证明这类单元对中厚和薄旋转壳具有良好的通用性和较高的精度。     

两种不同摄动算法的优化方法增强门板的抗弯曲刚度

分别采用了两种壳体结构的形状优化算法来提高门板结构的抗弯曲刚度,它们分别是控制算法与敏度算法的壳体珠状优化方法。优化结果表明,对于壳状门板的刚度优化,这两种算法都是采用材料单元的摄动迭代来降低壳单元的最大应变能。两类算法之间的明显不同在于:控制算法在优化完成后会产生典型的珠状结构,而敏度算法产生的珠状结构则更平缓且不明显;同时,对于门板结构刚度的优化计算,控制算法的优化结果将最大单元应变能从1.83×10~(-3)J降低至1.35×10~(-3)J,而敏度算法则降低至1.49×10~(-3)J。因此对于该目标优化方法来说,控制算法更优于敏度算法。     

板壳弹塑性屈曲的有限元分析

1 拟协调双曲壳单元为解决板壳有限元分析的C~1连续性问题,本文给出三角形拟协调双曲扁壳单元的刚度矩阵.拟协调单元是基于域内假设应变场和边界拟协调位移场,应用最小势能原理所构     

弹性中厚扁球壳的边界积分方程解法

1.前言近年来,边界元法已成功地求解了薄壳弯曲等问题。经典薄壳理论采用Kirchhoff假设,忽略了剪切变形,转动惯性效应.此理论计算厚壳,带有小孔洞的壳体会带来较大的误差。本文所讨论的球壳平衡方程中,不仅包含薄膜内力项和弯矩项,而且还反映了横向剪切变形。利用假设位移函数法,推导出其基本解。然后由虚功原理导出一组五个边界积分方程。其中含有五个广义位移(两个转角分量和三个位     

建立精密单元刚度矩阵的一种方法的改进

本文对文〔1〕的另一种建立精密单元刚度矩阵的方法提出了一个改进方案,此方案首先是求取形函数,然后用低阶的完全多项式来表示应变,再以分块形式给出刚度矩阵,并以18个自由度的板的弯曲为例说明此方案的实施.     

用于多种夹层板等效的有限元分析法

针对夹层板力学性能解析法难于计算复杂结构的夹层板且通用性差的问题,本文采用有限元分析法研究了夹层板性能的等效方法。对夹层板的代表体单元模型施加位移约束,模拟弯曲变形时线性独立的应变分量和弯曲内力;根据夹层板内力与应变的本构关系,求出刚度矩阵;最后由刚度矩阵得出宏观等效弹性常数,从而把夹层板等效成连续材料的单层板单元。将该方法与解析法计算结果进行比较得到的夹层板单元四个主要弹性常数误差在0.2%以内,验证了该方法的有效性;另外采用该方法等效三种典型结构夹层板,比较实际模型和等效模型的弯曲响应,得到的误差均在1.4%以内,表明该方法在不考虑复杂多变的夹芯结构时具有通用性。     

一种考虑横向剪切变形的三角形板弯曲单元

本文从部分协调的三角形薄板弯曲单元出发,并假设横向剪切应变在单元内线性变化,提出了一种考虑横向剪切变形的具有15个自由度的三角平板弯曲单元。该单元应用于薄板和中等厚度板分析均有较高的精度,计算效率高,可用于工程中具有复杂形状的薄板和中等厚度板结构的分析。     

壳体结构弹塑性大应变动态响应分析

本文利用假设剪切应和薄膜应变场的新型退化壳单元，并考虑大应主影响对壳体结构弹塑性动态分析进行了研究，并编制了相应的程度，此程序采用修正的Ｌａｇｒａｎｇｉａｎ公式，它不仅考虑了大变形大应变的影响，还对单元的节点坐标和厚度在每个时间步后都给予修正，通过对一些算例计算表明，此程序数值精度很好，可用于壳体结构的工程分析，并得出结论，对于应变问题考虑和忽略大应变影响将有较大的不同。     

Corotational nonlinear analyses of laminated shell structures using a 4-node quadrilateral flat shell element with drilling stiffness

A new 4-node quadrilateral flat shell element is developed for geometrically nonlinear analyses of thin and moderately thick laminated shell structures. The fiat shell element is constructed by combining a quadrilateral area co- ordinate method （QAC） based membrane element AGQ6- II, and a Timoshenko beam function （TBF） method based shear deformable plate bending element ARS-Q12. In order to model folded plates and connect with beam elements, the drilling stiffness is added to the element stiffness matrix based on the mixed variational principle. The transverse shear rigidity matrix, based on the first-order shear deformation theory （FSDT）, for the laminated composite plate is evaluated using the transverse equilibrium conditions, while the shear correction factors are not needed. The conventional TBF methods are also modified to efficiently calculate the element stiffness for laminate. The new shell element is extended to large deflection and post-buckling analyses of isotropic and laminated composite shells based on the element independent corotational formulation. Numerical re- sults show that the present shell element has an excellent numerical performance for the test examples, and is applicable to stiffened plates.     

Geometrically non-linear analysis of laminated composite structures using a 4-node co-rotational shell element with enhanced strains

To demonstrate the solutions of linear and geometrically non-linear analysis of laminated composite plates and shells, the co-rotational non-linear formulation of the shell element is presented. The combinations of an enhanced assumed strain (EAS) in the membrane strains and assumed natural strains (ANS) in the shear strains improve the behavior of 4-node shell element. To secure computational efficiency in the incremental non-linear analysis, the present element uses the form of the resultant forces pre-integrated through the thickness. The transverse shear stiffness of the laminates is defined by an equilibrium approach instead of the shear correction factor. Numerical examples of this study show very good agreement with the references.     

Asymptotic analysis of the non-linear behavior of long anisotropic tubes

An asymptotically correct beam model is obtained for a long, thin-walled, circular tube with circumferentially uniform stiffness (CUS) and made of generally anisotropic materials. By virtue of its special geometry certain small parameters cause unusual non-linear phenomena, such as the Brazier effect, to be exhibited. The model is constructed without ad hoc approximations from 3D elasticity by deriving its strain energy functional in terms of generalized 1D strains corresponding to extension, bending, and torsion. Large displacement and rotation are allowed but strain is assumed to be small. Closed-form expressions are provided for the 3D non-linear warping and stress fields, the 1D non-linear stiffness matrix and the bending moment–curvature relationship. In bending, failure could be caused by limit-moment instability, local buckling or material failure of a ply. A procedure to determine the failure load is provided based on the non-linear response, neglecting micro-mechanical failure modes, post-failure behavior, and hygrothermal effects. Asymptotic considerations lead to the neglect of local shell interlaminar and transverse shear stresses for the thin-walled configuration. Results of the theory are illustrated for a few symmetric, antisymmetric angle-ply and unsymmetric layups and show that some previously published theories are not asymptotically correct.     

基于宏观三角形分区平板壳单元的非线性有限元分析

针对剪切闭锁效应,本文研究了一种基于假设自然应变方法的宏观三角形分区平板壳单元。利用通用有限元软件ABAQUS所提供的用户自定义单元(UEL)和用户自定义材料(UMAT)子程序,本文将宏观三角形分区平板壳单元和基于损伤能释放率的混凝土弹塑性损伤本构模型成功嵌入了ABAQUS的主分析模块。经典试验McNeice双向混凝土板的数值模拟结果表明:宏观三角形分区平板壳单元对于描述板壳结构的非线性损伤行为是行之有效的。     

一种提高四边形四节点平面壳单元计算精度的新方法

平面壳单元是由平面应力单元和平板弯曲单元叠加组合而成,具有简单的理论表达,但是它在计算曲面壳体结构时误差较大。为了进一步提高平面壳单元的计算精度,本文提出了一种计算平面壳单元刚度矩阵的新方法。通过该方法在高斯积分点建立多个单元局部坐标系,并保证每个局部坐标系都位于单元在高斯点处的切平面上,从而可以有效适应曲面壳体形状,达到进一步提高平面壳单元计算精度的目的。为了在这种新坐标系下计算单元刚度矩阵,给出了求解形函数对局部坐标的导数、局部到自然坐标系积分转换的雅可比、以及局部到整体坐标系的转换矩阵的新型计算方法。通过将这些新坐标系以及新计算方法运用到平面壳单元DKQ24中,可以有效提高平面壳单元尤其是在计算曲面壳体时的精度。计算结果表明,本文方法和平面壳单元相结合,不仅具有平面壳单元简单的理论表达式,还能得到满意的精度。另外,本文方法还可以应用到其他类型的平面壳单元,为提高其他类型平面壳单元的计算精度提供了一种新的途径和思路,具有广阔的应用前景。     

A hybrid membrane/shell method for calculating springback of anisotropic sheet metals undergoing axisymmetric loading

To reduce the computation cost of finite element analyses aiding die design for sheet metal stamping, a hybrid membrane/shell method was developed to determine the springback of anisotropic sheet metal undergoing axisymmetric loading. The hybrid membrane/shell method uses a membrane model to analyze the stamping operation. The bending/unbending strains and stresses varying through thickness are calculated analytically from the incremental shape determined by the membrane analysis. These bending strains and stresses and the final membrane shape are used with a shell finite element model to unload the sheet and calculate springback. The accuracy of the springback prediction with the hybrid method was verified against the springback of 2036-T4 aluminum and a DQAK steel sheet drawn into a cup. It was found that, in comparison with a full shell model, a minimum of 50% CPU time saving and a comparable accuracy was achieved when the hybrid method was used to predict springback.     

A new beam element for analyzing geometrical and physical nonlinearity

Based on Timoshenko＇s beam theory and Vlasov＇s thin-walled member theory, a new model of spatial thin-walled beam element is developed for analyzing geometrical and physical nonlinearity, which incorporates an interior node and independent interpolations of bending angles and warp and takes diversified factors into consideration, such as traverse shear deformation, torsional shear deformation and their coupling, coupling of flexure and torsion, and the second shear stress. The geometrical nonlinear strain is formulated in updated Lagarange （UL） and the corresponding stiffness matrix is derived. The perfectly plastic model is used to account for physical nonlinearity, and the yield rule of von Mises and incremental relationship of Prandtle-Reuss are adopted. Elastoplastic stiffness matrix is obtained by numerical integration based on the finite segment method, and a finite element program is compiled. Numerical examples manifest that the proposed model is accurate and feasible in the analysis of thin-walled structures.     

Postbuckling analysis of laminated composite plates subjected to the combination of in-plane shear,compression and lateral loading

This study deals with postbuckling behavior of laminated composite plates under the combination of in-plane shear, compression and lateral loading using an Element-based Lagrangian formulation. Natural co-ordinate-based strains, stresses and constitutive equations are used in the present shell element. The Element-based Lagrangian formulation described in this paper, in comparison with the traditional approaches, is more attractive not only because it uses only single mapping but also it converges faster. In addition, the finite element (FE) formulation based on the assumed natural strain method for composite structures shows excellence from the standpoints of computational efficiency as well as its ability to avoid both membrane and shear locking behavior. The numerical results obtained are in good agreement with those reported by other investigators. In particular, new results reported in this paper show the influence of various types of loading, materials and number of layers on postbuckling behavior.     

Shear stress analysis in engineering beams using deplanation field of special 2-D finite elements

This paper deals with the 2-D finite element shear stress analysis in beams, loaded by bending with shear and St. Venant’s torsion. The properties of these finite elements, like stiffness matrices as well as load vectors, are derived on the basis of their axial nodal displacements, e.g. by warping field. Proposed finite elements enable stress analysis independently of both cross-sectional member shape and material properties. Stiffness matrices and load vectors are derived for several finite element types. Material is assumed to be isotropic and linear elastic. For justification of the proposed stress analysis procedure, some examples are presented.