挖补修理复合材料层合板拉伸性能研究

在试验研究的基础上,建立三维损伤累积模型研究拉伸载荷下挖补修理复合材料层合板的损伤扩展及其最终破坏规律,并讨论挖补角对挖补修理结构拉伸性能的影响,计算结果和试验结果吻合良好。研究结果表明:挖补胶层中的损伤首先发生在胶层连接0°铺层的地方,然后向四周扩展,当损伤扩展到整个胶层面积约40%时,挖补层合板的应力-位移曲线发生较大的刚度下降,此时的载荷为胶层失效载荷。母板和补片在胶层发生损伤前就出现了少量损伤,在胶层完全破坏前,损伤会沿胶界面扩展;在胶层完全破坏后,损伤会沿母板最窄处向两侧自由边快速扩展,而补片在胶层失效后就停止损伤;胶层失效载荷随挖补角的增大而减小,但挖补角的增大会使胶层破坏后母板的承载能力增加,从而使挖补层合板的最终破坏载荷反而增加。在工程应用中,挖补角的选择应综合考虑结构设计要求、工艺和功能等多方面的因素。     

面内线性变化载荷作用复合材料层合板的振动与屈曲优化

采用广义微分求积（GDQ）法开展了不同边界条件下承受面内线性变化载荷作用复合材料层合板振动与屈曲的分析与优化。针对GDQ法求解面内线性变化载荷工况复合材料层合板屈曲问题存在计算振荡、不收敛现象,提出载荷扰动策略实现了GDQ法对复合材料层合板屈曲问题的稳定高效求解。基于基础圆频率和临界屈曲载荷系数的归一化指标,分析了铺层角度对复合材料层合板综合性能的影响,并结合直接搜索模拟退火算法开展了复合材料层合板的铺层顺序优化。结果表明:铺层角度变化对屈曲性能的影响明显强于频率特性;面内线性变化载荷中,以弯曲载荷作用下复合材料层合板的优化综合性能受边界条件变化的影响最小,而优化铺层角度受边界条件变化的影响最大。研究结果为复杂载荷作用下复合材料层合板的设计提供了参考。      

考虑纤维面外起伏的变刚度层合板优化策略研究

针对变刚度层合板在自动铺放制造过程中因间隙/重叠缺陷产生大量纤维面外起伏缺陷的问题,提出采用铺层偏移法与断送纱策略两种铺层优化策略来进行变刚度层合板的铺层设计,在研究过程中同时引入考虑间隙/重叠缺陷建模的方法。根据变刚度层合板铺层的特点提出缺陷重复单元的概念,通过对缺陷重复单元的分析来反映纤维面外起伏的影响,并提出通过纤维面外系数来表征变刚度层合板的纤维面外起伏尺度,最后对不同优化策略的变刚度层合板的屈曲性能进行分析。研究表明:基准设计方案、铺层偏移法与断送纱策略所对应的纤维面外起伏系数为0.83、0.95、0.93,所提出的优化策略对变刚度层合板的纤维面外起伏尺度有着明显的抑制作用。铺层偏移法优化后的[±<50/65>]_6s变刚度层合板最大厚度超差为33%,所对应的屈曲载荷为9117.1 N,屈曲载荷提升17.6%;断送纱策略优化后的[±<50/65>]_6s变刚度层合板最大厚度超差为50%,所对应的屈曲载荷为9716.3N,屈曲载荷提升25.3%。      

FRP层合板自由边效应的变分渐近降维模型

针对变刚度层合结构,大多采用板壳理论或常规的位移有限元法分析其力学行为。相较位移元,非协调广义部分混合元同时引入位移和应力边界条件,提高了应力结果精度,且边界应力更符合真实情况。扩展了纯弹性体的非协调广义部分混合元理论,提出适用于变刚度层合结构修正的非协调广义部分混合元模型。与ABAQUS计算结果对比证明,即使在网格较稀疏的情况下,该文方法也具有较好的适用性,且数值结果精确度高。通过算例分析了纤维铺设角度的变化对变刚度层合板平面内位移场的影响,可为变刚度结构的设计提供一定的思路。

     

搭接长度和铺层方式对CFRP复合材料层合板胶接结构连接性能和损伤行为的影响

针对不同搭接长度和铺层方式的碳纤维增强树脂（CFRP）复合材料层合板单搭胶接结构进行了拉伸试验,观察了试件的受力过程和失效形态,获得了载荷-位移曲线;同时基于连续损伤力学模型和三维Hashin失效准则模拟了CFRP复合材料层合板的层内损伤形成和演化,并利用内聚力模型来模拟层间及胶层的失效损伤,对CFRP复合材料层合板单搭胶接结构在拉伸作用下的失效强度和损伤机制进行了预测,通过对比验证了该数值方法的有效性;通过数值试验比较不同搭接长度和铺层方式的单搭胶接结构及双搭胶接结构的连接强度和损伤行为,并提出了一种优化的CFRP复合材料层合板胶接结构。结果表明:CFRP复合材料层合板胶接结构的极限失效载荷随着搭接长度的增大逐渐增加并趋于稳定值,且结构的失效形式逐渐从胶层自身剪切失效过渡到邻近胶层的层合板层间分层失效;CFRP复合材料层合板胶接结构的连接强度和损伤行为随着铺层方式的不同而改变,通过对3种铺层方式的对比和分析,得到性能最好的铺层方式是[0₃/90₃]_2S;在搭接长度为5~20 mm时,通过对搭接长度进行优化,得到单搭胶接结构的最优搭接长度是17 mm,双搭胶接结构的最优搭接长度是19.3 mm,与搭接长度为20 mm相比,单搭胶接结构和双搭胶接结构的连接强度分别提高了13.26%和0.43%。      

云纹干涉法测定复合材料单孔连接件的应力场

本研究首次将云纹干涉法应用于复合材料单销钉连接件位移场的测量。从位移的云纹图用位移导数法求得销钉孔中心水平截面上的应变。根据复合材料层合板的直法线假设和层合板的折算刚度矩阵算出截面的平均应力分布。通过静力平衡,所得误差在6%以内。本研究结果证实,云纹干涉法测量复合材料连接件的应变场和应力场是有效的实验方法。      

引入减基法的压电层合板瞬态响应分析

摘要：用减基法（RBM）结合有限元法、傅里叶变换和Newmark直接积分法,研究了压电层合板在机电耦合载荷下的瞬态响应。用层单元将层合板沿厚度方向进行离散,得到时间域内的运动方程,通过傅里叶变换得到波数域内的控制方程。应用Newmark直接积分法求解波数域内的位移和电势,并在Newmark法求解过程嵌入减基法,构造减基空间,把结构的等效刚度矩阵、质量矩阵和载荷列向量映射到减基空间降阶,得到减缩的Newmark增量式,从而快速求解得到原结构波数域响应,通过傅里叶逆变换得到时域内的响应。以PZT-5A/0°PVDF铺层两相材料复合压电层合板为算例,分析了机电耦合线载荷激励下,位移场和电势场的瞬态响应情况。计算结果表明,求解过程引入减基法能更快得到结构的瞬态响应,并保证了精度。     

复合材料加筋层合板的极限强度分析

基于更新拉格朗日格式,应用非线性层合三维退化壳元,结合有效的复合材料失效准则、刚度退化模型以及提出的刚度矩阵奇异判断准则,对复合材料加筋层合板在轴向载荷作用下的压缩极限强度问题进行深入研究。讨论了铺层方式、板厚等对极限强度的影响。通过与试验结果进行比较,表明基于提出的刚度矩阵奇异判断准则,结合增量更新拉格朗日格式下非线性层合三维退化有限元的计算方法,能有效计算复合材料加筋层合板的轴向压缩极限强度,并具有很高的精度。     

复合材料低速冲击损伤研究及等效模型的应用

复合材料低速冲击损伤的特殊性及危害性使得对航空复合材料冲击损伤的评估尤为重要。该文通过建立数值计算模型并结合实验数据解决了4个方面的应用问题:1)在ABAQUS子程序VUMAT中引入损伤模式及损伤演化,结合层间连接单元对层合板低速冲击损伤进行了模拟;2)损伤容限设计方法要求对含缺陷结构的极限强度做出正确的评估,通过ABAQUS子程序USDFLD引入损伤模式及材料折减方案,得到了含圆孔的层合板极限拉压强度;3)通过ABAQUS子程序UMAT引入损伤模式及刚度折减方案,结合层间连接单元,模拟了含预制分层的层合板压缩失效问题;4)针对共用铺层结构的工程有限元计算问题,提出了力学等效模型,将该模型应用到结构级的静力实验模拟并拓展至结构冲击模拟。     

考虑制造因素的变刚度层合板的抗屈曲铺层优化设计

与常规层合板相比,变刚度层合板的制造、有限元建模分析和铺层设计有其特殊之处。首先对设计时需考虑的制造因素进行了归纳,提出了变刚度层合板的铺层设计要求。然后给出了变刚度层合板的理想模型和考虑丝束宽度模型的建模方法。基于理想模型对ABAQUS的前处理模块进行二次开发,利用编制的参数化建模程序分析了不同铺放角的变刚度层合板的屈曲性能,并讨论了最小曲率半径对铺层的限制和变刚度设计提高屈曲载荷的机制。基于变刚度层合板的抗屈曲机制建立了一种铺层优化设计方法,使用遗传算法经两步优化得到最优铺层。对最优铺层建立考虑丝束宽度的模型以研究丝束宽度和铺层偏移对变刚度层合板抗屈曲铺层优化结果的影响。研究表明,在变刚度层合板的抗屈曲铺层优化中使用简化的理想模型通常来说是可行的。在考虑制造因素的情况下,优化后的变刚度层合板较常规层合板屈曲载荷有显著提高。     

A boundary integral Trefftz formulation with symmetric collocation

The Galerkin and collocation methods are combined in the implementation of a boundary integral formulation based on the Trefftz method for linear elastostatics. A finite element approach is used in the derivation of the formulation. The domain is subdivided in regions or elements, which need not be bounded, simply connected or convex. The stress field is directly approximated in each element using a complete solution set of the governing Beltrami condition. This stress basis is used to enforce on average, in the Galerkin sense, the compatibility and elasticity conditions. The boundary of each element is, in turn, subdivided into boundary elements whereon the displacements are independently approximated using Dirac functions. This basis is used to enforce by collocation the static admissibility conditions, which reduce to the Neumann conditions as the stress approximation satisfies locally the domain equilibrium condition. The resulting solving system is symmetric and sparse. The coefficients of the structural matrices and vectors are defined either by regular boundary integral expressions or determined by direct collocation of the trial functions.     

HYBRID-TREFFTZ EQUILIBRIUM MODEL FOR CRACK PROBLEMS

A formulation based on the approximation of the stress field is used to compute directly the stress intensity factors in crack problems. The boundary displacements are independently approximated. In each finite element, the assumed stresses may model multipoint singularities of variable order. The differential equilibrium equations are locally satisfied as solutions of the governing differential system are used to build the stress approximation basis. The approximation on the boundary displacements is constrained to satisfy locally the kinematic boundary conditions. The remaining fundamental conditions, namely the differential compatibility equations, the constitutive relations and the static boundary conditions are enforced through weighted residual statements. The approximation criteria are so chosen as to ensure that the finite element model is described by a sparse, adaptive and symmetric governing system described by structural matrices with boundary integral expressions. Numerical applications are presented to show that accurate solutions can be obtained using structural discretizations based on coarse meshes of few but highly rich elements, each of which may have different geometries and alternative approximation laws.     

Applications of a reduction method for reanalysis to nonlinear dynamic analysis of framed structures

 This paper is concerned with the nonlinear dynamic analysis of framed structures using a reduction method recently proposed by the authors. The reduction method is originally devised for structural static reanalysis and has been applied in optimal design of structures to speed up the design process. For nonlinear dynamic analysis of framed structures, the incremental or iterative equations of motion can be transformed into an algebraic system of equations if appropriate integration methods such as Newmark's method are used to integrate the equations of motion. The resulting algebraic system, referred to as the effective system in this paper, changes during the simulation for a nonlinear dynamic problem. Therefore, from the point of view of solving systems of equations, a nonlinear dynamic problem is very similar to an optimal design problem in that the system of equations changes for both types of problems. Hence, any reanalysis technique can be readily applied to carry out a nonlinear dynamic analysis of structures. As demonstrated from the presented numerical examples, the response obtained by the adopted reduction method is as accurate as that obtained by the Cholesky method, and as estimated from the operation counts involved in the method, it is more efficient than the Cholesky method when the half-band width is greater than about 50. Received 23 March 2000     

AN EIGEN-FORCE METHOD FOR FINITE ELEMENT ANALYSIS AND REANALYSIS

This paper presents a force-based finite element method that involves eigen-space transformation of element stiffness matrices in the first analysis. In each subsequent analysis (‘reanalysis’) associated with structural variations, the solution obtained previously is modified making use of intrinsic properties of eigen solutions and avoiding the time-consuming task of solving a large system of equations. The structural variations may involve changes in material properties, birth or death of elements, or change in boundary conditions. Numerical examples are presented to compare the accuracy and computational efficiency of the proposed method with the displacement-based finite element method. © 1997 by John Wiley & Sons, Ltd.     

A universal method for structural static reanalysis of topological modifications

This paper presents a universal method, iterative combined approximation (iterative CA) approach, for structural static reanalysis of all types of topological modifications. The proposed procedure is basically an approximate two-step method. First, the newly added degrees of freedom (DOFs) are assumed to be linked to the original DOFs of the modified structure by means of the Guyan reduction so as to obtain the condensed equation. Second, the displacements of the original DOFs of the modified structure are solved by using the iterative CA approach. And the displacements of the newly added DOFs resulting from topological modification can be recovered. Four numerical examples are given to illustrate the applications of the present approach. The results show that the proposed method is effective for structural static reanalysis of all types of the topological modifications and it is easy to implement on a computer. Copyright © 2004 John Wiley & Sons, Ltd.     

Mesh independent analysis of shell‐like structures

Mesh independent analysis is motivated by the desire to use accurate geometric models represented as equations rather than approximated by a mesh. The trial and test functions are approximated or interpolated on a background mesh that is independent of the geometry. This background mesh is easy to generate because it does not have to conform to the geometry. Essential boundary conditions can be applied using the implicit boundary method where the trial and test functions are constructed utilizing approximate step functions such that the boundary conditions are guaranteed to be satisfied. This approach has been demonstrated for two‐dimensional (2D) and three‐dimensional (3D) structural analysis and is extended in this paper to model shell‐like structures. The background mesh consists of 3D elements that use uniform B‐spline approximations, and the shell geometry is assumed to be defined as parametric surfaces to allow arbitrarily complex shell‐like structures to be modeled. Several benchmark problems are used to study the validity of these 3D B‐spline shell elements. Copyright © 2012 John Wiley & Sons, Ltd.     

A new method for finite element calculation of micromagneticproblems

A novel method has been developed to compute static 2-D and 3-D micromagnetic structures using finite elements. The method can be applied to domain studies, i.e. bubble configuration, Bloch line memories, or magnetooptical materials. All energy terms are minimized without approximation, especially the long-range demagnetizing energy, which causes generally long running time; boundary finite elements are used in this program. The algorithm for minimizing the total energy is gradient or Newton type     

Reanalysis procedure for large structural systems

An efficient procedure is presented for repetitive analysis of structures, with large numbers of degrees of freedom and design variables, as they are progressively modified during the automated optimum design process. The three key elements of the procedure are: (a) lumping of the large number of design variables into a single tracing parameter; (b) operator splitting or additive decomposition of the different arrays in the governing finite element equations of the modified structure into the corresponding arrays of the original structure plus correction terms; and (c) application of a reduction method through the successive use of the finite element method and the classical Bubnov-Galerkin technique. The reanalysis procedure is applied to the linear static and free vibration problems of framed structures. Changes in both the sizing and shape (configuration) design variables are considered. For static problems the similarities between the proposed procedure and the preconditioned conjugate gradient technique are identified and are exploited to provide a physical meaning for the preconditioned residual vectors. The effectiveness of the proposed procedure is demonstrated by means of numerical examples.     

形状修改结构动特性快速分析的边界元摄动法

本文提出了一种用于结构特征值和特征矢量快速分析的边界元摄动法.该方法把结构的形状改变看作其边界节点坐标在某一确定值邻域内的摄动,利用以边界元为基础的摄动理论,得到修改后结构的特征对,避免了重复求解广义特征值问题.文中的算例证明了本方法的有效性.     

Strong discontinuities in antiplane/torsional problems of computational failure mechanics

This paper considers the analysis of localized failures and fracture of solids under antiplane conditions. We consider the longitudinal cracking of shafts in torsion, with the crack propagating through the cross section, besides pure antiplane problems (that is, with loading perpendicular to the plane of analysis). The main goal is the theoretical characterization and the numerical resolution of strong discontinuities in this setting, that is, discontinuities of the antiplane displacement field modeling the cracks. A multi-scale framework is considered, by which the discontinuities are treated locally in the (global) antiplane mechanical boundary value problem of interest, incorporating effectively the contributions of the discontinuities to the failure of the solid. We can identify among these contributions, besides the change in the stiffness of the solid or structural member, the localized energy dissipation associated to the cohesive law governing the physical response of the discontinuity surfaces. A main outcome of this approach is the development of new finite elements with embedded discontinuities for the antiplane problem that capture these solutions, and physical effects, locally at the element level. This local structure allows the static condensation at the element level of the degrees of freedom considered in the approximation of the antiplane displacement jumps along the discontinuity. In this way, the new elements result not only in a cost efficient computational tool of analysis for these problems, but also in a technique that can be easily incorporated in an existing finite element code, while resolving objectively those physical dissipative effects along the localized surfaces of failure. We develop, in particular, quadrilateral finite elements with the embedded discontinuities exhibiting constant and linear approximations of the displacement jumps, showing the superior performance of the latter given the stress locking associated with quadrilateral elements with constant jumps only. This limitation manifests itself in spurious transfers of stresses across the discontinuities, leading to severe oscillations in the stress field and an overall excessively stiff solution of the problem. These features are illustrated with several numerical examples, including convergence tests and validations with analytical results existing in the literature, showing in the process the treatment of characteristic situations like snap-backs, commonly encountered in the modeling of these structural members at failure.