基于内时大变形弹塑性本构模型的镦粗热力耦合分析

采用一个简单机械模型得到了热力耦合的弹塑性大变形本构方程,它满足不可逆热力学的基本约束,并考虑到了储存在残余微应力场中的能量对后续变形的贡献.发展了相应的算法,对弹性压板间的圆柱镦粗进行了分析.结果表明,在镦粗过程中的塑性耗散和工件两端的热传导造成工件中温度分布的不均匀,因此导致了材料力学性能的改变.与实验结果和等温假设下的计算结果进行了比较,表明计及塑性耗散热的计算结果与实验结果更为一致.     

任意的拉格朗日欧拉边界元—有限混合法分析物体撞水响应

计算物体的撞水响应目前已有了一些专用的算法，本文在分析和比较这些算法的基础上，提出了一个解撞水问题的任意的拉格朗日欧拉边界元－有限元混合法，这个方法不仅充分发挥了边界元法计算半空间流场的优越性，而且还能计及液面大晃动的非线性边界条件物体变形所造成的影响，文中给出圆柱刚体和楔形刚柱体两个撞水算例，结果有力表明该方法的可靠性和有效性。     

任意的拉格朗日欧拉边界元－有限元混合法分析物体撞水响应

计算物体的撞水响应目前已有了一些专用的算法．本文在分析和比较这些算法的基础上，提出了一个解撞水问题的任意的拉格朗日欧拉边界元－有限元混合法（ＡＬＥ－ＢＥ－ＦＥＭ），这个方法不仅充分发挥了边界元法计算半空间流场的优越性，而且还能计及液面大晃动的非线性边界条件和物体变形所造成的影响．文中给出圆柱刚体和楔形刚柱体两个撞水算例，结果有力表明该方法的可靠性和有效性。     

一种修正的形状记忆合金本构模型数值算法及应用

采用Hughes-Winget算法修正了已有文献所发展的考虑塑性和相变耦合效应的形状记忆合金(SMA)本构模型的积分算法,使其能适用于发生较大转动变形的问题。据此编制了ABAQUS用户子程序UMAT,对SMA弹簧拉伸和"三点弯"等发生较大转动的问题进行了模拟。结果表明,修正算法可减小结构在发生较大转动变形时采用小变形本构模型计算带来的误差,提高计算过程的收敛速度与稳定性。采用本文的修正算法模拟了Ni Ti SMA的大变形拉伸伪弹性和塑性、SMA板的大挠度弯曲伪弹性和SMA弹簧的大变形拉伸伪弹性行为,结果与试验和其他研究者的计算结果吻合较好,证明了该修正算法的有效性。     

具有非线性表面换热系数半圆柱薄壳在快速冷却过程中的热分析

用实验和数值计算相结合的方法，得到半圆柱壳体快速冷却过程中内外表面的非线性表面换热系数。在此基础上，用有限单元法对半圆柱壳体的热应力和变形进行了分析。在数值计算中，模拟钢的CCT图，计算了奥氏体、珠光体、贝氏体和马氏体的体积百分比，并将热物理性质和力学性能处理为相变体积百分比和温度的函数。所得结果表明，在半圆柱壳体快速冷却过程中的热应力和变形计算中，有必要考虑非线性表面换热系数、相变等非线性效应。     

简支梁大挠度弹性后屈曲载荷与变形的优化算法

针对简支梁结构大挠度后屈曲载荷与变形的计算问题,本文提出了一种直接求解其后屈曲载荷和变形的优化算法。在简支梁处于大挠度屈曲平衡状态下,将梁结构划分为有限子段,以待求后屈曲载荷为设计变量,根据起点的边界条件和每个子段满足的弯矩变形公式,累积计算出其他各个节点的坐标,以得到的终点坐标满足的边界条件构建目标函数模型。在此基础上,通过MATLAB编制优化程序分析了两个典型算例,并将理论结果与相关软件的计算结果进行对比,从而证明了本文算法的正确性。本文算法求解过程简单、快速,具有一定的实用性,为变截面结构大挠度弹性屈曲稳定性问题的研究提供了参考。     

简支梁大变形的优化算法

提出一种求解几何非线性问题的优化算法,并研究了简支梁的几何非线性大变形问题。首先取简支梁大变形后的平衡状态为研究对象,分别创建它的变分模型和微分模型;然后基于微分模型,通过动坐标的迭代关系式求得微段端点坐标,构建微段端点未知坐标的目标函数;最后确定简支梁几何非线性大变形的最优化问题,并编制相应优化程序进行求解。通过分析典型算例,并同有限元方法的计算结果相比较,表明提出的优化算法在求解强几何非线性大变形问题中的正确性,为处理几何非线性大变形问题提供了一种新方法。     

轴向应力波作用下圆柱壳弹性轴对称动力失稳有限元特征值分析

本文运用有限元特征值分析方法对应力波作用下圆柱壳弹性轴对称动力失稳问题进行了研究。基于应力波理论和相邻平衡准则导出了圆柱壳轴对称动力失稳时的有限元特征方程,在此方程中考虑了应力波效应及横向惯性效应,把圆柱壳弹性动力失稳问题归结为特征值问题。通过引入圆柱壳动力失稳时的波前约束条件实现了此类问题的有限元特征值解法。计算结果揭示了圆柱壳弹性轴对称动力屈曲变形发展的机理,以及轴向应力波和屈曲变形的相互作用规律。     

不可压缩流场多体运动问题的两种数值解法

不可压缩流场中多体运动的数值模拟是计算流体动力学的前沿课题,目前可以求解此问题的两种高精度方法是重叠网格法和移动网格法。本文详细讨论了两种方法的理论基础,典型算法的实现过程,并采用两种方法对单圆柱和多圆柱运动问题进行了数值试验。通过分析比较,本文认为重叠网格法计算效率高于移动网格法,重叠网格法比移动网格法更适合于求解物体大位移运动问题,尤其当计算区域几何形状复杂时重叠网格法的优势更加明显。     

光滑粒子法与有限元的耦合算法及其在冲击动力学中的应用

扼要讨论了光滑粒子法的离散思想,充分利用光滑粒子法和有限元方法各自的优点,提出了一种初始时刻用有限元建模,计算过程中大变形单元自动转换为光滑粒子的耦合算法。高速碰撞的系列算例说明,耦合算法不但适宜于计算大变形冲击动力学问题,而且由于集两种方法的优点于一身,可以更高效地模拟一些高速碰撞问题,提高计算效率。     

考虑微缺陷形状的细片层状珠光体钢的损伤本构模型

基于非经典塑性理论和连续介质损伤力学,利用在一个特殊坐标系下基于椭球形孔洞模型得到的可考虑孔洞形状变化混合强化材料的损伤演化率得到了铁素体相的损伤本构方程,通过混合物理论利用铁素体和渗碳体相各自本构关系并考虑其几何特征得到了珠光体团的损伤本构模型。进而采用Hill自洽方法,得到了珠光体材料的宏观损伤本构描述,发展了相应的数值方法与程序。讨论了孔洞形状对材料损伤的影响,并对典型珠光体双相材料BS11在非对称循环加载史下的弹塑性响应特性进行了分析,得到了与实验较为一致的结果。     

用于板料成形反向模拟的特殊应力更新算法

提出了一种改进的反向模拟法,以最终构型为研究对象,采用Euler坐标系,基于虚功原理获得有限元列式. 改进的反向模拟法采用了一种基于塑性流动理论的本构方程,可以充分考虑应变历史对塑性变形的影响. 为了避免流动理论应力更新算法过程中关于未知量\Delta\lambda 的非线性方程的求解,引入等效应力思想,无需Newton-Raphson迭代直接计算未知量\Delta \lambda . 盒形件的拉深实例中,传统的基于塑性形变本构方程的反向模拟法和改进的基于塑性流动本构方程的反向模拟法计算结果,分别与基于增量有限元法的正向数值模拟求解器LS-DYNA计算结果进行对比. 通过获得的坯料轮廓、成形极限图、等效应变分布、计算效率等的比较,验证了所提出的基于塑性流动理论本构模型的应力更新算法的有效性.      

大变形中摩擦接触问题的数值模拟及应用

大变形的摩擦接触是复杂的非线性问题 ,本文介绍了一种处理摩擦接触问题的数值方法。采用接触单元技术模拟接触界面 ,基于弹塑性理论形式的非经典Coulomb摩擦定律及罚函数方法建立了摩擦接触的增量本构关系。结合大变形的增量分析格式给出了积分摩擦接触本构方程的回映方法。这种处理摩擦接触问题的方法计算简单、使用方便。给出的计算实例及应用实例说明了方法的精度与稳定性     

Analysis for polycrystal nonproportional cyclic plasticity with a dissipated energy based rule for cross-hardening

Based on a nonclassical hardening law and the Hill’s self-consistent scheme, a new approach is proposed for the analysis of polycrystal nonproportional cyclic plasticity. A novel parameter related to the plastic dissipation on each slip system is proposed and embedded in the Bassani’s definition of cross-hardening. The tangential elastoplastic tensor relating the increments of stress and strain in a single crystal is derived and the corresponding numerical algorithm for polycrystal plasticity is developed. The elastoplastic response of 316 stainless steel subjected to typical biaxial nonproportional strain cycling is analyzed, and the main features are well replicated. The validity of the proposed approach is demonstrated by the satisfactory agreement between the computed results and experimental observation.     

Method of successive approximations for solving boundary-value problems of plasticity with allowance for the stress mode

A method for solving boundary-value problems of plasticity with allowance for the stress mode is developed. To describe the elastoplastic deformation of an isotropic material, use is made of constitutive equations that include two nonlinear functions dependent on the stress mode and determined experimentally. The elastoplastic state of a thin cylindrical shell under axisymmetric loading is calculated as a numerical example. The numerical results demonstrate good convergence of the method. The effect of the stress mode on the strain distribution in a cylindrical shell is assessed     

BUCKLING AND POSTBUCKLING ANALYSIS OF ELASTO-PLASTIC FIBER METAL LAMINATES

The elasto-plastic buckling and postbuckling of fiber metal laminates （FML） are studied in this research. Considering the geometric nonlinearity of the structure and the elasto- plastic deformation of the metal layers, the incremental Von Karman geometric relation of the FML with initial deflection is established. Moreover, an incremental elasto-plastic constitutive relation adopting the mixed hardening rule is introduced to depict the stress-strain relationship of the metal layers. Subsequently, the incremental nonlinear governing equations of the FML subjected to in-plane compressive loads are derived, and the whole problem is solved by the iterative method according to the finite difference method. In numerical examples, the effects of the initial deflection, the loading state, and the geometric parameters on the elasto-plastic buckling and postbuckling of FML are investigated, respectively.     

Analysis of material instabilities in inelastic solids by incremental energy minimization and relaxation methods: evolving deformation microstructures in finite plasticity

We propose an approach to the definition and analysis of material instabilities in rate-independent standard dissipative solids at finite strains based on finite-step-sized incremental energy minimization principles. The point of departure is a recently developed constitutive minimization principle for standard dissipative materials that optimizes a generalized incremental work function with respect to the internal variables. In an incremental setting at finite time steps this variational problem defines a quasi-hyperelastic stress potential. The existence of this potential allows to be recast a typical incremental boundary-value problem of quasi-static inelasticity into a principle of minimum incremental energy for standard dissipative solids. Mathematical existence theorems for sufficiently regular minimizers then induce a definition of the material stability of the inelastic material response in terms of the sequentially weakly lower semicontinuity of the incremental variational functional. As a consequence, the incremental material stability of standard dissipative solids may be defined in terms of the quasi-convexity or the rank-one convexity of the incremental stress potential. This global definition includes the classical local Hadamard condition but is more general. Furthermore, the variational setting opens up the possibility to analyze the post-critical development of deformation microstructures in non-stable inelastic materials based on energy relaxation methods. We outline minimization principles of quasi- and rank-one convexifications of incremental non-convex stress potentials for standard dissipative solids. The general concepts are applied to the analysis of evolving deformation microstructures in single-slip plasticity. For this canonical model problem, we outline details of the constitutive variational formulation and develop numerical and semi-analytical solution methods for a first-level rank-one convexification. A set of representative numerical investigations analyze the development of deformation microstructures in the form of rank-one laminates in single slip plasticity for homogeneous macro-deformation modes as well as inhomogeneous macroscopic boundary-value problems. The well-posedness of the relaxed variational formulation is indicated by an independence of typical finite element solutions on the mesh-size.     

Nonlinear finite element analysis of no-tension masonry structures

A numerical approach for structural analysis of masonry walls in plane stress conditions is presented. The assumption of a perfectly no-tension material (NTM) constitutive model, whose relevant equations are in the form of classical rate-independent associated flow laws of elastoplastic material, allows one to adopt numerical procedures commonly used in computational plasticity. An accuracy analysis on the integration algorithm employed in the solution of constitutive relations has been carried out. The results obtained for some relevant case-studies and their comparison with data, available in the literature show the effectiveness of the proposed method.

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Sommario Si presenta un approccio numerico per l'analisi strutturale di pareti in muratura in stato piano di tensione. L'assunzione di un modello costitutivo per materiale perfettamente non resistente a trazione (NTM), le cui equazioni sono esprimibili nella classica forma incrementale delle leggi dello scorrimento plastico di tipo associato per materiali elastoplastici, consente di adottare procedure numeriche comunemente utilizzate in plasticità computazionale. Si conduce un'analisi di accuratezza dell'algoritmo utilizzato nell'integrazione delle equazioni costitutive del modello esaminato. I risultati ottenuti per alcuni casi analizzati ed il confronto effettuato con esempi riportati in letteratura mostrano l'efficienza dell'approccio proposto.