基于拟应变法的壳单元大变形分析及在冲击动力问题中的应用

为了简便有效地解决板壳结构的大变形问题，本文针对八节点相对自由度壳单元进行研究。该单元的位移场由壳的中面节点位移和上表面节点的相对位移组成，不带有转动变量。所有的研究都是基于完全的三维位移、应力、应变场。采用拟应变法，对应变场另行假设，能够改善该单元在大变形情况下的计算精度。通过引入Wilson非协调模式，构造了大变形情况下的拟应变场表达式，给出了该单元用于解决非线性动力分析问题的有限元求解方程。通过算例表明，本文针对相对自由度壳单元提出的方法及推导的公式，能够解决冲击动力问题中的大变形问题。     

A new approach to on-line vibration monitoring and fault diagnosis

This paper presents a finite element method by deriving the stiffness matrix of cracked element from the stress intensity factor. The method can be used to evaluate the strain response of the cantilever beam with a single edge crack. By using the method of identification in time domain, the modal parameters are identified and at the same time the effect of crack closure is taken into consideration. Analysis has also been made of the sensitivity of the strain to the faults. Test results show that the strain response is more sensitive to faults than the displacement response. Then, a distinguishing function is introduced, which is more effective than any other existing ones in failure detection. Finally a new approach to on-line vibration monitoring and fault diagnosis is given.     

正装结构非线性应力应变累加规律研究

基于有限位移理论的正装结构非线性分析理论对解决超大跨度、柔性结构的非线性计算有重大意义.文中探讨了正装结构非线性的分析特点,研究了其应变场与应力场的Kirchhoff应力张量与Lagrange应变张量的适用性,提出了正装结构非线性分析中应力场与应交场的累加规律,导出了拖动坐标法的虚功增量方程,以此对杆系结构非线性分析常用的CR法和UL列式进行了精度比较分析.文中研究成果可为正装结构的非线性分析提供理论指导.     

Damage identification from flexural strain histories

Damage identification of a thin disk struck by a penetrating projectile is analyzed. The disk is segmented into annular regions each with different properties. The footprint and damage radii form two of several segments in the discretization. Modal response of the segmented disk is determined by combining transfer matrices of successive annular segments and dynamic impedance of the central segment. Transient response of the intact disk proceeds by modal analysis until damage occurs. Following damage, transient response continues for the segmented disk excluding the damaged zone with initial conditions equal to those of the final state of the intact disk at the instant of damage. Peak amplitude of the damaged disk is smaller than that of the intact disk. This is caused by cessation of the forcing pulse and sudden stress release along the damaged perimeter. Non-linear coupling with extensional motions reduces peak flexural strain while extensional strain remains comparatively small.     

基于应变脉冲响应协方差的损伤识别方法研究

基于振动参数的结构损伤识别,是近年来土木工程的热点研究课题,振动参数包括频率、振型、频响函数、模态应变能、应变响应和加速度响应等,当结构损伤时,损伤位置附近将产生应力重分布,从而引起应变的变化,因此对比损伤前后的应变或者应变响应参数,可以用来识别结构损伤.提出了一种应变脉冲响应协方差参数,它是应变脉冲响应在时间区间上的能量积分;推导并证明了该参数是结构模态参数(频率,位移模态,应变模态,阻尼等)的函数,可用来表征结构状态.相比于传统的模态参数识别方法,可以保留更高阶的模态参数,而且避免了模态识别可能引起的误差;基于简支钢梁的多种损伤工况,研究和展示了该参数的特性,通过数值模拟发现,该参数能简单直观地判定损伤发生和识别损伤位置,无需建立结构分析模型,只需比较结构损伤前后的应变脉冲响应协方差参数即可;该参数简便易算,具有较好的抗噪性能,对结构损伤敏感,而且对结构刚度减少呈现一致变化特性,所以适合实际工程结构的健康监测和损伤识别.     

Finite versus small strain discrete dislocation analysis of cantilever bending of single crystals

Plastic size effects in single crystals are investi-gated by using finite strain and small strain discrete dislo-cation plasticity to analyse the response of cantilever beam specimens. Crystals with both one and two active slip sys-tems are analysed, as well as specimens with different beam aspect ratios. Over the range of specimen sizes analysed here, the bending stress versus applied tip displacement response has a strong hardening plastic component. This hardening rate increases with decreasing specimen size. The hardening rates are slightly lower when the finite strain discrete disloca-tion plasticity (DDP) formulation is employed as curving of the slip planes is accounted for in the finite strain formulation. This relaxes the back-stresses in the dislocation pile-ups and thereby reduces the hardening rate. Our calculations show that in line with the pure bending case, the bending stress in cantilever bending displays a plastic size dependence. How-ever, unlike pure bending, the bending flow strength of the larger aspect ratio cantilever beams is appreciably smaller. This is attributed to the fact that for the same applied bend-ing stress, longer beams have lower shear forces acting upon them and this results in a lower density of statistically stored dislocations.     

模态理论的进展

传统模态理论的基本思想,近年来得到进一步发展和完善,并被引伸到非线性结构振动分析、应力应变振动分析等领域中,发展迅速．本文在总结近年来国内外文献的基础上,根据笔者自己的研究,较系统地介绍了线性位移实模态、复模态分析,广义模态分析,非线性结构系统模态分析,应力应变场模态分析等方面的研究情况．      

Large deformation of incompressible rubber cylinder under plane strain

The large deformation of incompressible rubber cylinder under inner pressure is analyzed by a kind of new rubber materials strain energy function. The theory formulation for the displacement and stress is presented. The penalty finite element formulation is established in order to analyze nonlinear rubber materials, and the results of finite element method agree well with theoretical ones. A new method for controlling the calculating stability and convergence rates is put forward. The selection of the appropriate penalty factor and its influence on calculated results are discussed.     

Displacement and strain of vibrating structures using time-average holography

A technique for computing the bending strain resulting from the resonant modal deformation of vibrating plate-like structures is described. Interferometric fringes obtained by time-average holography are used as the basis for generating a mathematically continuous series approximation of a plate-like structure's normal displacement. The terms of the series consist of the clamped-free or free-free eigenfunctions of a simple beam. The bending strain is then obtained by computing the second derivative of the displacement series. The coefficients of the terms of the displacement series are computed for a given segment of a cantilevered plate-like structure based upon the holographic-fringe values lying along the same plate segment. A linear least-squares-solution routine is used to solve for the series coefficients, called modal weighting coefficients, in terms of the normal displacement values obtained from the holographic-fringe value. A ‘best fit’ solution is thus obtained for the plate displacement. This least-squares approach in conjunction with the fact the beam-series functions exactly satisfy the plate's geometric boundary conditions and approximately satisfy the plate's natural boundary conditions, results in a displacement series that yields quite accurate displacement and bending strain values. The technique described above has been programmed for use on a Tektronix 4010 interactive computer terminal. The accuracy and effectiveness of the computer algorithm, called HOLOCURVE, is checked by determining the displacement and bending strain at selected segment locations for three different modes of vibration of a cantilevered plate. The results are compared to those of an eigenvalue analysis carried out on a finite-element model of the plate using the finite-element computer program, NASTRAN. The HOLOCURVE results are in excellent agreement with the finite-element analysis except for cases where the bending strain is essentially zero as in the case of chordwise segment for a torsional-mode shape.     

On the application of the additive decomposition of generalized strain measures in large strain plasticity

In the present paper two thermodynamically consistent large strain plasticity models are examined and compared in finite simple shear. The first model (A) is based on the multiplicative decomposition of the deformation gradient, while the second one (B) on the additive decomposition of generalized strain measures. Both models are applied to a rigid-plastic material described by the von Mises-type yield criterion. Since both models include neither hardening nor softening law, a constant shear stress response even for large amounts of shear is expected. Indeed, the model A exhibits the true constant shear stress behavior independent of the elastic material law. In contrast, the model B leads to a spurious shear stress increase or drop such that its applicability under finite shear deformations may be questioned.     

在线振动监测与故障诊断的一种新途径

文中由应力强度因子导出含裂纹单元的刚度矩阵,从而提出了一种有限元法.将该法用于单边裂纹悬臂梁,计算了应变响应.用时域法识别了模态参数,并考虑了裂纹闭合的影响.分析了应变响应对故障的敏感度,计算结果表明,应变响应相对于位移响应而言,对故障更敏感.本文还提出了一种判别函数,该函数对于损伤检测,比现有几种判别函数更有效.最后,给出了一种在线振动监测与故障诊断新方法.     

导弹适配器受压及弹射时摩擦力研究

针对导弹适配器的结构特征,分别建立了可压缩橡胶泡沫和不可压橡胶圆筒轴对称平面应变问题有限变形的平衡方程,基于Blatz-Ko应变能函数和三次缩减多项式应变能函数,得到了相应的位移和应力模式;在此基础上求解了适配器受压问题的非线性方程组和导弹发射时适配器所受到的摩擦力.算例分析与有限元数值模拟比较表明:解析解与数值解非常吻合,径向应力在发射筒内外表面误差最大为0.558%,周向应力在粘合面误差最大为0.246%,导弹发射时的最大量纲为一的摩擦力为1.0228.适配器径向应力在材料粘合交界面上最小,在适配器外表面最大,均为压应力;橡胶泡沫和不可压橡胶的周向应力均为压应力,橡胶泡沫的周向应力由内向外变大,不可压橡胶的周向应力由内向外变小.橡胶泡沫的径向受压大于周向受压,不可压橡胶的周向受压大于径向受压.研究不同过盈量对应力和摩擦力的影响表明:过盈量每增加0.0013,橡胶泡沫 层和不可压橡胶层的径向应力约增加0.13,不可压橡胶层的周向应力约增加2.14,而摩擦力约增加0.22.过盈量对不可压橡胶层的周向应力和导弹所受到的摩擦力影响非常大,对橡胶泡沫的径向应力有一定的影响,周向应力变化很小.     

Nonlinear coupled vibration of electrostatically actuated clamped–clamped microbeams under higher-order modes excitation

Nonlinear modal interactions have recently become the focus of intense research in micro-resonators for their use to improve oscillator performance and probe the frontiers of fundamental physics. Understanding and controlling nonlinear coupling between vibrational modes is critical for the development of advanced micromechanical devices. This article aims to theoretically investigate the influence of antisymmetry mode on nonlinear dynamic characteristics of electrically actuated microbeam via considering nonlinear modal interactions. Under higher-order modes excitation, two nonlinear coupled flexural modes to describe microbeam-based resonators are obtained by using Hamilton’s principle and Galerkin method. Then, the Method of Multiple Scales is applied to determine the response and stability of the system for small amplitude vibration. Through Hopf bifurcation analysis, the bifurcation sets for antisymmetry mode vibration are theoretically derived, and the mechanism of energy transfer between antisymmetry mode and symmetry mode is detailed studied. The pseudo-trajectory processing method is introduced to investigate the influence of external drive on amplitude and bifurcation behavior. Results show that nonlinear modal interactions can transit vibration energy from one mode to nearby mode. In what follows, an effective way is proposed to suppress midpoint displacement of the microbeam and to reduce the possibility of large deflection. The quantitative relationship between vibrational modes is also obtained. The displacement of one mode can be predicted by detecting another mode, which shows great potential of developing parameter design in MEMS. Finally, numerical simulations are provided to illustrate the effectiveness of the theoretical results.     

基于渐近传递函数解的截锥壳单元

普通截锥壳单元是分析旋转壳结构的常用单元,但应力计算的精度较差;而渐近传递函数解在圆锥壳的应力分析方面具有很高的计算精度。本文针对一般截锥壳单元应力计算精度不高的缺点,将传递函数法与有限元法进行结合,以圆锥壳的渐近传递函数解为插值函数,直接构造了一种高精度的截锥壳单元,该单元位移插值模式满足相容性和完备性要求,并具有力学概念清楚、计算精度高等特点。数值算例表明,采用该单元进行圆锥壳的内力和自由振动     

Incorporation of yield surface distortion in finite deformation constitutive modeling of rigid-plastic hardening materials based on the Hencky logarithmic strain

In this paper a constitutive model for rigid-plastic hardening materials based on the Hencky logarithmic strain tensor and its corotational rates is introduced. The distortional hardening is incorporated in the model using a distortional yield function. The flow rule of this model relates the corotational rate of the logarithmic strain to the difference of the Cauchy stress and the back stress tensors employing deformation-induced anisotropy tensor. Based on the Armstrong–Fredrick evolution equation the kinematic hardening constitutive equation of the proposed model expresses the corotational rate of the back stress tensor in terms of the same corotational rate of the logarithmic strain. Using logarithmic, Green–Naghdi and Jaumann corotational rates in the proposed constitutive model, the Cauchy and back stress tensors as well as subsequent yield surfaces are determined for rigid-plastic kinematic, isotropic and distortional hardening materials in the simple shear deformation. The ability of the model to properly represent the sign and magnitude of the normal stress in the simple shear deformation as well as the flattening of yield surface at the loading point and its orientation towards the loading direction are investigated. It is shown that among the different cases of using corotational rates and plastic deformation parameters in the constitutive equations, the results of the model based on the logarithmic rate and accumulated logarithmic strain are in good agreement with anticipated response of the simple shear deformation.     

Determination of elastic-plastic stresses and strains from measured surface strain data

A rigorous approach founded in the fundamental principles of plasticity is used to develop an accurate numerical algorithm for the determination of stresses and elastic and plastic strains from total strain data measured on a structure surface. The approach used to develop the algorithm and its relationship to both the flow theory of plasticity and recent advances in tangent stiffness-based numerical solution procedures for elastic-plastic boundary value problems are presented. Verification of the method for plane stress problems is demonstrated. A discussion of how the method can be used with measured surface displacement data is proved.     

岩石变形光纤光栅传感检测的应变传递分析

岩石变形过程可以通过光纤光栅的表面粘贴法进行检测。建立了考虑表面凹槽时的应变传递模型,经过力学分析得出了应变传递方程及传递系数的表达式;在MTS伺服机上进行了单轴压缩实验,借助光纤光栅对加载过程进行了测试。结果表明,传递方程与粘贴层厚度均匀分布时的方程形式相同,只是特征值k不同;换算后光栅的轴向应变与MTS位移计吻合很好,相对误差仅为3.2%;环向测试优于MTS的环向应变计,而两种方法都明显地优于应变片。实验验证了所建模型的正确性。经应变传递换算后,通过光纤光栅可以实现岩石变形过程中与MTS精度相当的高精确测试。     

PLANE STRAIN PROBLEM OF PIEZOELECTRIC SOLID WITH ELLIPTIC INCLUSION

By using the complex variables function theory, a plane strain electro-elastic analysis was performed on a transversely isotropic piezoelectric material containing an elliptic elastic inclusion, which is subjected to a uniform stress field and a uniform electric displacement loads at infinity. Based on the present finite element results and some related theoretical solutions, an acceptable conjecture was found that the stress field is constant inside the elastic inclusion. The stress field solutions in the piezoelectric matrix and the elastic inclusion were obtained in the form of complex potentials based on the impermeable electric boundary conditions.     

基于Hellinger-Reissner变分原理的应变梯度杂交元设计

从一般的偶应力理论出发，基于Hellinger-Reissner变分原理，通过对有限元 离散体系的位移试解引入非协调位移函数，得到了偶应力理论下有限元离散系统的能量相容 条件，并由此建立了应变梯度杂交元的应力函数优化条件. 根据该优化条件，构造了一 个C0类的平面4节点梯度杂交元，数值结果表明，该单元对可压缩和不可压缩状态的 梯度材料均可给出合理的数值结果，再现材料的尺度效应.     

Numerical validation of the shear compression specimen. Part I: Quasi-static large strain testing

The shear compression specimen (SCS), which is used for large strain testing, is thoroughly investigated numerically using three-dimensional elastoplastic finite element simulations. In this first part of the study we address quasi-static loading. A bi-linear material model is assumed. We investigate the effect of geometrical parameters, such as gage height and root radius, on the stress and strain distribution and concentration. The analyses show that the stresses and strains are reasonably uniform on a typical gage mid-section, and their average values reflect accurately the prescribed material model. We derive accurate correlations between the averaged von Mises stress and strain and the applied experimental load and displacement. These relations depend on the specimen geometry and the material properties. Numerical results are compared to experimental data, and an excellent agreement is observed. This study confirms the potential of the SCS for large strain testing of material.