复合材料层合梁在横向线载荷下的脱层扩展

基于可动边界变分原理对层合梁脱层扩展进行了分析;考虑了脱层间的接触效应,建立了层合梁在横向线载荷作用下的非线性控制微分方程及相应的定解条件;应用Griffith准则导出了脱层前缘各点处的能量释放率表达式;通过算例讨论了脱层长度、脱层深度、几何尺寸、材料性质等因素对脱层扩展的影响.研究表明:脱层越长、越深、横向载荷越大,脱层越容易扩展;梁的长高比L/h及材料的E_(11)/E_(22)越大,脱层越不易发生扩展.     

层合板脱层开裂混合状态Hamiltonian元的半解析法

采用准三维模型导出了层合板脱层开裂问题的Ｈａｍｉｌｔｏｎ正则方程，并将有限元法与状态空间法相结合给出一种有效的半解析法，此方法通过层间及裂纹传递矩阵的建立，保证了界面上位移和应力的连续，降低了计算中的未知量数目。     

层板脱层的能量释放率分析

含脱层的层板在承受压缩载荷作用时,很容易发生局部屈曲,导致脱层扩展和结构失效.本文利用可动边界变分问题对脱层扩展进行了分析,导出了脱层前缘各点处的能量释放率表达式.本文还对浅部椭圆脱层进行计算分析,指出:其能量释放率沿脱层边界有很大变化,脱层的扩展方向取决于脱层的形状、受载方式及铺层方向.     

层合厚板混合状态Hamiltonian动力元及其半解析解

文中在时间方向采用Ｌａｐｌａｃｅ变换，给出了层合厚板动力学问题混合状态Ｈａｍｉｌｔｏｎ正则方程及其半解析法．该方法在层板平面内采用通常的有限元离散，而沿板厚方向采用状态控制方程给出解析解答．在层与层之间采用迁移矩阵法，给出层合板上下表面力学量之间的关系式．利用打靶法得到响应在象空间的一般解，然后再利用拉氏逆变换的数值解求出层合板的瞬时位移场和应力场．     

两类有脱层损伤层合圆柱壳的半解析法研究

为了研究层合壳脱层,本文首先建立了柱坐标系下Hamilton 正则方程的8 节点等参元列式;然后分别采用了"先分后合" 模型和"弱粘接" 模型对开口壳的脱层损伤进行了模拟;通过利用层间的力学关系建立了整个壳的求解方程;最后分别从粘接完好和脱层两类情况对开口壳进行研究,并计算脱层前缘裂纹扩展的能量释放率. 数值实例的分析结果表明环向脱层受外载荷影响大于轴向脱层外载荷影响,脱层深度对两类脱层模型影响较大.     

轴压层合结构脱层屈曲及其扩展研究进展

脱层及其进一步扩展可以降低层合结构的强度．首先简单介绍了脱层的一般概念、起因及其分类．从一维脱层、二维脱层和柱壳脱层三个方面介绍了脱层问题的研究概况．指出拉弯耦合和横向剪切效应对脱层结构的屈曲载荷和后屈曲特性影响很大;对于不同的材料特性和尺寸比率,脱层结构的屈曲模态和最终承载能力也不同．最后提出了需进一步深入研究的问题      

复合材料条形域问题混合状态Hamiltonian元的半解析解

给出了复合材料条形域问题的混合状态Ｈａｍｉｌｔｏｎ正则方程及其有效的半解析法。该方法不同于通常的半解析法，需先给出满足规则几何形状和简单边界条件的解析函数，利用Ｈａｍｉｌｔｏｎ矩阵的正交性质，采用控制论中的理论与方法后给出复杂几何形状和边界条件的解析函数，这样沿板厚方向就不需引入任何有关位移和应力的人为假设，从而引入了复合材料计算中剪切效应的影响，且发挥了Ｈ型方程的传递矩阵法优点，保证了层间位移和应刀的连续，建立了条形梁上下表面相变量之间的关系式，然后利用打靶法进行求解。     

含脱层层合板的能量释放率各型分量分析

本文是文献［１］的继续。文献［１］利用可动边界变分问题，导出了层合板内部脱层前缘各点处的总能量释放的表达式。在此基础上，本文对文献［１］的分析模型作了进一步的完善，导出了层板理论分析下的能量释放率各型分量的表达式，并对圆形脱层进行了计算分析。     

用Hamilton半解析法分析固化降温过程中的层间热应力

推导了增量形式Ｈａｍｉｌｔｏｎ半解析法公式；给出了层合板瞬态热弹性问题的求解过程；对复合材料层合板在固化降温过程中的热应力进行了分析。结果表明，在降温过程中层合板内将会出现较大的应力峰值，这些应力峰值将是导致层合板在固化工艺过程中出现破坏的原因。本文的工作将对固化工艺研究具有参考价值。     

湿热条件下具脱层压电层合梁的后屈曲及脱层扩展分析

考虑湿热条件、横向剪切变形、几何非线性和压电效应的影响,建立具脱层压电层合梁的本构关系和非线性平衡微分方程,采用有限差分法和迭代法对问题进行求解;在此基础上.应用Griffith准则,导出了脱层前缘处的能量释放率表达式,讨论了不同因素对压电层合梁后屈曲性能和脱层扩展的影响.     

A finite element model for linear viscoelastic behaviour of pultruded thin-walled beams under general loadings

A finite element model for orthotropic thin-walled beams subject to long-term loadings is presented. The hypothesis, rather usual for thin-walled beams, of cross-sections remaining undistorted in their own planes after deformation is introduced, so reducing the number of d.o.f.’s and, consequently, the computational effort of the analysis. The model is used to perform linear viscoelastic analysis of prismatic beams with general cross-sections, i.e., open, closed or multi-cell. As far as the constitutive viscoelastic law is concerned, a generalized linear Maxwell model is adopted. Making use of the exponential algorithm, differential equations are written in incremental form and integration is performed adopting time intervals of variable length. Numerical examples are finally presented, concerning glass-fibre pultruded shapes under long-term loadings. Displacement evolution with time and stress redistribution adopting different creep laws are presented. Convergence features of the proposed finite element and time integration procedure are also shown.     

Asymptotic modelling of the linear dynamics of laminated beams

We study the linear dynamics of a layered elastic beam by means of the asymptotic expansion method. The beam consists of three linearly elastic isotropic layers: the middle layer is considered to be thinner and softer than the upper and lower ones. We characterize the limit models by distinguishing three cases of natural frequencies: the low frequencies associated with flexural vibrations, the mean frequencies associated with axial vibrations and the high frequencies, associated with transversal shear and pinching vibrations.     

Delamination growth for composite laminated cylindrical shells under external pressure

The delamination growth may occur in delaminated cylindrical shells under external pressure.This will lead to failure of structure.By using the variational principle of moving boundary and considering the contact effect between delamination regions,in this work,the delamination growth was investigated for cylindrical shells under the action of external pressure.At the same time,according to the Griffith criterion,the formulas of energy release rate along the delamination front were obtained.In the numerical calculation,the delamination growth of axisymmetrical laminated cylindrical shells was analyzed,and the effects of delamination sizes and depths,the geometrical parameters, the material properties,and the laminate stacking sequences on delamination growth were discussed.     

Improved torsional analysis of laminated box beams

The improved torsional analysis of the laminated box beams with single- and double-celled sections subjected to a torsional moment is performed by introducing 14 displacement parameters. For this, a thin-walled laminated box beam theory considering the effects of shear and elastic couplings is presented. The governing equations and the force-displacement relations are derived from the variation of the strain energy. The system of linear algebraic equations with non-symmetric matrix is constructed by introducing the displacement parameters and by transforming the higher order simultaneous differential equations into first order ones. This numerical technique determines eigenmodes corresponding to 12 zero and 2 non-zero eigenvalues and derives displacement functions for displacement parameters based on the undetermined parameter method. Finally, the element stiffness matrix is determined using the member force-displacement relations. The theory developed by this study is validated by comparing several torsional responses from the present approach with those from the finite element beam model using the Lagrangian interpolation polynomials and three-dimensional analysis results using the shell elements of ABAQUS for coupled laminated beams with single- and double-celled sections.     

Delamination growth of laminated composite cylindrical shells

The local buckling may occur in delaminated cylindrical shells under axial compression. This often causes delamination growth and structure failure. Based on the variational principle of moving boundary, in this paper, the postbuckling governing equations for the laminated cylindrical shells are derived, and the corresponding boundary and matching conditions are given. At the same time, according to the Griffith criterion, the formulas of energy release rate along the delamination front are obtained and the delamination growth is studied. In the numerical calculation, the delamination growth of axisymmetrical laminated cylindrical shells is analyzed, and the effects of delamination sizes and depths, the boundary conditions, the material properties and the laminate stacking sequences on delamination growth are discussed.     

Anomalous behavior of elastoplastic and viscoelastic beams under pulsed and harmonic loadings

S. P. Timoshenko Mechanics Institute, Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 30, No. 3, pp. 82–88, March, 1994.     

Stress and strain analysis in elastic laminated composite beams

A detailed theoretical analysis of stress and strain in fiber-reinforced, laminated composite beams is presented within the framework of three-dimensional theory of thermo-elastodynamics. Each of reinforcing and matrix layers is made of different anisotropic material and is of different constant thickness. By the use of a variational theorem, the fully non-linear governing equations are consistently obtained for the case when the displacement components of each layer are taken to vary linearly over the cross-section of the layer. Then the linear version of the resulting equations, including the uniqueness of its solution is given, and the general results are briefly discussed.

---

Zusammenfassung In der vorliegenden Abhandlung wird eine detaillierte Spannungs-und Verzerrungsuntersuchung von faserverstärkten laminierten Balken innerhalb der dreidimensionalen thermo-elastodynamischen Theorie durchgeführt. Für jede Verstärkungs-und Bindeschicht wird unterschiedliches anisotropes Verhalten und unterschiedliche Schichtstärke vorausgesetzt. Unter Annahme eines linearen Verlaufs der im Querschnitt liegenden Verformungskomponenten über jede einzelne Schicht werden mit Hilfe eines Satzes der Variationsrechnung die vollständigen nichtlinearen Grundgleichungen abgeleitet. Damit ist auch die linearisierte Form der Gleichungen mit eindeutiger Lösung bestimmt. Eine kurze Untersuchung der Ergebnisse in ihrer allgemeinen Form ist angeschlossen.

     

Uniform strength design of beams with non-zero minimum flexural rigidity under multiple loadings

The analytical method for uniform strength design (U.S.D.) of statically indeterminate beams is extended to deal with a preassigned constraint of non-zero minimum flexural rigidity and multiple load cases. And a numerical method of finding the U.S.D. is presented. Therefore we have a uniform procedure of solution of U.S.D. to beams with arbitrary cross-sectional shape and acted upon by several loadings and subjected to the constraint of minimum flexural rigidity.     

Transient response of laminated plates with arbitrary laminations and boundary conditions under general dynamic loadings

The dynamic analysis of laminated plates with various loading and boundary conditions is presented employing generalized differential quadrature (GDQ) method. The first-order shear deformation theory is considered to model the transient response of the plate. The GDQ technique together with Newmark integration scheme is employed to solve the system of transient equations governing dynamics of the plate. Different symmetric and asymmetric lamination sequences together with various combinations of clamped, simply supported, and free boundary conditions are considered. Particular interest of this study regards to asymmetric orthotropic plates having free edge and mixed boundary conditions. It is shown that the method provides reasonably accurate results with relatively small number of grid points. Comparison of the results with those of other methods demonstrates a very good agreement. It is also revealed that the present method offers similar order of accuracy for all variables including displacements and stress resultants.     

Linear viscoelastic analysis of straight and curved thin-walled laminated composite beams

This paper is devoted to study the behavior, in the range of linear viscoelasticity, of shear flexible thin-walled beam members constructed with composite laminated fiber-reinforced plastics. This work appeals to the correspondence principle in order to incorporate in unified model the motion equations of a curved or straight shear-flexible thin-walled beam member developed by the authors, together with the micromechanics and macromechanics of the reinforced plastic panels. Then, the analysis is performed in the Laplace or Carson domains. That is, the expressions describing the micromechanics and macromechanics of a plastic laminated composites and motion equations of the structural member are transformed into the Laplace or Carson domains where the relaxation components of the beam structure (straight or curved) are obtained. The resulting equations are numerically solved by means of finite element approaches defined in the Laplace or Carson domains. The finite element results are adjusted with a polynomial fitting. Then the creep behavior is obtained by means of a numerical technique for the inverse Laplace transform. Predictions of the present methodology are compared with experimental data and other approaches. New studies are performed focusing attention in the flexural–torsional behavior of shear flexible thin-walled straight composite beams as well as for thin-walled curved beams and frames.