钢管混凝土结构材料非线性的一种有限元分析方法

为了更简单地考虑梁单元的材料非线性受力性能,把断面广义力和广义应变的概念运用于单元分析中,将单元的弹塑性刚度矩阵分离为弹性刚度矩阵和塑性刚度矩阵。这样,梁单元的变形可以由弹性变形和塑性变形简单地迭加,结构内力可通过弹性应变能的斜率(弹性刚度矩阵)与位移的乘积求得,从而在增量-迭代计算时可较准确且较快地计算出结构变形后的不平衡力。应用这一计算方法,推导了基于纤维模型的三维梁单元的钢管混凝土结构的有限元基本公式,并将其植入能考虑几何非线性的三维梁单元非线性计算程序NL_Beam3D中以计算结构的双重非线性问题。算例分析表明该方法和程序能较准确地反映钢管混凝土结构的双重非线性特性。     

A simple computer implementation of membrane wrinkle behaviour via a projection technique

A simple computer implementation of membrane wrinkle behaviour is presented within the classical elastic plane stress constitutive model. In the present method, a projection technique is utilized for modelling of the wrinkle mechanisms, in which the total strains in wrinkled membranes are decomposed into elastic and zero‐strain energy parts, and a projection matrix that extracts the elastic parts from the total strains is derived. The resulting modified elasticity matrix that represents the stress–strain relations in wrinkled membranes is thus obtained as product of the classical elasticity matrix and the projection matrix. The modified elasticity matrix is straightforward to implement within the context of the finite element method. Numerical examples are presented to demonstrate the accuracy and effectiveness of the proposed method. Copyright © 2007 John Wiley & Sons, Ltd.     

On the determination of interfacial stresses in a composite material

The conventional finite element method has been modified to allow the elastic stresses along the fibre matrix interfaces of a composite to be determined with improved accuracy. The results obtained by this 'modified' method are compared with both a photoelastic and some traditional finite element solutions.     

Flexural response to impulsive loads of a fluid-saturated thin poroelastic circular plate

Biot's poroelastic theory is used with classic plate theory and plane stress theory to determine the constitutive relationships for a thin poroelastic plate. The dynamic equations for the thin poroelastic plate are derived from the extended Hamilton's principle. The dynamic equations are then transformed to frequency domain and Galerkin's finite element method is used to derive the stiffness matrix of a triangular plate element. When impulsive loads and elastic boundary conditions are applied, the finite element frequency domain analysis for the thin poroelastic plates is achieved. Vibration behavior of thin elastic and poroelastic circular plates is accurately predicted.     

基于单胞解析模型的复合材料层合板渐进损伤数值分析

基于单胞解析模型,建立一种从复合材料细观组分到宏观层合板的渐进损伤分析模型。根据连续介质力学和均匀化方法构建细-宏观关联矩阵,通过该矩阵将细观组分材料的弹性和损伤性能传递到宏观复合材料中。该模型只需给出纤维和基体的材料属性及纤维体积含量无需层合板的弹性和强度参数,通过组分材料的损伤失效判据确定其是否损伤,如果发生损伤则用损伤因子折算成相应的刚度衰减。通过用户材料子程序UMAT 及VUMAT将单胞解析模型以及损伤理论嵌入到有限元软件ABAQUS 中,对开孔复合材料层合板的渐进损伤过程进行模拟,预测了层合板强度。结果表明:预报的强度与试验值吻合较好,验证了该方法的有效性。     

A numerical procedure for multiple circular holes and elastic inclusions in a finite domain with a circular boundary

This paper describes a numerical procedure for solving two-dimensional elastostatics problems with multiple circular holes and elastic inclusions in a finite domain with a circular boundary. The inclusions may have arbitrary elastic properties, different from those of the matrix, and the holes may be traction free or loaded with uniform normal pressure. The loading can be applied on all or part of the finite external boundary. Complex potentials are expressed in the form of integrals of the tractions and displacements on the boundaries. The unknown boundary tractions and displacements are approximated by truncated complex Fourier series. A linear algebraic system is obtained by using Taylor series expansion without boundary discretization. The matrix of the linear system has diagonal submatrices on its diagonal, which allows the system to be effectively solved by using a block Gauss-Seidel iterative algorithm.     

Some issues on nanoindentation method to measure the elastic modulus of particles in composites

The application of the indentation method to measure the elastic modulus of particles embedded in a composite is theoretically investigated in this paper by finite element simulation. The Oliver–Pharr method, which is widely used in commercial nanoindentation instruments, is used to probe the elastic modulus of the particle from the simulated indentation curve. The predicted elastic modulus is then compared with the inputted value. Two cases are studied, that of a stiff particle embedded in a soft matrix and a soft particle embedded in a stiff matrix. In both of these cases, there exists a particle-dominated depth. If the indentation depth lies within this particle-dominated depth, the Oliver–Pharr method is able to be applied to measure the particle’s elastic modulus with sufficient accuracy if the real contact area is used. This could lead to an experimentally-convenient method of determining the primary properties of individual particle, providing they can be well dispersed in the polymeric matrix.     

Machining of UD-GFRP composites chip formation mechanism

The chip formation mechanism in orthogonal machining of unidirectional glass fiber reinforced polymer (UD-GFRP) composites is simulated using quasi-static analysis. Dynamic explicit finite element method with mass scaling is used for analysis to speed up the solution. A two-dimensional, two-phase micromechanical model with elastic fiber, elasto-plastic matrix and a cohesive zone is used to simulate the debonding interface between the fiber and the matrix. The elements of the fiber are failed once the maximum principal stress reaches the tensile strength and the matrix elastic modulus is degraded once the ultimate strength is reached. The effect of fiber orientation, tool parameters and operating conditions on fiber and matrix failure and chip size is also investigated. The degradation of the matrix adjacent to the fiber occurs first, followed by failure of the fiber at its rear side. The extent of sub-surface damage due to matrix cracking and interfacial debonding is also determined.     

Evaluation of elastic accommodation energies during solid-state phase transformations by the finite element method

The precipitation of a solid phase in a rigid matrix leads to the creation of strain energy in the system as the transformation strain cannot be relaxed in the case of solid state transformations. A finite element model based on the initial strain approach has been presented to evaluate elastic accommodation energies during solid-state transformations. The finite element analysis (FEA) reveals that the total system energy increases with increase in the ratio of the modulus of the precipitate to that of the matrix, and with increase in misfit strain between the matrix and the precipitate. The analysis has been performed by considering the transformation to progress from the centre to the surface and from the surface to the centre of the three dimensional axisymmetric system. The elastic accommodation energies obtained by the FEA are comparable to energies obtained by continuum mathematical models.     

Diametral compression of pultruded composite rods

Diametral compression tests were performed on pultruded composite rods comprised of unidirectional glass or carbon fibers in a common matrix. During compression tests, acoustic emission (AE) activity was recorded and images were acquired from the sample for analysis by digital image correlation (DIC). In both composite systems, localized tensile strain developed in the transverse plane under the load platens prior to failure, producing non-linearity in the load–displacement curve and AE signals. In situ SEM diametral compression tests revealed the development of matrix microcracking and debonding in regions of localized strain, perpendicular to the tensile strain direction (parallel to the load axis). Comparison of linear finite element simulations and experimental results showed a deviation from linear elastic behavior in the load displacement curve. The apparent transverse modulus, in plane shear modulus, and transverse tensile strength of the GF rod was greater than that of the CF rod, and fracture surfaces indicated greater fiber/matrix adhesion in the GF system compared to the CF system. A mixed mode fracture surface showed that two failure modes were active – matrix tensile failure and matrix compression failure by shear near the loading edge.     

Finite layer analysis of layered elastic materials using a flexibility approach. Part 1—Strip loadings

It is well known that the analysis of a horizontally layered elastic material can be considerably simplified by the introduction of a Fourier or Hankel transform and the application of the finite layer approach. The conventional finite layer (and finite element) stiffness approach breaks down when applied to incompressible materials. In this paper these difficulties are overcome by the introduction of an exact finite layer flexibility matrix. This flexibility matrix can be assembled in much the same way as the stiffness matrix and does not suffer from the disadvantage of becoming infinite for an incompressible material. The method is illustrated by a series of examples drawn from the geotechnical area, where it is observed that many natural and man-made deposits are horizontally layered and where it is necessary to consider incompressible behaviour for undrained conditions.     

Inclusion problem of a two-dimensional finite domain: The shape effect of matrix

With the advance in composite mechanics and micromechanics, there are increasing demands for analytical solutions of inclusion problems in a bounded domain. To echo this need, this study is focused on establishing explicit expressions of elastic fields for a 2D elastic domain containing a circular inclusion at center. Unlike the configuration in the classical Eshelby formulation, the elastic domain in this study is bounded and has shapes other than a circle. To circumvent the mathematical difficulty in solving Green’s function in a finite domain, an approach powered by complex potential method, which has been successfully employed to formulate the elastic fields for inclusion problems where matrix is unbounded or bounded by a circle, is extended to finite domains displaying complicated shapes, particularly, a Pascal’s limaçon and a curved square (an approximation of perfect square) in this study. In order to take advantage of the mathematical simplicity inherent in expressing a circular geometry, conformal mapping is used to transform the complex geometry of the finite domain of interest to a unit circle. The governing complex potentials, which capture the discontinuity on the inclusion–matrix interface due to the uniform eigenstrain within the inclusion, are formulated with the aid of Cauchy integral and then explicitly identified by satisfying the prescribed boundary conditions. In this study, the displacement fields for finite domains bounded by a Pascal’s limaçon and a curved square are obtained based on Dirichlet (displacement) boundary conditions imposed by the far field strain. In addition to asymptotical behaviors, firm agreement is also achieved when the analytical solutions based on complex potentials are compared with the FEM results. Furthermore, inverse of the conformal mapping is discussed here in order to get the explicit expression for elastic fields.     

Numerical characterization of CNT-based polymer composites considering interface effects

Carbon nanotubes (CNTs) possess exceptional mechanical properties and are therefore suitable candidates for use as reinforcements in composite materials. Load transfer in nanocomposite materials is achieved through the CNT/matrix interface. Thus, to determine nanocomposite mechanical properties, the interface behavior must be determined. In this investigation, finite element method is used to investigate the effects of interface strength on effective CNT-based composite mechanical properties. Nanocomposite mechanical properties are evaluated using a 3D nanoscale representative volume element (RVE). A single nanotube and the surrounding polymer matrix are modeled. Two cases of perfect bonding and an elastic interface are considered. For the perfect bonding interface, the no slip conditions are applied. To better investigate the elastic interface behavior, two models are proposed for this type of interface. The first elastic interface model consists of a thin layer of an elastic material surrounding the CNT. In the second elastic interface model, a series of spring elements are used as the nanotube/matrix interface. The results of numerical models indicate the importance of adequate interface bonding for a more effective strengthening of polymer matrix by CNT’s.     

Nonlinear Viscoelastic Response of Unidirectional Polymeric Laminated Composite Plates Under Bending Loads

Nonlinear bending analysis of polymeric laminated composite plate is examined considering material nonlinearity for viscoelastic matrix material through a Micro–macro approach. The micromechanical Simplified Unit Cell Method (SUCM) in three-dimensional closed-form solution is used for the overall behavior of the unidirectional composite in any combination of loading conditions. The elastic fibers are transversely isotropic where Schapery single integral equation in multiaxial stress state describes the matrix material by recursive-iterative formulation. The finite difference Dynamic Relaxation (DR) method is utilized to study the bending behavior of Mindlin annular sector plate including geometric nonlinearity under uniform lateral pressure with clamped and hinged edge constraints. The unsymmetrical laminated plate deflection is predicted for different thicknesses and also various pressures in different time steps and they are compared with elastic finite element results. As a main objective, the deflection results of viscoelastic laminated sector plate are obtained for various fiber volume fractions in the composite system.     

A mechanical analysis of metallic tritide aging by helium bubble growth

A simple mechanical model is proposed for the aging of a metallic tritide. The material is assumed to be elastic–power law viscoplastic. Part of the helium atoms generated by tritium decay form spherical bubbles that weaken the elastic moduli of the overall material. By contrast, others can be stored in solid solution in the matrix and are likely to increase the moduli. Two variants of the model are compared, assuming either instantaneous or finite rate diffusion of helium. They predict globally similar evolutions of the gas pressure inside the bubbles, the geometrical parameters (bubble radius, overall swelling), as well as the matrix and overall elastic moduli. The results are in good agreement with atomistic calculations of the pressure evolution. Furthermore, recent experimental measurements of the Young modulus changes during aging are better reproduced when He diffusion rate is finite, thus supporting the second variant of the model.     

A material model for the finite element analysis of metal matrix composites

A finite element based procedure is presented which accounts for micromechanical nonlinear behavior of the matrix material in continuous fiber reinforced composites. The micromechanical model is a periodic hexagonal array of elastic fibers embedded in an elastic-plastic matrix material. This model is used to calculate the overall instantaneous material matrix at material points of a macromechanical finite element model of the structure being analyzed. The procedure is applied to a number of metal matrix composite systems subjected to thermomechanical loads.     

3D-analysis of the effect of interfacial debonding on the plastic behaviour of two-phase composites

The present paper deals with the interfacial debonding processes in Al/SiC metal matrix composites, by using 3D finite element calculations on representative cells. The reinforcements are considered as elastic, while the behaviour of the matrix is described by an elastoviscoplastic law. The debonding of the reinforcement is allowed for by using a non-linear elastic dependence between the stress vector and the separation vector at the interface. The results obtained show that the macroscopic behaviour of the composite depends to a large extent on the ratio between the the normal and tangential strength of the interface and the characteristic lengths defining the geometry of the reinforcements.     

Micromechanical multiplane finite element modeling of crack growth in fiber reinforced materials

The purpose of this study was to devise and verify a scheme of analysis which can be used to investigate the micromechanical failure mechanisms and determine an effective fracture toughness for a class of fiber reinforced materials. The material of primary interest in this study consists of a linearly elastic matrix material reinforced with rows of parallel, linearly elastic and straight fibers. Micromechanical multiplane finite element and experimental studies of the stress conditions near a crack front in a side cracked fiber reinforced epoxy tensile specimen were conducted. The 2-D multiplane method of analysis, recently developed at Syracuse University for approximate analysis of a class of 3-D problems, was the basis of the micromechanical finite element analytical technique developed in this study. Since failure of a member fabricated from a fiber reinforced material is generally proceeded by local failures, sequential finite element analyses were performed to model the progressive failure mechanism. Local failure modes considered in the analysis are yield in either the matrix material or fibers, crack extension in the matrix material, and failure of the matrix to fiber bond. The agreement between the multiplane analytical and laboratory test results show that the multiplane method provides a useful tool for micromechanical study of fiber reinforced composite materials.     

Elastic buckling analysis of 3-D trusses and frames with thin-walled members

 A finite element method is presented for the determination of the elastic buckling load of three-dimensional trusses and frames with rigid joints. The beam element stiffness matrix is constructed on the basis of the exact solution of the governing equations describing the coupled flexural-torsional buckling behaviour of a three-dimensional beam with an open thin-walled section in the framework of a small deformation theory. Large deformation effects are taken into account approximately through consideration of P−Δ effects. The structural stiffness matrix is obtained by an appropriate superposition of the various element stiffness matrices. The axial force distribution in the members is obtained iteratively for every value of the externally applied loading and the vanishing of the determinant of the structural stiffness matrix is the criterion used to numerically determine the elastic buckling load of the structure. The effect of initial member imperfections is also included in the formulation. Comparisons of accuracy and efficiency of the present exact finite element method against the conventional approximate finite element method are made. Cases where the axial force distribution determination can be done without iterations are also identified. The effect of neglecting the warping stiffness of some mono-symmetric sections is also investigated. Numerical examples involving simple and complex three-dimensional trusses and frames are presented to illustrate the method and demonstrate its merits. Received: 2 May 2000 / Accepted: 15 July 2002