Analysis of two-dimensional mixed-mode crack problems by finite element alternating method

A finite element alternating method is presented and applied to analyze two-dimensional linear elastic mixed-mode fracture problems with single or multiple cracks. The method involves the iterative superposition of the finite element solution of a bounded uncracked plate and the analytical solution of an infinite two-dimensional plate with a crack subjected to arbitrary normal and shear loadings. The normal and shear residual stresses evaluated at the location of fictitious cracks are fitted by appropriate polynomials through the least-squares method. Based on those coefficients of the determined polynomials, the mixed-mode stress intensity factors can be calculated accurately. The interaction effects among cracks are also considered. This method provides a highly efficient way to deal with two-dimensional fracture problems.     

基于Abaqus柔度标定法的Q235材料断裂韧性仿真

为简便、准确地获得Q235材料的应力强度因子值和J积分值,用Abaqus对Q235材料进行有限元仿真,得到三点弯曲试样及其裂纹尖端区域的应力分布情况;针对裂纹尖端的奇异性,引入折叠单元进行裂纹尖端单元的奇异性建模.不同尺寸试件应力强度因子仿真值与试验值基本一致,表明该方法可以准确预测材料断裂参数.     

Finite element analysis of a laminated composite plate subjected to circularly distributed central impact loading

A two dimensional finite element analysis has been made for a fiber-reinforced composite laminate subjected to circularly distributed impact load which results, for example, from impacting the plate with a blunt-ended projectile. A finite element displacement model which includes the effects of transverse shear deformation and rotary inertia was used along with Hamilton's principle to derive the finite element matrices. Newmark's direct integration technique was used to integrate with respect to time. The interaction force between the projectile and the plate was calculated by using the Hertzian law of contact. Results for laminate deformations are shown to compare quantitatively with experimental results. Numerical values for stresses in the plate were calculated.     

A three-dimensional nonlinear analysis of cross-ply rectangular composite plates

The results of a three-dimensional, geometrically nonlinear, finite-element analysis of the bending of cross-ply laminated anisotropie composite plates are presented. Individual laminae are assumed to be homogeneous, orthotropic and linearly elastic. A fully three-dimensional isoparametric finite element with eight nodes (i.e. linear element) and 24 degrees of freedom (three displacement components per node) is used to model the laminated plate. The finite element results of the linear analysis are found to agree very well with the exact solutions of cross-ply laminated rectangular plates under sinusiodal loading. The finite element results of the three-dimensional, geometrically nonlinear analysis are compared with those obtained by using a shear deformable, geometrically nonlinear, plate theory. It is found that the deflections predicted by the shear deformable plate theory are in fair agreement with those predicted by three-dimensional elasticity theory; however stresses were found to be not in good agreement     

Characterizing mechanical behaviors of a flexible AMOLED during the debonding process

The stress distribution of a flexible active-matrix organic light-emitting diode (AMOLED) display during the debonding process was investigated using finite element analysis. During the fabrication of an AMOLED display, an AMOLED with a polyimide (PI) substrate is detached from a glass carrier; this is a critical process and generally results in failure of the AMOLED. To enhance the yielding rate of AMOLEDs, their stress states generated during the debonding process must be reduced. The interfacial fracture behavior between the PI substrate and glass carrier was characterized on the basis of bimaterial fracture mechanics, and the fracture toughness associated with mode mixity determined through peeling tests was considered a criterion for detaching the AMOLED from the glass carrier. The stress distribution of the AMOLED at the inception of debonding crack extension was evaluated according to fracture toughness. In addition, the parameters possibly influencing the stress states of the AMOLED in the debonding process are discussed.     

A generalised technique for fracture analysis of cracked plates under combined tensile,bending and shear loads

The objective of this paper is to propose a generalized technique called numerically integrated modified virtual crack closure integral (NI-MVCCI) technique for fracture analysis of cracked plates under combined tensile, bending and shear loads. NI-MVCCI technique is used for post-processing the results of finite element analysis (FEA) for computation of strain energy release rate (SERR) components and the corresponding stress intensity factor (SIF) for cracked plates. NI-MVCCI technique has been demonstrated for 4-noded, 8-noded (regular and quarter-point) and 9-noded (regular and quarter-point) isoparametric plate finite elements. These elements are based on Mindlin’s plate theory that considers shear deformation. For all the elements, reduced integration/selective reduced integration techniques have been employed in the studies. In addition, for 9-noded element assumed shear interpolation functions have been used to overcome the shear locking problem. Numerical studies on fracture analysis of plates subjected to tension–moment and tension–shear loads have been conducted employing these elements. It is observed that among these elements, the 9-noded Lagrangian plate element with assumed shear interpolation functions exhibits better performance for fracture analysis of cracked plates.     

半椭圆表面裂纹前缘应力强度因子的计算

在断裂力学中,如何求取应力强度因子一直是一个重要的课题.该文通过MSC.Marc提供的断裂力学模块,采用三维J积分法计算含有半椭圆表面裂纹前缘应力强度因子.首先通过MSC.Marc.Mentat建立特定裂纹体有限元模型,假设裂纹前缘处在平面应变状态下.由MSC.Marc计算出裂纹前沿的J积分,再由J积分计算出裂纹前缘的应力强度因子值.最后将计算结果与经验公式得到的结果进行了比较.仿真结果表明,通过MSC.Marc采用三维J积分法计算的应力强度因子具有较高的准确性和可靠性.     

Stability of plates using a mixed finite element formulation

A rectangular plate finite element is developed according to a variational principle due to Prager The element is applied to plate stability analysis. The results obtained compare very favorably with results based on previous formulations.     

New approach in the determination of interlaminar shear stresses from the results of MSC/NASTRAN

A finite difference technique is applied to the strains and curvatures obtained from MSC/NASTRAN thin plate solutions to determine their derivatives. These quantities are then incorporated into classical thin plate theory to calculate interlaminar shear stresses. Several analyses are performed comparing the interlaminar shear stresses calculated by this method with those calculated theoretically and using MSC/NASTRAN beam theory approach. In all cases, the interlaminar shear stresses calculated by this method compare favorably with theoretical values. In addition, the interlaminar shear stresses are determined using MSC/NASTRAN beam theory approach and the method presented in this paper for a simply supported plate with a 30/-30/-30/30 layup subject to a uniform pressure. The technique presented in this paper can also be applied to other finite element programs.     

Validated finite element models of the proximal femur using two-dimensional projected geometry and bone density

Two-dimensional finite element models of cadaveric femoral stiffness were developed to study their suitability as surrogates of bone stiffness and strength, using two-dimensional representations of femoral geometry and bone mineral density distributions. If successfully validated, such methods could be clinically applied to estimate patient bone stiffness and strength using simpler and less costly radiographs. Two-dimensional femur images were derived by projection of quantitative computed tomography scans of 22 human cadaveric femurs. The same femurs were fractured in a fall on the hip configuration. Femoral stiffness and fracture load were measured, and high speed video was recorded. Digital image correlation analysis was used to calculate the strain distribution from the high speed video recordings. Two-dimensional projection images were segmented and meshed with second-order triangular elements for finite element analysis. Elastic moduli of the finite elements were calculated based on the projected mineral density values inside the elements. The mapping of projection density values to elastic modulus was obtained using optimal parameter identification in a set of nine of the 22 specimens, and validated on the remaining 13 specimens. Finite element calculated proximal stiffness and strength correlated much better with experimental data than areal bone mineral density alone. In addition, finite element calculated strain distributions compared very well with strains obtained from digital image processing of the high speed video recordings, further validating the two-dimensional projected subject-specific finite element models.     

基于CT 图像股骨个体化固定钢板数字设计及仿真分析

针对股骨骨折内固定,依据CT 断层扫描数据,论文完成股骨骨折部位的 三维模型重构,提出个体化固定钢板及设计方法和固定方案;在Solidworks 中完成固定钢板 的虚拟装配,通过Ansys12.0 对其进行静力学有限元仿真分析。数据表明：其静力学性能较 标准固定钢板有较大提高,与股骨表面的匹配性好,贴合程度高,提高了患者的舒适度。该 方法对骨外科手术具有一定的实际参考价值。     

基于模态分析的静电驱动圆薄板宏模型建立方法

为了研究静电致动圆板静态和动态特性,在模态分析法的基础上,利用多维非线性函数的Levenberg-Marquardt拟合方法,将板的动能、弹性能和电容写成以模态坐标表示的解析式.结合Hamilton原理,导出静电致动微圆板的动力学特性方程的宏模型.以此为基础研究了板的静态特性及其三角波、方波信号激励下的动态响应.结果表明,模态分析方法能够考虑到残余应力的影响,所建立的动态宏模型不仅大大地减少了计算费用,而且具有足够的仿真精度.     

Finite element modal analysis of a rotating disk–spindle system in a HDD with hydrodynamic bearings considering the flexibility of a complicated supporting structure

This paper presents a method to analyze the free vibration of a rotating disk–spindle system in a HDD with hydrodynamic bearings (HDBs) considering the flexibility of a complicated base structure by using finite element method. Finite element equations of each component of a HDD spindle system from the spinning flexible disk to the flexible base plate are consistently derived by satisfying the geometric compatibility in the internal boundary between each component. The rigid link constraints are also imposed at the interface area between the sleeve and hydrodynamic bearings to describe the physical motion at this interface. A global matrix equation obtained by assembling the finite element equations of each substructure is transformed to a state-space matrix-vector equation, and both damped natural frequencies and modal damping ratios are calculated by solving the associated eigenvalue problem by using the restarted Arnoldi iteration method. The validity of the proposed method is verified by comparing the calculated damped natural frequencies and modes with the experimental results. This research also shows that the supporting structure which includes the stator, housing and base plate plays an important role in determining the natural frequencies and mode shapes of a HDD spindle system     

Mixed elements in the optimal design of plates

The theory of design sensitivity analysis of structures, based on mixed finite element models, is developed for static, dynamic and stability constraints. The theory is applied to the optimal design of plates with minimum weight, subject to displacement, stress, natural frequencies and buckling stresses constraints. The finite element model is based on an eight node mixed isoparametric quadratic plate element, whose degrees of freedom are the transversal displacement and three moments per node. The corresponding nonlinear programming problem is solved using the commercially available ADS (Automated Design Synthesis) program. The sensitivities are calculated by analytical, semi-analytical and finite difference techniques. The advantages and disadvantages of mixed elements in design optimization of plates are discussed with reference to applications.     

Asymmetric buckling of bimodulus thick annular plates

An annular element with Lagrangian polynomials and trigonometric functions as shape functions is developed for asymmetric finite element stability analysis. The annular element is based on the Mindlin plate theory so that the effect of transverse shear deformation is included. Using the asymmetric finite element model, the asymmetric static buckling of bimodulus thick annular plates subjected to a combination of a pure bending stress and compressive normal stress is investigated. The obtained results of non-dimensional critical buckling coefficients are shown to be very accurate when compared with the exact solutions. The effects of various parameters on the buckling coefficients are studied. The bimodulus properties are shown to have significant influences on the buckling coefficients.     

Error estimation through the constitutive relation for Reissner–Mindlin plate bending finite elements

This paper deals with the so-called ‘error estimation through the constitutive relation’ for Reissner–Mindlin plate bending finite element analysis, which is based on the calculation of statically admissible stress resultant fields. Further an energy norm through the constitutive relation is introduced to quantify the difference between the calculated statically admissible stress resultant fields and the stress resultants given by the finite element analysis. The statically admissible stress resultant fields are obtained by local calculations at the node or at the element level. The procedures involve an optimization for estimating the statically admissible quantities as close as possible to the finite element result, and thus lead to a more accurate error estimation, considering the Pragger–Synge theorem. The set of examples shows the good agreement between the proposed indicator and the error obtained from the analytical solution. It is concluded that plate bending analysis is a field of application which is well fitted for error estimation through the constitutive relation.     

Axisymmetric dynamic stability of a bimodulus thick circular plate

The object of the present paper is to investigate the dynamic stability of bimodulus thick circular and annular plates subjected to a combination of a pure dynamic bending and a uniform dynamic extensional stress in the plane of the plate. The Mindlin plate finite element model is established to solve the dynamic stability problems of an axisymmetric circular plate. A ring type element is chosen to approach the axisymmetric problem. The obtained results of the dynamic stability region are shown to be very good when compared with the closed form solutions for ordinary plates. The influences of various parameters on the dynamic stability boundary are studied.     

Steady state stress analysis of centrifugal fan impellers

Cyclic symmetric structures such as centrifugal fan impellers are considered in this paper. One of the identical sectors is chosen for the finite element analysis. A triangular plate element is employed. The stiffness and load matrices are obtained in cylindrical coordinates. The displacements are obtained using a modified submatrices elimination scheme. The efficiency of this scheme is discussed. Impeller stresses are calculated and checked with the results obtained using a strain gauge technique.     

Electric potential approximations for an eight node plate finite element

The aim of this work is to develop a computational tool for multilayered piezoelectric plates: a low cost tool, simple to use and very efficient for both convergence velocity and accuracy, without any classical numerical pathologies. In the field of finite elements, two approaches were previously used for the mechanical part, taking into account the transverse shear stress effects and using only five unknown generalized displacements: C⁰ finite element approximation based on first-order shear deformation theories (FSDT) [Polit O, Touratier M, Lory P. A new eight-node quadrilateral shear-bending plate finite element. Int J Numer Meth Eng 1994;37:387–411] and C¹ finite element approximations using a high order shear deformation theory (HSDT) [Polit O, Touratier M. High order triangular sandwich plate finite element for linear and nonlinear analyses. Comput Meth Appl Mech Eng 2000;185:305–24]. In this article, we present the piezoelectric extension of the FSDT eight node plate finite element. The electric potential is approximated using the layerwise approach and an evaluation is proposed in order to assess the best compromise between minimum number of degrees of freedom and maximum efficiency. On one side, two kinds of finite element approximations for the electric potential with respect to the thickness coordinate are presented: a linear variation and a quadratic variation in each layer. On the other side, the in-plane variation can be quadratic or constant on the elementary domain at each interface layer. The use of a constant value reduces the number of unknown electric potentials. Furthermore, at the post-processing level, the transverse shear stresses are deduced using the equilibrium equations.Numerous tests are presented in order to evaluate the capability of these electric potential approximations to give accurate results with respect to piezoelasticity or finite element reference solutions. Finally, an adaptative composite plate is evaluated using the best compromise finite element.     

Optimality criterion approach using tapered finite elements with nodal averaging technique for two-dimensional problems

Use of tapered finite elements with three design variables per element and nodal averaging technique in the optimality criterion approach is studied in this paper. Minimum volume design of a uniformly heated square plate with a single temperature constraint is obtained using the proposed method. The present results with a lower order finite element mesh compare very well with those obtained with optimality criterion approach using constant thickness elements and with mathematical programming techniques using a higher order finite element mesh.