Finite Element Computation of Woven Ply Laminated Composite Structures up to Rupture

For unidirectional ply laminates, the great diversity of the damage mechanisms and their patterns of evolution make it extremely difficult to estimate the strength margins. In the case of woven ply laminates, the number of damage mechanisms is fairly small (no transverse rupture occurs and the material has a greater resistance to delamination) and the behaviour of the material is fairly simple to model up to rupture. In this study, a numerical model for woven ply laminated composite structures up to rupture is developed. The implementation is performed in a Euler Backward scheme and the consistent tangent stiffness matrix is calculated. Comparison with some experiments on structures are made and the model predicts these experiments well.     

A New Locking Free Higher Order Finite Element Formulation for Composite Beams.

A refined 2-node, 7 DOF/node beam element formulation is presented in this paper. This formulation is based on higher order shear deformation theory with lateral contraction for axial-flexural-shear coupled deformation in asymmetrically stacked laminated composite beams. In addition to axial, transverse and rotational degrees of freedom, the formulation also incorporates the lateral contraction and its higher order counterparts as degrees of freedom. The element shape functions are derived by solving the static part of the governing equations. The element considers general ply stacking and the numerical results shows that the element exhibits super convergent property. The efficiency of the element in capturing both the static and dynamic inter-laminar stresses is demonstrated. The accuracy of the element to capture free vibration and wave propogation responses with small problem sizes is also demonstrated.     

缠绕图型对纤维缠绕复合材料力学性能影响的有限元模拟

针对纤维缠绕复合材料结构中存在纤维束交叉起伏和铺层走向交替的特点,建立了一种分析缠绕图型对缠绕复合材料结构力学性能影响的有限元方法。采用ABAQUS有限元软件,分析了考虑纤维束交叉起伏和铺层走向交替后缠绕复合材料圆柱壳的应力、应变分布规律,并且研究了缠绕图型对缠绕圆柱壳屈曲临界载荷的影响。结果表明:采用层合板模型计算得到的圆柱壳的应力分布比较均匀;考虑纤维束交叉起伏和铺层走向交替后,缠绕复合材料圆柱壳的应力不再均匀分布,应力云图出现规则分布的菱形图案,在菱形区域中纤维交叉起伏和铺层走向交替处的应力有明显的波动。本实验有限元模型中的菱形特征单元可以反映缠绕复合材料纤维交叉起伏和铺层走向交替的实际情况。     

A Numerical Comparison of Finite Difference and Finite Element Methods for a Stochastic Differential Equation with Polynomial Chaos

A numerical comparison of finite difference (FD) and finite element (FE) methods for a stochastic ordinary differential equation is made. The stochastic ordinary differential equation is turned into a set of ordinary differential equations by applying polynomial chaos, and the FD and FE methods are then implemented. The resulting numerical solutions are all non-negative. When orthogonal polynomials are used for either continuous or discrete processes, numerical experiments also show that the FE method is more accurate and efficient than the FD method.     

颗粒填充二元复合材料等效介电特性的修正通用有效介质计算公式

介电特性在复合材料的电磁效应研究和材料设计中具有重要的作用。本工作在研究传统通用有效介质(GEM,General Effective Medium)公式的局限性基础上,提出了用于预测和计算颗粒填充二元复合材料等效介电特性的修正通用有效介质(MGEM,Modified General Effective Medium)公式。运用MC-FEM(Monte Carlo-Finite Element Method)方法分析计算各种参数条件下颗粒随机填充二元复合材料的等效介电特性,并与MGEM公式计算结果进行比较,验证MGEM公式的正确性和有效性。此外,还将MGEM的预测结果与部分经典理论公式的计算结果、部分文献报道的实验测量数据进行了比较。研究表明,在不同介电常数比(1/50~50)和不同体积分数(0~1)的情况下,MGEM公式预测结果与MC-FEM模型结果完全吻合,与实验测量结果基本一致,为颗粒填充二元复合材料等效介电性能分析提供了一种具有较高计算精度的理论计算方法。     

应用哈密尔顿原理计算动力响应的单步时间元法

本文应用哈密尔顿原理和里兹法,给出了计算动力响应的一种无条件稳定的计算格式,具有计算量小、精度高等优点.     

B-Spline Wavelet on Interval Finite Element Method for Static and Vibration Analysis of Stiffened Flexible Thin Plate

A new wavelet finite element method (WFEM) is constructed in this paper and two elements for bending and free vibration problems of a stiffened plate are analyzed. By means of generalized potential energy function and virtual work principle, the formulations of the bending and free vibration problems of the stiffened plate are derived separately. Then, the scaling functions of the B-spline wavelet on the interval (BSWI) are introduced to discrete the solving field variables instead of conventional polynomial interpolation. Finally, the corresponding two problems can be resolved following the traditional finite element frame. There are some advantages of the constructed elements in structural analysis. Due to the excellent features of the wavelet, such as multi-scale and localization characteristics, and the excellent numerical approximation property of the BSWI, the precise and efficient analysis can be achieved. Besides, transformation matrix is used to translate the meaningless wavelet coefficients into physical space, thus the resolving process is simplified. In order to verify the superiority of the constructed method in stiffened plate analysis, several numerical examples are given in the end.     

A Unit‐Cell Approach of Finite Element Analysis for Transverse Impact Damage of 3‐D Biaxial Spacer Weft‐Knitted Composite

Abstract: This paper evaluates the transverse impact damage of a 3‐D biaxial spacer weft‐knitted composite using experimental results and complimentary finite element analysis. The load–displacement curves and damage morphologies during impact loading were obtained to analyse energy absorption and impact damage mechanisms of the knitted composite. A unit‐cell model based on the microstructure of the 3‐D knitted composite was established to calculate the deformation and damage evolution when the composite is impacted by a hemisphere‐ended steel rod. An elastoplastic constitutive equation is incorporated into the unit‐cell model and the critical damage area failure theory developed by Hahn and Tsai has been implemented as a user‐defined material law (VUMAT) for commercial available finite element code ABAQUS/Explicit. The load–displacement curves, impact damages and impact energy absorption obtained from ABAQUS/Explicit are compared with those FROM experiments. The good agreement of the comparisons supports the validity of the unit‐cell model and user‐defined subroutine VUMAT. The unit‐cell model can also be extended to evaluate the impact crashworthiness of engineering structures made out of the 3‐D knitted composites.     

General numerical implementation of a new piezoelectric shunt tuning method based on the effective electromechanical coupling coefficient

Abstract

A recently proposed tuning method for resistive-inductive (RL) shunts is implemented in a commercial finite element (FE) code (ANSYS^®). A main result of the paper is therefore the consistent formulation of the tuning method in terms of variables directly available as solutions in any commercial FE code: The two natural frequencies associated with short- and open-circuit (SC and OC) electrodes and a modal charge obtained as the electrical SC reaction force. An alternative method is based on quasi-static solutions with SC and OC electrodes, convenient for both numerical analysis and experiments. The proposed shunt tuning method is suitable for implementation in any commercial FE software supporting electromechanical analysis and ANSYS^® has been used to assess its accuracy for a piezoelectric smart plate benchmark problem. The method is finally extended to multiple piezoceramic patches, placed symmetrically on the structure and shunted to a single RL network, whereby more vibration modes can be effectively controlled for the specific plate problem.     

A Posteriori Error Estimates of Semidiscrete Mixed Finite Element Methods for Parabolic Optimal Control Problems

A posteriori error estimates of semidiscrete mixed finite element methods for quadratic optimal control problems involving linear parabolic equations are developed. The state and co-state are discretised by Raviart-Thomas mixed finite element spaces of order $k$, and the control is approximated by piecewise polynomials of order $k$ ($k≥0$). We derive our a posteriori error estimates for the state and the control approximations via a mixed elliptic reconstruction method. These estimates seem to be unavailable elsewhere in the literature, although they represent an important step towards developing reliable adaptive mixed finite element approximation schemes for the control problem.     

A Posteriori Error Estimates of Lowest Order Raviart-Thomas Mixed Finite Element Methods for Bilinear Optimal Control Problems

A Raviart-Thomas mixed finite element discretization for general bilinear optimal control problems is discussed. The state and co-state are approximated by lowest order Raviart-Thomas mixed finite element spaces, and the control is discretized by piecewise constant functions. A posteriori error estimates are derived for both the coupled state and the control solutions, and the error estimators can be used to construct more efficient adaptive finite element approximations for bilinear optimal control problems. An adaptive algorithm to guide the mesh refinement is also provided. Finally, we present a numerical example to demonstrate our theoretical results.